Laser selective cutting of biological tissues by impulsive heat deposition through ultrafast  vibrational excitations

doi:10.1364/OE.17.022937

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Laser selective cutting of biological tissues by impulsive heat deposition through ultrafast  vibrational excitations

Kresimir Franjic, Michael L. Cowan, Darren Kraemer, and R. J. Dwayne Miller »View Author Affiliations

Optics Express, Vol. 17, Issue 25, pp. 22937-22959 (2009)
http://dx.doi.org/10.1364/OE.17.022937

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▸ Article Outline
– Abstract
1. Introduction: laser tissue ablation
2. Experimental studies of dental enamel ablation under IHDVE conditions
3. Theoretical considerations and numerical modeling
4. Summary and conclusions
– References and links

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Abstract

Mechanical and thermodynamic responses of biomaterials after impulsive heat deposition through vibrational excitations (IHDVE) are investigated and discussed. Specifically, we demonstrate highly efficient ablation of healthy tooth enamel using 55 ps infrared laser pulses tuned to the vibrational transition of interstitial water and hydroxyapatite around 2.95 µm. The peak intensity at 13 GW/cm² was well below the plasma generation threshold and the applied fluence 0.75 J/cm² was significantly smaller than the typical ablation thresholds observed with nanosecond and microsecond pulses from Er:YAG lasers operating at the same wavelength. The ablation was performed without adding any superficial water layer at the enamel surface. The total energy deposited per ablated volume was several times smaller than previously reported for non-resonant ultrafast plasma driven ablation with similar pulse durations. No micro-cracking of the ablated surface was observed with a scanning electron microscope. The highly efficient ablation is attributed to an enhanced photomechanical effect due to ultrafast vibrational relaxation into heat and the scattering of powerful ultrafast acoustic transients with random phases off the mesoscopic heterogeneous tissue structures.

1. Introduction: laser tissue ablation

The laser was envisioned as a potential surgical tool shortly after its first demonstration [1

L. R. Solon, R. Aronson, and G. Gould, “Physiological implications of laser beams,” Science 134(3489), 1506–1508 ( 1961). [CrossRef] [PubMed]

]. In principle, laser surgery provides a non-contact approach capable of cutting with single cell precision, the fundamental resolution limit of a surgical process, while being capable of selectively cutting different tissue types through control of the laser spectrum in relation to the absorption properties of the targeted tissue. However, despite this great promise, widespread adoption of lasers in surgery has been limited only to specific niches like laser eye surgery. There are several reasons for the slow adoption of surgical lasers. Primarily, current laser surgery techniques still incur various types of residual tissue damage making these techniques attractive only if such damage can be tolerated and if such damage is smaller compared to alternative techniques. The extent of residual tissue damage is an important parameter since wound healing is a diffusive process and healing times are roughly proportional to the square of the wound size [2

J. D. Murray, Mathematical Biology, (Springer, New York, 2008).

The character of the residual tissue damage generally depends on the parameters of the laser beam, type of laser-tissue interactions, and tissue properties [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

–6

Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds., (Plenum Press, New York, 1995).

]. The most important laser parameters in this regard are wavelength, pulse duration, and pulse fluence which is defined as pulse energy per unit area (continuous wave lasers induce large thermal tissue damage and are not considered here). In a tissue, the optical absorption length, d_ABS , is strongly dependant on wavelength. If the absorption length is not much longer than the wavelength, light scattering can be neglected. For a given absorption length, the pulse fluence determines the deposited energy density, ε, available for the ablation. Normally this is in the range of 1-10 kJ/cm³, which is enough to superheat the material and drive ablation. In order to minimize collateral damage, it is essential to minimize the threshold energy density, ε_TH , to put as much of the available laser energy as possible into the ablation process, to maximize the amount of energy leaving the ablation site within the ejected plume, and limit the residual energy left behind. Residual heating below the ablation threshold and propagation of thermal and acoustic transients to the surrounding tissue makes this a challenge.

For a given type of laser-tissue interaction, these requirements largely depend on the laser pulse duration t_P . In this respect, ablation under thermal and stress confinement are usually considered. If the duration of the laser pulse t_P and duration of the subsequent ablation process are shorter than the thermal relaxation time τ_TH=d_ABS ²/χ_D of the irradiated volume, the ablation is thermally confined. Here, χ_D is the tissue thermal diffusivity and d_ABS is the shortest dimension of the irradiated volume, defining a lower limit to τ_TH . The ablation dynamics depend on the rate of superheating which is intimately related to the fundamental photo-physical properties of molecules that govern the transduction of the absorbed optical energy into lattice heating. Once the energy shows up as heat, the ablation process and confinement are in competition with thermal diffusion to adjacent tissue. The relaxation time, τ_TH , for tissue volumes excited by typical laser parameters is generally on the order of several µs. In this case most of the heat remains confined during the ablation, however, complete thermal confinement is not possible because of unavoidable non-uniform longitudinal and transverse absorption profiles. This peripheral heat can induce thermal necrosis of cells especially if it is accumulated over long exposures. For this reason, ablation with the lowest possible energy density will result in the benefit of the lowest peripheral heating.

If the pulse duration is shorter than the stress relaxation time τ_AC= d_ABS /v_S , the ablation occurs under stress confinement. Here, v_S is the effective speed of sound in the tissue. The stress relaxation times are typically around a nanosecond, shorter than the thermal relaxation times by three orders of magnitude. The stress field generated within the ablation volume can have important consequences for the ablation process either catalyzing different ablation thermodynamic pathways or generating photomechanical effects [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. Incomplete confinement of the laser-induced stress results in propagating acoustic transients outside the target zone which can have adverse tissue effects [7

A. G. Doukas and T. J. Flotte, “Physical characteristics and biological effects of laser-induced stress waves,” Ultrasound Med. Biol. 22(2), 151–164 ( 1996). [CrossRef] [PubMed]

] but may also have beneficial uses if amplitudes of the leaked acoustic transients are sufficiently attenuated [8

A. G. Doukas and N. Kollias, “Transdermal drug delivery with a pressure wave,” Adv. Drug Deliv. Rev. 56(5), 559–579 ( 2004). [CrossRef] [PubMed]

]. For the purpose of this work we will distinguish between the primary stress field generated and relaxed during τ_AC , and the secondary stress field for times > τ_AC which is dominated by the recoil effects due to fast material removal, phase explosions, or quasi static stresses due to thermal gradients.

Laser-tissue interactions are usually categorized as thermal, photochemical, plasma induced, photo-mechanical, or a combination thereof [4

M. H. Niemz, Laser-Tissue Interactions, Fundamentals and Applications, (Springer-Verlag, Berlin Heidelberg, 2007).

]. Thermal ablation is based on tissue melting and vaporization through simple heating using laser pulse durations in the > 10 ns range, usually under thermal but not stress confinement. In most cases, the target chromophore is the tissue’s water which has the lowest phase transition temperature and undergoes phase explosions for short pulses [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. The hot pressurized vapour fractures the tissue and leads to ablation. Common tools in this class are free running and Q-switched CO₂ lasers at 10.6 µm and Er:YAG lasers at 2.94 µm. These devices typically remove 10-50 µm of tissue per pass using 5-50 J/cm² fluence depending on the tissue type. The energy density needed to vaporize the material is quite high, accompanied by large peripheral heating and a zone of thermal tissue damage that is 50-300 µm deep depending on fluence, repetition rate, and the number of passes. In some cases, this peripheral heat damage is a desirable effect for cauterizing the wounds, but ultimately limits the precision of the ablation process. During the ablation phase, heat can alter the mechanical properties of the tissue facilitating the ablation. An interesting method in this class has been reported [9

G. Edwards, R. Logan, M. Copeland, L. Reinisch, J. Davidson, B. Johnson, R. Maciunas, M. Mendenhall, R. Ossoff, J. Tribble, J. Werkhaven, and D. Oday, “Tissue ablation by a free-electron laser tuned to the amide II band,” Nature 371(6496), 416–419 ( 1994). [CrossRef] [PubMed]

] where the laser wavelength is tuned to the amide II band at 6.45 µm targeting mainly collagen in the extracellular matrix. A model has been developed to explain observed effects in which collagen experiences denaturation which subsequently weakens the tissue making possible lower ablation energy densities and more efficient ablation. However, the most recent studies [10

M. S. Hutson, B. Ivanov, A. Jayasinghe, G. Adunas, Y. W. Xiao, M. S. Guo, and J. Kozub, “Interplay of wavelength, fluence and spot-size in free-electron laser ablation of cornea,” Opt. Express 17(12), 9840–9850 ( 2009). [CrossRef] [PubMed]

] have reinterpreted the original results as primarily a focusing issue in comparing different wavelengths and it remains to be seen what is the true potential of this approach.

In the case of photo-chemically driven ablation, the laser wavelength is tuned to molecular states of one or more of the major constituent molecules in the target tissue. The laser energy deposition results ultimately in photochemical bond cleavage and heat generation that causes material weakening and fracture [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. UV ablation with excimer lasers targeting electronic states belongs to this class. Although they provide very precise cuts there is a concern of potentially dangerous mutagenic cell effects caused by the energetic UV photons [4

M. H. Niemz, Laser-Tissue Interactions, Fundamentals and Applications, (Springer-Verlag, Berlin Heidelberg, 2007).

] since both proteins and DNA strongly absorb in that spectral region. There is also a long history of induced acoustic damage with typical laser parameters possible using excimer lasers. As will be discussed below, there is a problem with laser pulses with nanosecond durations since their deposited energy couple to acoustic transients and shockwave formation at MHz frequencies that have long propagation lengths and large associated damage zones. For this reason the adoption of these lasers has been limited to laser eye correction procedures where there is little vascularized tissue and damages of this sort can be tolerated.

The method that has attracted a lot of attention in recent years is plasma induced ablation by ultrashort pulsed lasers with peak powers large enough to cause multiphoton ionization in tissue (typically > 10¹¹ W/cm²) [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

M. H. Niemz, Laser-Tissue Interactions, Fundamentals and Applications, (Springer-Verlag, Berlin Heidelberg, 2007).

]. This ionization process creates energetic free electrons that generate a hot electron plasma through avalanche ionization. Although the plasma is formed within the duration of the laser pulse, which can be only several femtoseconds short, the lattice heating, increased rms atomic motions, happens on an intrinsic time scale determined by recombination processes and electron-phonon inelastic collisions. This thermalization time scale, which for most materials is in the 10-100 ps range, is most relevant for the ablation process since lattice heat triggers thermodynamic transitions leading to material removal. Nevertheless, the 10-100 ps time scale is much shorter than any other relevant one for the ablation process making the total deposited energy initially spatially well confined. The ultrafast thermalization rates and well defined multi-photon ionization threshold lead to extremely precise cuts with minimum collateral thermal damage generating hopes for a perfect laser scalpel [11

T. Juhasz, R. Kurtz, C. Horvath, C. Suarez, F. Raksi, and G. Spooner, “The femtosecond blade: Applications in corneal surgery,” Opt. Photonics News 13, 24–29 ( 2002). [CrossRef]

]. However, a few studies have indicated that the generated plasma may cause biochemical damage to surrounding cells by creating transient molecular species that are highly reactive and result in the formation of toxic free radicals [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. Ultrafast laser processes using non-resonant multi-photon ionization necessarily represent a highly ionizing light source well beyond radiation damage densities of X-rays. This hypothesis was supported with tissue healing studies performed by Girard et al [12

B. Girard, M. Cloutier, D. J. Wilson, C. M. L. Clokie, R. J. D. Miller, and B. C. Wilson, “Microtomographic analysis of healing of femtosecond laser bone calvarial wounds compared to mechanical instruments in mice with and without application of BMP-7,” Lasers Surg. Med. 39(5), 458–467 ( 2007). [CrossRef] [PubMed]

] who created bone calvarial wounds using both mechanical and femtosecond laser tools. Despite much higher cutting precision, the wounds created by the femtosecond laser actually healed slower than the ones created by standard mechanical tools. The implications were that although the cells were structurally intact, many of the biochemical pathways had been destroyed by the localized dose of reactive ions. The healing process speeded up only after additional bone morphogenic protein (BMP) was applied, recreating biochemical signaling pathways of cells remote to the tissue damage. Beyond the immediate consequences of such radiation damage, the prospect of long-term effects is high and likely to be an unacceptable risk factor if ionization can be avoided.

All aforementioned ablation processes involve photomechanical effects to smaller or larger extent but they are secondary [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

–5

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. Dingus and Scammon were the first to point out that the photomechanical effect itself could be the dominant ablation mechanism by using a front surface spallation effect [13

R. S. Dingus and R. J. Scammon, “Gruneisen-Stress Induced Ablation of Biological Tissue,” Proc. SPIE 1427, 45–54 ( 1991). [CrossRef]

]. If a region of tensile stress is created within the irradiated tissue volume that exceeds the tissue’s ultimate tensile strength (UTS), the tissue fractures allowing ablation. Typical tissue UTS values range from –10 to –100 MPa [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. The photomechanical spallation effect is a very efficient ablation mechanism. It takes many orders of magnitude less energy to break a material into small fragments through spallation than to vaporize it [5

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. These insights inspired research on photo-mechanically driven tissue ablation during 1990-s but without significant success since it was realized that although a stress field is an efficient fracture agent, creation of a large enough stress through the front surface spallation mechanism as proposed by Dingus and Scammon is not practical [5

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. The energy needed to generate large enough tensile amplitudes was big enough to trigger mechanisms other than photomechanical that dominate the ablation process.

The findings of the present work indicate that the photomechanical spallation effect can be greatly enhanced by impulsive heat deposition through ultrafast excitation of vibrational modes of the tissue’s constituent molecules characterizing the tissue type. It is the explicit exploitation of these fast vibrational relaxation processes that is the key to a new mechanism for laser driven ablation. The lifetimes of vibrational transitions in the condensed phase are typically around several picoseconds and in the case of liquid water they can be even faster than 1 ps i.e. they can be an order of magnitude faster than even the electron-lattice energy transfer times during ultrafast plasma mediated ablation. There is also an important difference in the structure and dynamics of the stress fields induced in the tissue by these two processes. While the acoustic shock wave front produced by a rapidly expanding plasma is more or less uniform, the thermoelastic stress field deposited by Impulsive Heat Deposition through Vibrational Excitations (IHDVE) is mapped by the initial vibrational chromophore distribution which is generally inhomogeneous. These topics and their consequences for tissue ablation are discussed in more details in the Section 3. In the next section, we present results on healthy tooth enamel ablation under IHDVE conditions. The enamel tissue was chosen as a proof of concept because of its hard brittle structure but also because of potential important applications in dentistry.

2. Experimental studies of dental enamel ablation under IHDVE conditions

2.1 Dental enamel as a model tissue

Dental enamel is the hardest tissue in the human body. It is a composite material consisting of minerals, water, and organic materials with respective contributions 96%, 3%, 1% by weight and 90%, 8%, 2% by volume [14

Handbook of Biomaterial Properties, J. Black and G. Hastings, eds., (Chapman & Hall, London, 1998).

]. The predominant mineral is hydroxyapatite, Ca₁₀(PO₄)₆(OH)₂ which due to the vibrational excitation of its O-H group contributes along with the O-H stretching modes of water to the high absorption around the 3 µm wavelength. The healthy enamel used in the experiment was part of extracted human teeth (molars) that were cross-sectioned along a longitudinal plane and polished. Samples were kept in phosphate buffered saline until the experiment and left to dry out in air under room temperature conditions for 10 minutes immediately before the ablation. No water or other substance was applied at the target spot during the ablation tests. The cuts were made at the polished cross-sectioned planes approximately at the center of the enamel layer using four different samples that were mounted in an acrylic holder. Polished surfaces were used to make it possible to accurately quantify the amount of material removed per pulse. Scattering effects from natural tissues is not an issue in the strong absorption regime where the absorption depth and the wavelength are comparable. Effectively all the incident energy is absorbed in the same volume element. We have been able to cut all tissue types without any pretreatment.

2.2 The laser system

The key design concept of these experiments is the use of infrared pulses tuned to one of the dominant vibrational states of the tissue with pulse durations that are short enough to impulsively deposit heat through ultrafast vibrational relaxation but with intensities small enough to avoid plasma formation. The experimental setup is illustrated in Fig. 1(a) . Ablative laser pulses tuned to a wavelength of 2.95 µm, with 55 ps pulse duration, and 500 µJ of energy, were produced using a home built laser system comprising an optical parametric amplifier (OPA) pumped by 70 ps pulses from a Nd:YLF regenerative amplifier at 1053 nm. The regenerative amplifier was seeded with a passively mode-locked Nd:YLF laser. The 5 mJ 1053 nm amplified pulse with nearly diffraction limited beam pumped an OPA consisting of three 15 mm long KTA crystals. The OPA was seeded with a 15 mW CW output from a distributed feedback (DFB) fiber coupled telecom laser diode at 1637 nm to reduce the parametric threshold and to improve beam quality giving the idler at the desired 2950 nm. The signal and pump pulses were filtered out using a germanium filter. This arrangement produced about 1.5 mJ of signal+idler energy giving in total 30% conversion efficiency. Due to delivery losses, only 320 µJ of 2.95 µm idler was present at the sample. The beam was profiled with a knife edge and pinholes of various sizes to determine the spot diameter, d = 330 μm (1/e ²), giving a peak fluence of 0.75 J/cm² at the sample surface assuming a Gaussian beam profile. The peak fluence F_P was calculated using the expression F_P =(2E_P )/(r ²π) where E_P is the pulse energy and r is the beam radius.

Fig. 1 (a) Schematic of the experimental setup (not in scale). The system’s numerical parameters are given in Section 2.2. The elements in the dashed rectangle were placed in the plane perpendicular to the one corresponding to the image. The galvo scanner GS steered the beam in the y-plane across the sample S while simultaneously the motorized stage MTS traveled in the x-plane. DBS-dichroic beam-splitter, L-lens, M-mirror, GF-germanium filter. (b) Image of a typical crater for fluences around 0.5 J/cm² created by single pulse impacts. The highly irregular crater shape can be observed with feature sizes on the order of a few µm. (c) SEM image of a typical crater ablated using scanned laser beam with 330 µm diameter, 1 kHz repetition rate, and 0.75 J/cm² pulse peak fluence. (d) Magnified detail of the crater’s top corner.

The mid-IR pulse duration was measured to be 55 ps by autocorrelation, corresponding to a peak intensity of 13 GW/cm² assuming a Gaussian temporal shape. This is well below the plasma generation threshold of healthy enamel (~160 GW/cm²) for 55 ps long near-IR and visible wavelengths [15

F. H. Loesel, M. H. Niemz, J. F. Bille, and T. Juhasz, “Laser-induced optical breakdown on hard and soft tissues and its dependence on the pulse duration: Experiment and model,” IEEE J. Quantum Electron. 32(10), 1717–1722 ( 1996). [CrossRef]

]. For the 3 µm wavelength this threshold should be even higher due to I^k multiphoton plasma threshold dependence on the laser intensity I and the number of photons k needed to cooperate to reach the ionization limit. The ionization resonant enhancements are not expected to arise for 50 ps pulse durations due to fast thermalization of vibrations on the timescale of several picoseconds as will be discussed in the Section 3. Also, avalanche ionization initiated by thermionic electrons is not expected on this timescale [4

M. H. Niemz, Laser-Tissue Interactions, Fundamentals and Applications, (Springer-Verlag, Berlin Heidelberg, 2007).

]. The laser pulses were scanned across the target spot with both a single axis scanning mirror and a motorized translation stage.

2.3 Scanning electron microscopy

After the ablation, uncoated samples were examined using an environmental scanning electron microscope (SEM Hitachi S3400). Ablation thresholds were investigated by looking at visible modifications of the polished enamel surface by single pulse impact. Pulses were scanned randomly across the enamel surface for various fluences with 20 pulses per fluence. Fluences were controlled by inserting filters into the collimated beam path for attenuation without changing the beam profile. Surface modifications with sizes smaller than the laser diameter could be observed for fluences as small as 0.35 J/cm². For low fluences, modifications didn’t occur for each pulse but happened randomly across the surface. Defining the ablation threshold for single pulses as the fluence for which surface modifications were observed about 50% of time, the ablation threshold fluence F_TH was found to be around 0.5 J/cm². Typical surface modification due to a single pulse is shown in Fig. 1(b). Highly irregular crater shapes were observed with feature sizes on the order of a few µm including sharp valleys that extended as much as 5 µm deep as estimated using both an optical profilometer and calibrated focusing positioning in an optical microscope. Irregularities of the crater shape and their dependence on the position on the enamel surface imply the absence of plasma driven ablation.

To test the ablation efficiency at the maximum available fluence of 0.75 J/cm², the laser beam was scanned over 1 mm across the surface with 1 Hz frequency while the sample was moved simultaneously in a perpendicular plane with 0.15 Hz frequency and 1 mm travel. The pulse repetition rate during the ablation was 1 kHz and each sample was ablated over

80 seconds with a total of 80,000 pulses deposited. Figure 1(c) shows a typical ablated crater and Fig. 1(d) shows magnified details of the crater’s top corner. The craters’ average lateral dimensions were 1×1 mm² with corner radius of curvature around 75 µm. Assuming a Gaussian beam transverse fluence distribution and that corners were ablated with overlapping pulses, we can estimate the effective ablative beam diameter to be 150 µm and that fluence at the corner edge corresponds to around 0.5 J/cm² in agreement with average ablation threshold measured with single pulse impacts. This means around 20% of the pulse energy was absorbed as heat in transverse non-ablative wings. The use of flat top beam profiles could remove this residual loss in efficiency and potential for collateral damage completely. The average crater depth was 0.45 mm estimated using calibrated focus positioning in an optical microscope. The crater walls were cut under angle due to beam diffraction of the Gaussian beam at the crater edges. Ridges appeared at the crater bottom parallel to the tooth longitudinal axis and therefore to enamel rods (enamel structure is described in Section 3.2). The averaged total ablated volume was estimated to be 0.37 mm³. Dividing the ablated volume by total number of pulses (80,000) and effective ablative beam diameter (150 µm) gives 0.26 µm to be average etch depth. This is much smaller than the typical absorption length for 2.95 µm optical wavelength in enamel (10-15 µm) so it is reasonable to assume that increasing the energy density by increasing the input fluence should increase the etch depth as well. A simple phenomenological blow-off model [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

,16

R. Hibst and U. Keller, “Experimental studies of the application of the Er:YAG laser on dental hard substances: I. Measurement of the ablation rate,” Lasers Surg. Med. 9(4), 338–344 ( 1989). [CrossRef] [PubMed]

] can be used to make some estimates. The model is based on assumptions that material removal doesn’t start before the complete laser energy absorption and that fluence F(z) decreases with tissue depth z relative to the fluence F₀ at the surface according to Beer's law

F (z) = F_{0} \exp (- α z)

(1)

where α is the absorption coefficient. The first assumption is certainly valid in our case of 55 ps long laser pulses. The second assumption implies that optical scattering can be neglected which is true for small absorption lengths at infrared wavelengths and that α doesn’t depend on F which generally is not true but is a reasonable approximation for relatively low fluences. Shori et al [17

R. K. Shori, A. A. Walston, O. M. Stafsudd, D. Fried, and J. T. Walsh, “Quantification and modeling of the dynamic changes in the absorption coefficient of water at λ=2.94 μm,” IEEE J. Sel. Top. Quantum Electron. 7(6), 959–970 ( 2001). [CrossRef]

] measured and characterized the α(F) dependence in case of pure water but no such studies for enamel are known to us. Using the unsaturated enamel absorption coefficient measured by Fried et al [18

D. Fried, M. Zuerlein, J. D. B. Featherstone, W. Seka, C. Duhn, and S. M. McCormack, “IR laser ablation of dental enamel: mechanistic dependence on the primary absorber,” Appl. Surf. Sci. 127(1-2), 852–856 ( 1998). [CrossRef]

], 800 cm^–1 at λ=2.94 µm, the etch depth d can be estimated by [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]

d = α^{- 1} \ln (F_{0} / F_{t h}) .

(2)

For the effective etch depth 0.26 µm that was measured, Eq. (2) gives 0.73 J/cm² as the effective threshold in case of large volume ablation. These estimates imply that fluences on the order of 2 J/cm² are needed for the etch depth to match the 12 µm absorption length. Nevertheless, the measured ablation threshold is about 6× smaller than previously measured for 250 µs pulses [16

] and about 3.5× smaller than in the case of 150 ns pulses [19

D. Fried, R. Shori, and C. Duhn, “Backspallation due to ablative recoil generated during Q-switched Er:YAG ablation of dental hard tissue,” Proc. SPIE 3248, 78–85 ( 1998). [CrossRef]

] using an Er:YAG laser at the same wavelength. This large reduction in ablation threshold for 55 ps pulses points to photomechanical effects on < 1 ns time scale as the main ablation mechanism.

Figure 2 shows images of a crater floor and of a crater wall perpendicular to the enamel rod axis recorded under a 35° observation angle relative to the polished surface under different magnifications. It can be observed that rod structure is completely lost in both parallel and perpendicular planes relative to the rods and texture with uniform roughness of 1 µm that is apparent across surfaces without signs of fissures or vitrification that would indicate melting.

Fig. 2 SEM images of a crater floor (left) and a crater wall perpendicular to the enamel rod axis recorded under 35 degree angle relative to the polished surface (right) at different levels of magnification. The applied laser fluence was 0.75 J/cm². Uniform texture with roughness of around 1 µm can be observed in both directions with rod structure completely gone. No signs of melting or cracking could be detected.

These results can be also compared to the ones obtained with plasma driven ablation of enamel by Niemz [20

M. H. Niemz, “Cavity preparation with the Nd:YLF picosecond laser,” J. Dent. Res. 74(5), 1194–1199 ( 1995). [CrossRef] [PubMed]

] using pulses with similar pulse lengths (30 ps at 1053 nm wavelength) but with much higher peak intensity due to tight focusing (30 µm spot diameter) needed to cause multi-photon absorption at a non-resonant wavelength and dielectric breakdown. By scanning 160,000 pulses with 1 mJ energy, a cavity was created of similar size (1×1×0.4 mm³) as in the present work giving the ablation energy efficiency of 400 J/mm³. This is 5.7× smaller efficiency than observed in our case (70 J/mm³) although the heat per pulse was deposited on a similar timescale which signals again a different more efficient ablation mechanism under the IHDVE regime. This distinction is important as it is often assumed that the use of ultrashort pulses to remove material through plasma formation is the most efficient mechanism for material removal. However, the lattice is no longer a bound state of matter and it completely disintegrates upon plasma formation. For IHDVE mechanisms, there is no additional energy lost to the process of plasma formation and the material retains it mechanical properties and heterogeneous structure so that stress fields lead to fracture and more efficient material removal in the ablation process. The higher efficiency of the IHDVE mechanism indicates the important role of stress confined fields in driving ablation. The increased efficiency is important, as the smaller the required energy density for ablation, the smaller the residual damage to surrounding tissue.

3. Theoretical considerations and numerical modeling

3.1 Vibrational relaxation in the condensed phase

There is a unique vibrational spectrum for every molecule. The corresponding transition dipoles for polar molecules can be very large. In cases where one molecular species can be considered as host matrix, the absorptivity in the infrared wavelength corresponding to vibrational states of the host material can be extremely high, with penetration depths of less than one µm in the case of water around λ=2.9 µm. Equally important, the vibrational lifetimes of excited vibrational modes in the condensed phase are exceedingly short. Due to the high density of low frequency bath modes that act as acceptor modes, virtually all vibrational modes of polyatomic molecules have lifetimes on the picosecond time scale [21

A. Nitzan, Chemical Dynamics in Condensed Phases, (Oxford University Press, New York, 2006).

,22

R. J. D. Miller, “Vibrational energy relaxation and structural dynamics of heme proteins,” Annu. Rev. Phys. Chem. 42(1), 581–614 ( 1991). [CrossRef] [PubMed]

]. In the case of water, energy transfer between vibrationally excited O-H stretching modes at 3400 cm^–1 and intermolecular librations of the hydrogen bond network occurs within 200 fs with complete thermalization happening within 1 ps [23

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H₂O,” Nature 434(7030), 199–202 ( 2005). [CrossRef] [PubMed]

]. These extremely fast vibrational energy relaxation processes lead to an equally rapid increase in the lattice temperature and are much faster than thermal expansion of the material, or superheated driven nucleation and spinodal decomposition. For short IR pulses selectively tuned to a molecular vibrational state of the tissue matrix, the heat deposition could be so fast that the subsequent ablation process occurs in the truly impulsive limit. We note here that the lattice heating through vibrational relaxation of water vibrational modes in particular is the fastest such process known. It is faster than even electron-phonon coupling associated with avalanche ionization using femtosecond laser pulses which for liquid water happens on the order of 10 ps [24

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 ( 2005). [CrossRef]

]. In fact, both the absorption depth and the timescales for lattice heating are either comparable or shorter than processes driven by non-resonant multiphoton avalanche ionization with the distinct advantage that resonant IR excitation does not lead to ionization and plasma formation which may cause deleterious biochemical tissue damage. The timescale of transduction of the optical energy into heat is the ultimate bottleneck for impulsive laser driven ablation processes that in turn is determined by the target material’s fundamental physical properties. Once superheating occurs in the lattice, the phase transition may proceed extremely quickly, on the timescale of several picoseconds as recently demonstrated with an atomic level perspective [25

B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302(5649), 1382–1385 ( 2003). [CrossRef] [PubMed]

The most abundant vibrational chromophores in the human body are water (λ=2.9 µm for the stretching and λ=6.1 µm for the bending mode), collagen (λ=6.1 µm for the amide I-band and λ=6.4 µm for the amide II-band), and hydroxyapatite (phosphate modes around λ=9.5 µm and also λ=2.9 µm for the O-H stretch). Water is by far the most predominant component of tissue and also, as mentioned above, displays the fastest ultrafast vibrational relaxation dynamics. Besides, water possesses the lowest critical temperature among the tissue matrix components so it can act as the most efficient ablation propellant. However, in order to be used for impulsive heat deposition in relation to tissue cutting, water has to retain ultrafast vibrational energy redistribution efficiency even in hot thermodynamic states and under the large vibrational excitation rates required for material ablation. For 1 J/cm² fluence and assuming 1 µm absorption length, 5% of the leading edge of a 100 ps pulse is enough to raise the temperature of water above 100 C which means that the majority of the laser pulses energy is absorbed under superheated conditions. If the rate of energy deposition in water is much faster than τ_AC , it happens under approximately isochoric conditions so thermodynamic pathways enter the supercritical region for large enough deposited energy density. What happens to the hydrogen bond network in the supercritical region is a matter of ongoing studies but results with neutron and X-ray scattering experiments [26

P. H. L. Sit, C. Bellin, B. Barbiellini, D. Testemale, J. L. Hazemann, T. Buslaps, N. Marzari, and A. Shukla, “Hydrogen bonding and coordination in normal and supercritical water from X-ray inelastic scattering,” Phys. Rev. B 76(24), 245413 ( 2007). [CrossRef]

] as well as theoretical simulations [27

A. G. Kalinichev, “Molecular simulations of liquid and supercritical water: thermodynamics, structure, and hydrogen bonding,” Rev. Mineral. Geochem. 42, 83–129 ( 2001). [CrossRef]

] indicate that large numbers of hydrogen bonds persists even at temperatures and pressures well above the critical point values. The details are far from clear but the rough picture that has emerged is that the hydrogen bond network gets broken into hydrogen-bonded clusters with the average number of bonds per molecule and the lifetime of these bonds decreasing with increasing temperature and decreasing density. Although hydrogen bonds in these clusters weaken and their number are reduced, as confirmed with the blue shift of the absorption peak and increase in the absorption length, it appears that for isochoric conditions, ~1 g/cm³, the couplings between intermolecular and intramolecular degrees of freedom remain strong enough to keep O-H stretch relaxation rates within several picoseconds even for temperatures exceeding 2000 C. This fact was first observed by Vodopyanov et al [28

K. L. Vodopyanov, M. E. Karasev, L. A. Kulevskii, A. V. Lukashev, and G. R. Toker, “Dynamics of Interaction of λ=2.94 μm Laser-Emission with Thin-Layer of Liquid Water,” Pis'ma Zh. Tekh. Fiz. 14, 324–329 ( 1988).

,29

K. L. Vodopyanov, “Saturation studies of H₂O and HDO Near 3400 cm^–1 using intense picosecond laser pulses,” J. Chem. Phys. 94(8), 5389–5393 ( 1991). [CrossRef]

] in a simple and yet insightful experiment monitoring the changes in transmission coefficient for laser pulses with λ=2.9 µm through a thin layer of water confined in a few micron thick cell. The change in transmission appeared to be the same for a single energetic 110 ps long pulse and for a long pulse train of weak pulses with the same total energy, implying that the change in transmission was a function of pulse energy and not of the pulse intensity. From these results, an O-H stretch lifetime smaller than 3 ps can be estimated for temperatures up to 2000 C, corresponding to energy densities on the order of 10 kJ/cm³ and deposited with high vibrational excitation rates within 100 ps [29

K. L. Vodopyanov, “Saturation studies of H₂O and HDO Near 3400 cm^–1 using intense picosecond laser pulses,” J. Chem. Phys. 94(8), 5389–5393 ( 1991). [CrossRef]

]. Recently, more direct time-resolved infrared pump-probe spectroscopy of O-H stretch relaxation time of HOD in liquid to supercritical H₂O up to 663 K temperatures under isochoric conditions was investigated by Schafer et al [30

T. Schäfer, J. Lindner, P. Vöhringer, and D. Schwarzer, “OD stretch vibrational relaxation of HOD in liquid to supercritical H(₂)O,” J. Chem. Phys. 130(22), 224502 ( 2009). [CrossRef] [PubMed]

] and several picosecond long O-H stretch lifetimes were confirmed.

Impulsively generated heat in a finite volume of material induces thermoelastic stress on the same time scale. With water’s short absorption length at λ=2.9 µm, which for large fluences remains within several µm [17

], and speed of sound in water of 1500 m/s, GHz acoustic transients can be expected to arise due to the absorbed picosecond infrared laser pulses. Such ultrafast pressure waves were indeed detected by Vodopyanov et al [31

K. L. Vodopyanov, L. A. Kulevsky, V. G. Mikhalevich, and A. M. Rodin, “Laser-Induced Generation of Subnanosecond Sound Pulses in Liquids,” Zh. Eksp. Teor. Fiz. 91, 114–121 ( 1986).

] and Strokel et al [32

U. Störkel, K. L. Vodopyanov, and W. Grill, “GHz ultrasound wave packets in water generated by an Er laser,” J. Phys. D 31(18), 2258–2263 ( 1998). [CrossRef]

] using 110 ps long pulses at λ=2.9 µm absorbed in pure water. The initial amplitudes of such pressure waves for isochoric conditions can be estimated using the material properties. Increasing heat density by an amount dq increases the thermoelastic stress σ by an amount

d σ = Γ d q .

(3)

The dimensionless quantity Γ is called Grüneisen coefficient and is equal to

Γ = (B β) / (ρ C_{v})

(4)

where B is the bulk modulus, β is the volume expansion coefficient, ρ is the density, and C_V is the constant volume heat capacity [5

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. The Grüneisen coefficient for water increases monotonically from 0.11 to 0.75 between 300 and 650 K and then monotonically decreases to 0.7 for temperatures between 650 and 1000 K as calculated using temperature dependences for B, β, and C_V [33

W. Wagner and A. Pruss, “The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use,” J. Phys. Chem. Ref. Data 31(2), 387–535 ( 1999). [CrossRef]

]. This means that stress amplitudes on the order of 1 GPa can be generated for modest fluences on the order of 1 J/cm² assuming effective optical absorption lengths of several µm.

Recently, Franjic et al [34

K. Franjic, F. Talbot, and R. J. D. Miller, (to be submitted)

] performed time resolved measurements of the dynamic optical reflectivity and the expansion velocity of plumes created by ablating the free surface of pure water with 100 ps pulses tuned to λ=2.9 µm. The results were in agreement with modeling based on an assumption of impulsive heat deposition and the presence of GPa pressure amplitudes generated on the picosecond time scale has been inferred.

3.2. Enhancement of the photomechanical ablation effect in biological tissues through ultrafast vibrational excitations

As discussed above, it has been known for some time that photomechanical effects may play an important role in laser driven material ablation under stress confinement conditions. So far, the majority of experimental and theoretical investigations on this subject focused on materials with homogenous absorption and acoustic properties relative to the laser parameters. In this case, the characteristic acoustic wavelength of the induced thermoelastic field is on the order of the absorption length resulting in a transient tensile stress region of similar size. Due to the free surface boundary conditions during the relaxation, a negative pressure field is formed that can enhance the ablation either by exceeding the material’s ultimate tensile strength (UTS) (front surface spallation) or by lowering the threshold for cavitation and phase transition processes [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. Although the photomechanical mechanism is a highly efficient ablation process, the creation of sufficiently strong tensile amplitudes in the regime described above is not. However, photomechanical effects can be enhanced by exploiting the wave nature of sound, focusing acoustic energy at specific points through interference effects, even if the total integrated elastic energy is low. To ablate a certain amount of material it is not necessary to have a thermodynamic transition throughout the whole irradiated volume, but only to break the main structural elements which can be a significantly more energy efficient process, similar to a controlled explosive demolition of a building. Esenaliev et al [35

R. O. Esenaliev, A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Laser-Ablation of Aqueous-Solutions with Spatially Homogeneous and Heterogeneous Absorption,” Appl. Phys. B 59(1), 73–81 ( 1994). [CrossRef]

] and Jacques et al [36

S. L. Jacques, A. A. Oraevsky, R. Thompson, and B. S. Gerstman, “A Working Theory and Experiments on Photomechanical Disruption of Melanosomes to Explain the Threshold for Minimal Visible Retinal Lesions for Sub-ns Laser-Pulses,” Proc. SPIE 2134, 54–65 ( 1994).

] were the first to experimentally observe that photomechanical effects can be greatly increased in materials possessing a heterogeneous absorption profile with characteristic heterogeneity length d_HET much shorter than the optical absorption length d_ABS . If the laser pulse duration is shorter than d_HET /v_S , the initial thermoelastic stress field has a form of “acoustic speckle”. In this context, we refer to this situation as the micro-stress confinement condition. Relaxation of such acoustic fields creates localized negative pressure points through acoustic interference [5

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. If these amplitudes exceed the material UTS, the material fractures, leading to ablation. In the case of retina ablation investigated by Jacques et al, melanin granules acted as localized absorbers. Melanin has a large absorption band in the visible and UV, and its electronic states have unusually short lifetimes with intramolecular vibrational energy redistribution occurring on sub-ps timescale [37

S. Meng and E. Kaxiras, “Mechanisms for ultrafast nonradiative relaxation in electronically excited eumelanin constituents,” Biophys. J. 95(9), 4396–4402 ( 2008). [CrossRef] [PubMed]

]. The subsequent thermalization occurs on the 10 ps timescale [22

R. J. D. Miller, “Vibrational energy relaxation and structural dynamics of heme proteins,” Annu. Rev. Phys. Chem. 42(1), 581–614 ( 1991). [CrossRef] [PubMed]

] making impulsive heat deposition possible. The characteristic size of a melanin granule is 10 nm, so ablation using pulses with <10 ps duration satisfies the micro-stress confinement conditions assuming a speed of sound of 1500 m/s. For tissues, the photomechanical effect of micro-stress confinement is further amplified by the fact that acoustic impedance also has a mesoscopic spatial dependence due to the composite structure of the tissue; thus negative stress components are also created through acoustic reflections off boundaries in the tissue’s mesoscopic structures, due to mismatches in acoustic impedance [36

]. Both Esnaliev et al and Jacques et al noticed almost an order of magnitude reduction in ablation threshold under micro-stress confinement. Studies of photomechanical material fracture due to isolated absorbers [38

G. Paltauf and H. Schmidt-Kloiber, “Photoacoustic cavitation in spherical and cylindrical absorbers,” Appl. Phys.Mater. Sci . 68, 525–531 ( 1999). [CrossRef]

] and theoretical studies of the propagation of heterogeneous acoustic fields [39

M. I. Khan, T. Sun, and G. J. Diebold, “Photoacoustic Waves Generated by Absorption of Laser-Radiation in Optically Thin Cylinders,” J. Acoust. Soc. Am. 94(2), 931–940 ( 1993). [CrossRef]

], [40

J. M. Sun and B. S. Gerstman, “Photoacoustic generation for a spherical absorber with impedance mismatch with the surrounding media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(5 5 Pt B), 5772–5789 ( 1999). [CrossRef] [PubMed]

], [41

A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 ( 1996).

] have since confirmed that under micro-confinement stress conditions transient tensile stress points are created within the irradiated volume with a more or less complex distribution depending on the geometry of isolated absorbers.

In all experimental studies of laser ablation under micro-stress confinement conditions so far, energy was deposited through electronic excitations of dyes or pigments. As mentioned earlier, electronic excitations can induce chemically reactive species with the potential to cause cell damage. Besides, lifetimes of electronic excitations are generally longer than 1 ns with melanin being an exceptional case, which occurs in only a few tissue types. Long thermalization times limit the usefulness of this energy deposition channel for photomechanical enhancement through micro-stress confinement. On the other hand, it can be observed that natural vibrational chromophores are omnipresent in biological tissues. If the spatial scale d_HET of strong density fluctuations of a vibrational chromophore is much smaller than the optical absorption length d_ABS and if both infrared laser pulse duration and vibrational relaxation times are shorter or not much longer than d_HET /v_S , conditions for micro-stress confinement will be satisfied and the initial thermoelastic field will be mapped by the non-uniform heterogeneous spatial distribution of initial chromophores.

We can make some estimates related to water distribution in several real tissues. In tooth enamel, the basic structural elements are rods directed from the dentin-enamel junction to the top surface of the tooth [42

A. Nanci, and A. Ten Cate, Ten Cate's oral histology: development, structure, and function, (Mosby, St. Louis, 2003).

]. The rod cross section has a keyhole shape about 4-8 µm in diameter. The rod core, built predominantly of closely packed hydroxyapatite crystals, is surrounded by a sub-micron thick sheath in which most of the enamel proteins and water reside. Although organic components contribute less than 1% in weight, they significantly modify the enamel’s mechanical properties. The interrod material also consists mostly of hydroxyapatite but with crystals positioned under angle with respect to the rods. About 4% of enamel by weight and 8% by volume consists of water, and of that amount about one half is loosely bound in the sheath and the other half is caged in small pores that are around 100 nm in diameter [43

G. H. Dibdin, “The Water in Human Dental Enamel and Its Diffusional Exchange Measured by Clearance of Tritiated Water from Enamel Slabs of Varying Thickness,” Caries Res. 27(2), 81–86 ( 1993). [CrossRef] [PubMed]

]. For “matrix-continuous” soft tissues like dermis or cartilage, collagen fibrils are the main mesoscopic structural elements [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. Their diameter is on the order of 100 nm and they are embedded within an amorphous matrix called ground substance, composed of water and proteinaceous components. Almost all the water in matrix-continuous tissues is located in the ground substance. For “cell continuous” tissues such as liver, the average cell is made of ~60-70% water and its size is about 10 µm. About 85% of the intracellular water has bulk-like properties, with the remaining 15% being modified by interactions on the biomolecular surfaces [44

E. Persson and B. Halle, “Cell water dynamics on multiple time scales,” Proc. Natl. Acad. Sci. U.S.A. 105(17), 6266–6271 ( 2008). [CrossRef] [PubMed]

]. The dry matter is mostly located in large organelles like mitochondria or lysosomes that are immersed in the intracellular fluid. The number and positions of these organelles varies as well as their sizes which are in the several hundred nanometers range. Hence, in all these tissues, there are strong variations of water density on the 100 nm spatial scale. For typical tissue speeds of sound in the range 1500-5000 m/s and typical tissue absorption lengths for vibrational chromophores on the order of several µm, the stress relaxation time τ_AC is on the order of 1 ns. Hence, for infrared pulses with durations on the order of 100 ps, the conditions for micro-stress confinement should be met providing the thermalization of optically excited vibrations proceeds on the picosecond timescale which is the case as discussed above.

It is important to distinguish the transient acoustic field generated under micro-confinement stress conditions from the quasi steady-state one as defined by Itzkan et al [45

I. Itzkan, D. Albagli, M. L. Dark, L. T. Perelman, C. von Rosenberg, and M. S. Feld, “The Thermoelastic Basis of Short Pulsed Laser Ablation of Biological Tissue,” Proc. Natl. Acad. Sci. U.S.A. 92(6), 1960–1964 ( 1995). [CrossRef] [PubMed]

] and discussed by Paltauf and Dyer [5

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 ( 2003). [CrossRef] [PubMed]

]. The quasi steady-state stress field can be created in heterogeneous solids (e.g. tissues) due to temperature gradients after absorption of a laser pulse with a duration longer than the acoustic relaxation time τ_AC but shorter than the thermal relaxation time τ_TH . In this case, the system is in a quasi mechanical equilibrium all the time with net forces in any direction being equal to zero but individual stress components not being zero. Additional sources of stress can also arise for times due to phase explosions of pockets of water or other constituent chromophores [46

A. D. Yablon, N. S. Nishioka, B. B. Mikic, and V. Venugopalan, “Physical mechanisms of pulsed infrared laser ablation of biological tissues,” Proc. SPIE 3343, 69–77 ( 1998). [CrossRef]

]. This is the typical ablation regime in the case of free running and Q-switched Er:YAG and CO₂ lasers. Relaxation of these stress fields generates low frequency stress transients that can contribute more or less to the ablation process but also rapidly propagate out of the irradiated zone to cause unwanted deep cracks in tissues. Indeed, cracks up to 300 µm deep were observed for ablation of dental enamel by microsecond pulses from Er:YAG lasers [47

M. H. Niemz, L. Eisenmann, and T. Pioch, Vergleich von drei Lasersystemen zur Abtragung von Zahnschmelz 103, 1252–1256 ( 1993).

]. Large tooth tissue fracturing was observed also with 150 ns nanosecond Er:YAG lasers [19

D. Fried, R. Shori, and C. Duhn, “Backspallation due to ablative recoil generated during Q-switched Er:YAG ablation of dental hard tissue,” Proc. SPIE 3248, 78–85 ( 1998). [CrossRef]

]. These findings were supported by numerical studies of Verde et al [48

A. V. Verde, M. M. D. Ramos, and A. M. Stoneham, “The role of mesoscopic modelling in understanding the response of dental enamel to mid-infrared radiation,” Phys. Med. Biol. 52(10), 2703–2717 ( 2007). [CrossRef] [PubMed]

] who used finite element analysis to compare effects of 0.1-10 µs long infrared laser pulses on enamel ablation. The cracks and fissures are certainly not desirable since they may serve as an origin for the development of new decay [4

M. H. Niemz, Laser-Tissue Interactions, Fundamentals and Applications, (Springer-Verlag, Berlin Heidelberg, 2007).

In the case of enamel ablation under the IHDVE regime reported in our work, we observe an absence of any deeper tissue cracks. One of the main reasons is certainly low applied pulse fluence but the other likely contributing factor is the high frequency nature of the acoustic transients. As discussed in the next subsection, it can be expected that GHz acoustic transients get significantly attenuated over distances comparable to optical absorption length. This means that in the case of the photomechanical action initiated by IHDVE, these ultrafast transients should remain largely confined within the irradiated volume without causing damage away from the ablated zone. These observations are supported by the work of Niemz who performed plasma mediated enamel ablation with 30 ps long pulses. Despite large shock wave amplitudes in GHz frequency range due to the relatively large plasma energy densities, no deep cracks were observed as confirmed with dye penetration tests [20

M. H. Niemz, “Cavity preparation with the Nd:YLF picosecond laser,” J. Dent. Res. 74(5), 1194–1199 ( 1995). [CrossRef] [PubMed]

]. Since acoustic attenuation is a consequence of both absorption and scattering, the attenuation of the heterogeneous acoustic field with random phases produced by IHDVE may have some additional features that would be interesting to examine.

Another comment should be made related to the picosecond time scale in case of ablation performed with the free electron lasers. These lasers produce a few microsecond long macropulses that contain 10,000-20,000 several picosecond long micropulses. The tissue ablation effect of such pulse structure is determined mainly by the integrated macropulse energy since the energy of individual picosecond micropulses is too small to separately induce ablation effects through one of the mechanisms described in the introduction. Therefore, the effect of free electron lasers is similar to the effect of other 50 ns to 10 µs lasers operating in the same wavelength [49

M. A. Mackanos, J. A. Kozub, and E. D. Jansen, “The effect of free-electron laser pulse structure on mid-infrared soft-tissue ablation: ablation metrics,” Phys. Med. Biol. 50(8), 1871–1883 ( 2005). [CrossRef] [PubMed]

3.3 Propagation of high-frequency high-power ultrasound in tissue structures

Faithful modeling of the propagation of acoustic transients through tissue with GHz frequencies and amplitudes large enough to cause fractures is challenging for several reasons. First, the tissues mechanical properties on the mesoscopic level with large strain rates are still poorly understood. More importantly, these properties generally have dynamic characteristics depending on strain amplitude and strain rate [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. The available data suggest that at high strain rates, tissue strain doesn’t change much at the fracture limit but the UTS generally gets bigger. For lower strain rates, the UTS increases in proportion to the logarithm of the strain rate, but this dependence hasn’t been confirmed for very large strain rates [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. The complex tissue response to fast mechanical load is related to the inherent protection function against fractures and deformations. Bone tissue, which is a composite material consisting of collagen fibrils reinforced with nano-sized hydroxyapatite particles, provides the best example [50

H. Peterlik, P. Roschger, K. Klaushofer, and P. Fratzl, “From brittle to ductile fracture of bone,” Nat. Mater. 5(1), 52–55 ( 2006). [CrossRef] [PubMed]

Second, acoustic attenuation processes in tissues for high acoustic frequencies are still not fully understood even in the MHz range extensively studied in ultrasonic diagnostics. In this part of the spectrum, it is established that attenuation is dominated by absorption over scattering [51

K. K. Shung, and G. A. Thieme, Ultrasonic Scattering in Biological Tissues, (CRC, Boca Raton, 1993).

]. The complex tissue response is reflected in the linear dependence of the attenuation coefficient on frequency in contrast to more common f ² dependences due to classic viscoelastic attenuation in pure substances [52

K. K. Shung, “Ultrasound and Tissue Interaction,” in Encyclopedia of Biomaterials and Biomedical Engineering , G. E. Wnek and G. L. Bowlin, eds., (Informa HealthCare, 2008).

]. Table 1 gives the measured pressure amplitude attenuation coefficients for several common tissues [53

G. W. C. Kaye, and T. H. Laby, Tables of Physical and Chemical Constants: And Some Mathematical Functions, (Longman, 1995).

]. The 1/e attenuation lengths at f=1 GHz were estimated by extrapolation using the linear frequency attenuation law. The 1/e attenuation lengths for the acoustic intensities are even smaller by factor of 2 due to square dependence of the acoustic intensity on the pressure amplitude.

Table 1 Pressure amplitude attenuation coefficients for common tissues.

Tissue	Reference frequency f_REF (in MHz)	Attenuation coefficient α(f_REF) (in 10² neper/m)^a	1/e pressure amplitude attenuation length at 1 GHz (in µm)^b
Bone	3	9	3.5
Enamel	18	14	13
Dentin	18	9.2	20
Skin	5	1.06	41
Muscle	4.3	0.54	80

^a Experimental data collected from reference [53

G. W. C. Kaye, and T. H. Laby, Tables of Physical and Chemical Constants: And Some Mathematical Functions, (Longman, 1995).

]. The exponential dependence p = exp(-α(f)∙z) of pressure p on distance z is assumed.

^b The pressure amplitude attenuation lengths at 1 GHz were calculated by extrapolation assuming linear dependence of the attenuation coefficient α(f) on frequency f and using experimental values for α at the reference frequency f_REF.

It is reasonable to expect that attenuation physics becomes far more complex for GHz acoustic transients created under shock conditions. Scattering contributions should increase due to the strong f ⁴ dependence of the scattering cross section [54

C. M. Sehgal, “Quantitative relationship between tissue composition and scattering of ultrasound,” J. Acoust. Soc. Am. 94(4), 1944–1952 ( 1993). [CrossRef] [PubMed]

]. In addition, contribution of higher order frequency terms due to viscous dissipation is also likely to increase. A further level of complexity must be considered for large acoustic amplitudes comparable to the materials’ UTS, which are able to initiate formation of cracks and voids. Tissue structures are optimized to dissipate deformation energy without propagation of micro-cracks [50

H. Peterlik, P. Roschger, K. Klaushofer, and P. Fratzl, “From brittle to ductile fracture of bone,” Nat. Mater. 5(1), 52–55 ( 2006). [CrossRef] [PubMed]

] and these mechanisms are still under study. In all cases, it is clear that energy dissipation increases with frequency and amplitude so the values in Table 1 can be taken as lower limits. For hard tissues, these values are comparable to the infrared optical absorption lengths which means that the photomechanical action of induced GHz stress transients should remain confined within the irradiated volume. For soft tissues, this could be possible if high frequency dissipation increases or if >1 GHz transients are created using short pulses in which case strong attenuation may occur over distances comparable to typical cell sizes of 10 µm.

The third reason for complexity of the IHDVE driven process, are strong nonlinear effects associated with large initial acoustic amplitudes. The usual approaches for ultrasound description with (B/A) parameters [52

K. K. Shung, “Ultrasound and Tissue Interaction,” in Encyclopedia of Biomaterials and Biomedical Engineering , G. E. Wnek and G. L. Bowlin, eds., (Informa HealthCare, 2008).

] are insufficient for amplitudes on the order of 1 GPa created under shock wave conditions, which require more elaborate analysis.

Finally, the fast oscillating stress field should generate strong cavitation in tissue water with bubbles expanding or collapsing at a rapid pace due to negative pressure conditions and/or homogenous nucleation and spinodal decomposition due to high temperatures. It is well known that such events are sources of strong acoustic transients themselves [3

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 ( 2003). [CrossRef] [PubMed]

]. Since the rate of these events is determined by the frequency of the driving stress field it is expected that cavitation processes create positive feedback in the IHDVE initiated photomechanical effects.

3.4 Simplified numerical modeling of IHDVE generated acoustic fields in tissues using a k-space propagation method

Considering the complexity of the tissue microstructure and the large strain rates involved, sophisticated methods based on finite element analysis (FEA) are the only option for more realistic numerical modeling of the IHDVE driven process. At present, computer software and hardware powerful enough to handle FEA modeling on this scale are not available to us. Lack of complete dynamic thermoelastic and inelastic micro properties of tissues is also a problem. Here we present a simplified model using a computationally efficient k-space propagation method for acoustically heterogeneous media recently developed by Mast et al [55

T. D. Mast, L. P. Souriau, D. L. D. Liu, M. Tabei, A. I. Nachman, and R. C. Waag, “A k-space method for large-scale models of wave propagation in tissue,” IEEE T. Ultrason. Ferr. 48(2), 341–354 ( 2001). [CrossRef]

] and Cox et al [56

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: Application to biomedical photoacoustics,” J. Acoust. Soc. Am. 121(6), 3453–3464 ( 2007). [CrossRef] [PubMed]

]. The purpose of this model is to demonstrate the possibility of tensile stress amplitudes exceeding the UTS inside the irradiated volume, on time and spatial scales small compared to τ_AC and d_ABS respectively using reasonable assumptions about spatial variations of the model tissue’s acoustic and optical properties.

In the k-space propagation method, the spatial differential equations are solved using fast Fourier transforms and temporal iteration is performed using a k-t space propagator. In our model, the coupling between compressive and shear waves, nonlinear effects, and acoustic absorption effects have been neglected. It is plausible to expect that nonlinear effects and couplings between compressive and shear waves should increase the spectrum of temporal and spatial acoustic field fluctuations further contributing to the IHDVE photomechanical effect. For the same reason, nucleation and phase explosions of tissue water have also been neglected on this time scale. Optical scattering was neglected because the optical absorption length is only 10 μm which is comparable to the laser wavelength and much smaller than the beam size. Energy of the scattered light is not lost but absorbed within the same layer. The net effect is a more heterogeneous absorbed heat profile which should further enhance the IHDVE photomechanical effect. The subsequent strain relaxation effects may have a more complex role since acoustic absorption diminishes the acoustic amplitudes but the acoustic absorption process itself may influence the mechanical integrity of the tissue. As stated in the previous section, the attenuation coefficient for 1 GHz acoustic transients in enamel is about 10 µm. This is approximately equal to the optical absorption length but it is much longer than the spatial scale of the optical and acoustic property variations of the tissue that are of interest in the simulations; therefore the attenuation was neglected as well. Because coupling between compressive and shear waves was neglected, only the equation for compressive waves was considered to illustrate the magnitudes of the nascent strain fields, i.e [57

A. D. Pierce, “The wave theory of sound,” in Acoustics: An Introduction to Its Physical Principles and Applications, (Acoustical Society of America, Woodbury, NY, 1989).

\frac{\partial^{2} p (x, t)}{\partial t^{2}} - v_{s} {(x)}^{2} ρ (x) \nabla \cdot (\frac{1}{ρ (x)} \nabla p (x, t)) = Γ (x) \frac{\partial Ψ (x, t)}{\partial t}

(5)

where the tissue speed of sound v_S (x), density ρ(x), and Grüneisen coefficient Γ(x) are spatially dependent. The source term Ψ(x,t) represents the heat deposition rate per unit volume. Under the IHDVE assumption, this term can be represented as

Ψ (x, t) = H (x) \frac{d S (t)}{d t};

(6)

where H(x) was the total heat deposited per unit volume, and S(t) was the temporal envelope of the laser pulse which was normalized so

\int d S (t) = 1

and assumed to be Gaussian with a FWHM duration τ. Numerically, H(x) was evaluated with

H (x) = \frac{F_{I N C} α (x) Δ y}{Δ y} = F_{I N C} α (x)

(7)

where F_INC is the incident fluence of a laser pulse propagating along the y direction, α( x ) is spatially dependent optical absorption coefficient, and ∆x and ∆y are the grid spacings along x and y axes, respectively. Optical attenuation due to absorption was neglected for simplicity hence laser fluence F_INC = 0.75 J/cm² was taken to be constant over all spatial points in the excited volume elements. Equation (5) was integrated using the second-order k-space method described by Cox et al [56

] except the scaled heat source term h(x ,t) (as defined in [56

]) was modified by multiplying with the additional factor v_S0 ²/v_S (x) ² to account for variations of v_S (x) and Γ(x) over the same spatial points [58

Ben Cox, Department of Medical Physics and Bioengineering, University College London, UK, (personal communication, 2009).

h (x, t) = - \frac{v_{S 0}^{2}}{v {(x)}^{2}} ρ {(x)}^{- \frac{1}{2}} Γ (x) H (x, t)

(8)

where v_S0 is the maximum speed of sound in the structure. This model has been successfully tested on several structures for which solutions are known.

The enamel model structure consists of four different elements: water, rods, interrods, and rod sheaths. Because of the approximate rod cylindrical symmetry, it was enough to consider a two-dimensional solution in the rod cross-sectional plane. The simulation space (Fig. 3 ) consisted of a single rod with cumulative effect of a periodic array of enamel rods taken into account though the periodic nature of Fourier solutions.

Fig. 3 The enamel tissue model consists of a single rod cross section made of water, interrod, rod, and sheath. The water is contained in small pores with 70-150 nm in diameter and randomly distributed mainly around the sheath. The simulation space size was 4.8×4.8 µm. The profile shown at the image was created after averaging and filtering to avoid aliasing.

The geometry of elements given in Fig. 3 was as follows: the size of the simulation space was 4.8×4.8 µm, the outer sheath diameter was 4.5 µm, the rod diameter was 3.3 µm, the water pores had random diameters in the range 70-150 nm and were distributed mainly around the sheath with the total surface being around 6% of the size of the simulation space. The material parameters used in the simulation are given in the Table 2 .

Table 2 Material parameters for the structural elements of the model enamel used in numerical simulations.

	Water	Rod	Interrod	Sheath
Density (g/cm³)	1	3	3	3
Sound speed (m/s)	1500	6500	6500	4500
Optical absorption coefficient(cm^-1)	12500	300	300	300
Grüneisen coefficient	0.1	0.38	0.38	0.19

In contrast to water parameters that are well known, the parameters of other enamel components had to be estimated based on several bulk enamel values reported in the literature. The organic components are mainly located in the sheath (vide supra) and although they are present in small concentrations they significantly alter the elastic properties of the sheath. Therefore, the density and optical absorption coefficient values for rod, interrod, and sheath were taken to be the same and equal to the values for hydroxyapatite crystal used by Verde et al [48

] but the speed of sound and Grüneisen coefficient that depend on elastic properties are expected to be modified. These values were estimated using recent measurements of Young’s moduli for the rod and sheath [59

J. Ge, F. Z. Cui, X. M. Wang, and H. L. Feng, “Property variations in the prism and the organic sheath within enamel by nanoindentation,” Biomaterials 26(16), 3333–3339 ( 2005). [CrossRef] [PubMed]

]. The speed of sound v_i in components other than water was calculated from their volume fractions and the bulk speed of sound of enamel v_EN =5000 m/s [14

Handbook of Biomaterial Properties, J. Black and G. Hastings, eds., (Chapman & Hall, London, 1998).

], using the relation 1/v_EN=∑w_i /v_i [54

C. M. Sehgal, “Quantitative relationship between tissue composition and scattering of ultrasound,” J. Acoust. Soc. Am. 94(4), 1944–1952 ( 1993). [CrossRef] [PubMed]

], and assuming the speed of sound in rod, interrod, and sheath scale as the square root of the Young’s modulus. The terms w_i were taken to be 36%, 30%, 6%, and 28% based on the geometry depicted at Fig. 5 . The enamel aggregate Grüneisen coefficient Γ _EN was evaluated by rewriting the Eq. (4) in the form Γ=3BK_m where K_m=α/ρC_V with α=β/3 being the coefficient of linear expansion. The value K_m for enamel was measured by Meredith et al [60

N. Meredith, D. J. Setchell, and S. A. V. Swanson, “The application of thermoelastic analysis to study stresses in human teeth,” J. Oral Rehabil. 24(11), 813–822 ( 1997). [CrossRef] [PubMed]

] to be 2.25×10^–12 m²/N and the bulk modulus was taken from [61

D. E. Grenoble, J. L. Katz, K. L. Dunn, K. L. Murty, and R. S. Gilmore, “The Elastic Properties of Hard Tissues and Apatites,” J. Biomed. Mater. Res. 6(3), 221–233 ( 1972). [CrossRef] [PubMed]

] to be 4.6×10¹⁰ N/m² which gave the value Γ _EN =0.31. The Grüneisen coefficients of the components were then estimated by writing the aggregate enamel value in the form Γ _EN=∑w_i Γ _i and assuming the Grüneisen coefficients Γ _i scale linearly with Young’s modulus. The value for water is known and was set to 0.1.

Fig. 5 (Color) Spatial domain spectra of stress field fluctuations were averaged over the simulation time, normalized to unity, and fitted to discrete points. For pulse durations less than 1 ns, the spectra rapidly broaden as a consequence of micro-stress confinement and heterogeneous distribution of vibrational chromophores.

The numerical parameters were the following: grid size of 1024×1024 with grid spacing being equal to 4.5 nm in each direction and Courant–Friedrichs–Lewy number was set to 0.5. The total simulation time and the pulse peak arrival were 5 ns and t=2τ respectively for the pulses shorter than 1 ns, and 15 ns and t = τ correspondingly for the pulses longer than 1 ns. The profiles v_S (x), ρ(x), Γ(x), and H(x) were averaged over 7×7 cells and then filtered with a half-band k-space filter that was found to greatly reduce Gibbs phenomenon artifacts while still maintaining high enough spatial frequency components of inhomogeneities to provide accurate backscatter results [55

]. The incident fluence was the same for all cases so the different outcomes were due to varying pulse durations only. The simulation was implemented in MATLAB (Release 13, The Mathworks, Inc.).

Figure 4 shows snapshots of the compressive stress field created by depositing a 50 ps FWHM long pulse at λ=2.95 µm into the structure defined in Fig. 3. The field was recorded at 10 ps, 150 ps, 650 ps, and 800 ps after the pulse peak arrival. Large localized positive and negative stress amplitudes can be noticed to develop within 1 ns after the pulse deposition with maximum values of tensile components greatly exceeding the static enamel UTS that was reported to be –42 MPa and –12 MPa in directions parallel and perpendicular to the rod axis respectively [62

M. Giannini, C. J. Soares, and R. M. de Carvalho, “Ultimate tensile strength of tooth structures,” Dent. Mater. 20(4), 322–329 ( 2004). [CrossRef] [PubMed]

]. Large pressure jumps from –1 GPa to 1 GPa sometimes occurred over distances of only several hundred nanometers. The stress field fluctuations for different laser pulse durations were quantified by measuring their spatial and temporal spectra. Figure 5 presents the spatial spectra of the stress fields induced by laser pulses with four different pulse durations: 50 ps, 500 ps, 3 ns, and 6 ns. The spectrum for each pulse was averaged over the total simulation time, its area normalized to unity, and fitted to discrete points. The spectra for 3 ns and 6 ns are dominated by the peak at k=1.5 µm^–1 corresponding to the acoustic wavelength λ=4.2 µm that arises due to partial stress confinement on the spatial scale of the rod diameter. As pulse durations get reduced below d/2v_S ≈500 ps, where d=4 µm is the medium sheath diameter and v_S =5000 m/s is the average speed of sound, the initial stress gets confined on spatial scales smaller than the rod diameter so the spectrum gets broadened and new spectral peaks develop, reflecting the rod internal chromophore distribution. For even shorter pulses at 50 ps, the initial stress gets confined in individual small water pores whose positions and sizes vary randomly as reflected in the irregular, very broad, spatial frequency spectrum. During the stress field temporal development, large random spatial fluctuations in stress can be expected due to acoustic impendence mismatched boundaries and strong k ⁴ dependence of the scattering cross-section [63

L. A. Chernov, Wave propagation in a random medium, (Dover Publications, 1967).

]. The normalized time domain spectra are given in Fig. 6 and were created by averaging spectra of time dependent stress fields at 144 uniformly spaced points across the simulation space and were fitted to discrete points. These spectral shapes roughly resemble the spatial spectra as expected from the dispersion relation f=(kv_S )/(2π) and the average speed of sound v_S =5000 m/s. Strong spectral broadening in the case of 50 ps pulses results in high frequency spectral components up to 12 GHz.

Fig. 4 (Color) Snapshots of the compressive stress fields created by depositing 50 ps FWHM long pulse with F=0.75 J/cm² incidence fluence into the enamel model structure defined in Fig. 3 taken at 10 ps (a), 150 ps (b), 650 ps (c), and 800 ps (d) after the pulse peak arrival. Large localized positive and negative stress amplitudes appear within 1 ns after the pulse deposition with maximum tensile amplitudes greatly exceeding the static enamel UTS of –40 MPa.

Fig. 6 (Color) Averaged and normalized time domain spectra of field fluctuations observed at 144 uniformly distributed spatial points and fitted to discrete points. The spectra roughly resample the spatial domain as expected through dispersion relations. Broadband high frequency transients become excited using the 50 ps pulse and are not excited with longer pulses.

Therefore, this simple model supports the conjecture that by depositing laser energy in tissues under IHDVE conditions, the induced thermoelastic energy gets spread into a broadband high frequency acoustic spectrum due to micro-stress confinement and the heterogeneous distribution of vibrational chromophores. This feature implies two important consequences. First, large positive and negative stress amplitude spikes are expected to arise within the excited volume shortly after the pulse absorption due to low spatial and temporal coherence of the stress field. This is confirmed by detecting the maximum tensile stress component during the total simulation time. As can be seen from Fig. 7 , the amplitude rapidly increases as conditions approach micro-stress confinement. For 50 ps pulses, values up to 1600 MPa were observed, almost two orders of magnitude higher then the enamel static UTS. Hence, under IHDVE conditions, strong photomechanical effects can be created even by depositing a small amount of total heat using laser pulses with modest energies. Second, since the acoustic attenuation coefficient increases with frequency, the spread of the acoustic energy into the high frequency spectrum should strongly localize the action of these transients within the irradiated volume and reduce stress induced damage away from the ablated region. Both of these novel features of IHDVE likely act together to greatly increase the efficiency of the ablation process and to minimize collateral damage outside the targeted zone.

Fig. 7 Maximum tensile amplitude detected during the simulation time for different pulse durations. The maximum tensile amplitude rapidly increases as conditions for micro-stress confinement are approached.

4. Summary and conclusions

In this work, we report on the highly efficient ablation of healthy tooth enamel using 55 ps long laser pulses tuned to the O-H stretch vibrational band present in water molecules and hydroxyapatite crystals centered at 3400 cm^–1. The operating ablation fluence at 0.75 J/cm² was several times smaller than the typical ablation thresholds previously reported for laser pulses at the same wavelength but with ~100 nanosecond and microsecond pulse durations. Equally important, the peak power at 13 GW/cm² was an order of magnitude lower than the plasma generation threshold. The ablation was performed without adding any superficial water layer at the enamel surface. The large increase in ablation efficiency under strong stress confinement conditions implies the presence of significant photomechanical effects.

Closer analysis of the IHDVE process indicates the key role ultrafast relaxation rates of the molecular vibrational transitions in the condensed phase play in the process. These rates for polyatomic molecules are generally on the order of 1-10 ps and in the case of liquid water could be even less than 1 ps for moderate laser fluences. This means the vibrationally resonant photon energy gets thermalized on the picosecond timescale with corresponding thermoelastic stress generated on the same timescale. The thermalization of optical energy into the lattice structure during IHDVE occurs at a rate comparable to ultrafast plasma driven ablation but with two key differences.

First, in the case of IHDVE, the photon energy gets directly converted into mechanical degrees of freedom and lattice motions initiating ablation with molecules remaining neutral and intact. In contrast, thermalization of optical energy during ultrafast plasma driven ablation occurs on approximately the same time scale but indirectly through recombination and inelastic scattering of free electrons created through multiphoton and avalanche ionization. Plasma formation is by definition a highly ionizing process that can be damaging to surrounding cells by influencing biochemical and genetic processes and therefore creates significant health risks. The IHDVE mechanism completely avoids this risk.

Second, the IHDVE generated initial stress field is inhomogeneous due to the initial heterogeneous distribution of vibrational chromophores and micro-stress confinement conditions. In contrast, the initial stress amplitude in the plasma driven ablation is determined by the initial plasma density which is more or less uniform since the dielectric breakdown leads to disintegration of material and loss of structural heterogeneity. This difference is immediately apparent when one compares uniform, smooth, ablation craters produced by non-resonant multiphoton processes to strongly structured craters produced by IHDVE.

We attribute the relatively high efficiency of the IHDVE mechanism to the heterogeneous nature of the associated stress field under stress confinement conditions that acts to enhance the ablation efficiency through photomechanical effects. By depositing acoustic energy into broadband high frequency spectra and spatial components, it is possible to achieve very large tensile amplitudes spikes (compared to UTS) through interference of low coherence, high-bandwidth, stress fields. This conjecture is supported by the experimental results of 5.7× higher ablation efficiency compared to plasma driven ablation for similar pulse durations and also through numerical simulations using a simplified model tissue. Due to complex tissue mesoscopic structure, the IHDVE photomechanical effects during the stress relaxation time, τ_AC , are probably further amplified by acoustic reflections off the acoustic impedance mismatched mesoscopic surfaces, coupling between compressive and shear stress waves, nonlinear effects, and microscopic cavitation. The experimental IHDVE threshold energy density ε_th was less than 1 kJ/cm³ and was even smaller than the value reported for 100 fs pulses during plasma driven ablation of enamel [15

]. Higher ablation efficiency reduces potential tissue damage since photo-disruptive effects like recoil stress or residual heat scale approximately linearly with the deposited energy density. Furthermore, the large amplitude, high frequency acoustic transients responsible for the photo-mechanical effect are confined to the irradiated volume through rapid attenuation in tissues over distances comparable to the optical absorption length. Benefits of the ultrashort lifetimes of vibrational chromophores in tissues and especially the extraordinary ability of liquid water to dissipate vibrational energy on ultrafast time scales have not been exploited previously in this manner to fully optimize laser removal of tissue to the best of our knowledge. Since vibrational chromophores are widespread in the human body, benefits of IHDVE driven tissue ablation should have a universal character, independent of targeted vibrational mode. Equally important for biological applications, this mechanism does not involve ionizing radiation effects.

In order to exploit all the potential benefits of IHDVE based tissue ablation, robust and cost-effective laser sources are required. The laser pulse duration domain around 100 ps is accessible with simple passively Q-switched microchip lasers [65

B. Braun, F. X. Kärtner, G. Zhang, M. Moser, and U. Keller, “56-ps passively Q-switched diode-pumped microchip laser,” Opt. Lett. 22(6), 381–383 ( 1997). [CrossRef] [PubMed]

]. Their typical pulse energy output of 0.1-100 µJ can be further amplified using compact solid state diode pumped amplifiers and converted to desired infrared wavelengths using nonlinear optical parametric devices. For more sophisticated applications involving arbitrary laser pulse shaping and infrared wavelength multiplexing, the recent extension of high-power broadband OPCPA techniques into the infrared spectral region [66

D. Kraemer, M. L. Cowan, R. Z. Hua, K. Franjic, and R. D. Miller, “High-power femtosecond infrared laser source based on noncollinear optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 24(4), 813–818 ( 2007). [CrossRef]

] is a viable option. Since average and peak powers achievable in the OPCPA parametric devices are fundamentally limited only by pump pulse energy at λ=1 µm and size of the nonlinear crystals, table-top devices with infrared average power comparable to free-electron lasers and orders of magnitude higher peak power are possible with additional potential benefits of arbitrary temporal and spectral shaping to further optimize the ablation process.

Acknowledgements

This research was supported by the Ontario Centers of Excellence, Canadian Institute of Photonics Innovation, and the Natural Sciences and Engineering Research Council of Canada.

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50.	H. Peterlik, P. Roschger, K. Klaushofer, and P. Fratzl, “From brittle to ductile fracture of bone,” Nat. Mater. 5(1), 52–55 ( 2006). [CrossRef] [PubMed]
51.	K. K. Shung, and G. A. Thieme, Ultrasonic Scattering in Biological Tissues, (CRC, Boca Raton, 1993).
52.	K. K. Shung, “Ultrasound and Tissue Interaction,” in Encyclopedia of Biomaterials and Biomedical Engineering , G. E. Wnek and G. L. Bowlin, eds., (Informa HealthCare, 2008).
53.	G. W. C. Kaye, and T. H. Laby, Tables of Physical and Chemical Constants: And Some Mathematical Functions, (Longman, 1995).
54.	C. M. Sehgal, “Quantitative relationship between tissue composition and scattering of ultrasound,” J. Acoust. Soc. Am. 94(4), 1944–1952 ( 1993). [CrossRef] [PubMed]
55.	T. D. Mast, L. P. Souriau, D. L. D. Liu, M. Tabei, A. I. Nachman, and R. C. Waag, “A k-space method for large-scale models of wave propagation in tissue,” IEEE T. Ultrason. Ferr. 48(2), 341–354 ( 2001). [CrossRef]
56.	B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: Application to biomedical photoacoustics,” J. Acoust. Soc. Am. 121(6), 3453–3464 ( 2007). [CrossRef] [PubMed]
57.	A. D. Pierce, “The wave theory of sound,” in Acoustics: An Introduction to Its Physical Principles and Applications, (Acoustical Society of America, Woodbury, NY, 1989).
58.	Ben Cox, Department of Medical Physics and Bioengineering, University College London, UK, (personal communication, 2009).
59.	J. Ge, F. Z. Cui, X. M. Wang, and H. L. Feng, “Property variations in the prism and the organic sheath within enamel by nanoindentation,” Biomaterials 26(16), 3333–3339 ( 2005). [CrossRef] [PubMed]
60.	N. Meredith, D. J. Setchell, and S. A. V. Swanson, “The application of thermoelastic analysis to study stresses in human teeth,” J. Oral Rehabil. 24(11), 813–822 ( 1997). [CrossRef] [PubMed]
61.	D. E. Grenoble, J. L. Katz, K. L. Dunn, K. L. Murty, and R. S. Gilmore, “The Elastic Properties of Hard Tissues and Apatites,” J. Biomed. Mater. Res. 6(3), 221–233 ( 1972). [CrossRef] [PubMed]
62.	M. Giannini, C. J. Soares, and R. M. de Carvalho, “Ultimate tensile strength of tooth structures,” Dent. Mater. 20(4), 322–329 ( 2004). [CrossRef] [PubMed]
63.	L. A. Chernov, Wave propagation in a random medium, (Dover Publications, 1967).
64.	K. Franjic, F. Talbot, and R. J. D. Miller, (to be submitted)
65.	B. Braun, F. X. Kärtner, G. Zhang, M. Moser, and U. Keller, “56-ps passively Q-switched diode-pumped microchip laser,” Opt. Lett. 22(6), 381–383 ( 1997). [CrossRef] [PubMed]
66.	D. Kraemer, M. L. Cowan, R. Z. Hua, K. Franjic, and R. D. Miller, “High-power femtosecond infrared laser source based on noncollinear optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 24(4), 813–818 ( 2007). [CrossRef]

OCIS Codes
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(140.3390) Lasers and laser optics : Laser materials processing
(170.1020) Medical optics and biotechnology : Ablation of tissue
(170.1610) Medical optics and biotechnology : Clinical applications

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: September 9, 2009
Revised Manuscript: November 10, 2009
Manuscript Accepted: November 11, 2009
Published: December 1, 2009

Virtual Issues
Vol. 5, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Kresimir Franjic, Michael L. Cowan, Darren Kraemer, and R. J. Dwayne Miller, "Laser selective cutting of biological tissues by impulsive heat deposition through ultrafast  vibrational excitations," Opt. Express 17, 22937-22959 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22937

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B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302(5649), 1382–1385 (2003). [CrossRef] [PubMed]
P. H. L. Sit, C. Bellin, B. Barbiellini, D. Testemale, J. L. Hazemann, T. Buslaps, N. Marzari, and A. Shukla, “Hydrogen bonding and coordination in normal and supercritical water from X-ray inelastic scattering,” Phys. Rev. B 76(24), 245413 (2007). [CrossRef]
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R. O. Esenaliev, A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Laser-Ablation of Aqueous-Solutions with Spatially Homogeneous and Heterogeneous Absorption,” Appl. Phys. B 59(1), 73–81 (1994). [CrossRef]
S. L. Jacques, A. A. Oraevsky, R. Thompson, and B. S. Gerstman, “A Working Theory and Experiments on Photomechanical Disruption of Melanosomes to Explain the Threshold for Minimal Visible Retinal Lesions for Sub-ns Laser-Pulses,” Proc. SPIE 2134, 54–65 (1994).
S. Meng and E. Kaxiras, “Mechanisms for ultrafast nonradiative relaxation in electronically excited eumelanin constituents,” Biophys. J. 95(9), 4396–4402 (2008). [CrossRef] [PubMed]
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M. I. Khan, T. Sun, and G. J. Diebold, “Photoacoustic Waves Generated by Absorption of Laser-Radiation in Optically Thin Cylinders,” J. Acoust. Soc. Am. 94(2), 931–940 (1993). [CrossRef]
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A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).
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H. Peterlik, P. Roschger, K. Klaushofer, and P. Fratzl, “From brittle to ductile fracture of bone,” Nat. Mater. 5(1), 52–55 (2006). [CrossRef] [PubMed]
K. K. Shung and G. A. Thieme, Ultrasonic Scattering in Biological Tissues, (CRC, Boca Raton, 1993).
K. K. Shung, “Ultrasound and Tissue Interaction,” in Encyclopedia of Biomaterials and Biomedical Engineering, G. E. Wnek and G. L. Bowlin, eds., (Informa HealthCare, 2008).
G. W. C. Kaye, and T. H. Laby, Tables of Physical and Chemical Constants: And Some Mathematical Functions, (Longman, 1995).
C. M. Sehgal, “Quantitative relationship between tissue composition and scattering of ultrasound,” J. Acoust. Soc. Am. 94(4), 1944–1952 (1993). [CrossRef] [PubMed]
T. D. Mast, L. P. Souriau, D. L. D. Liu, M. Tabei, A. I. Nachman, and R. C. Waag, “A k-space method for large-scale models of wave propagation in tissue,” IEEE T. Ultrason. Ferr. 48(2), 341–354 (2001). [CrossRef]
B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: Application to biomedical photoacoustics,” J. Acoust. Soc. Am. 121(6), 3453–3464 (2007). [CrossRef] [PubMed]
A. D. Pierce, “The wave theory of sound,” in Acoustics: An Introduction to Its Physical Principles and Applications, (Acoustical Society of America, Woodbury, NY, 1989).
B. Cox, Department of Medical Physics and Bioengineering, University College London, UK, (personal communication, 2009).
J. Ge, F. Z. Cui, X. M. Wang, and H. L. Feng, “Property variations in the prism and the organic sheath within enamel by nanoindentation,” Biomaterials 26(16), 3333–3339 (2005). [CrossRef] [PubMed]
N. Meredith, D. J. Setchell, and S. A. V. Swanson, “The application of thermoelastic analysis to study stresses in human teeth,” J. Oral Rehabil. 24(11), 813–822 (1997). [CrossRef] [PubMed]
D. E. Grenoble, J. L. Katz, K. L. Dunn, K. L. Murty, and R. S. Gilmore, “The Elastic Properties of Hard Tissues and Apatites,” J. Biomed. Mater. Res. 6(3), 221–233 (1972). [CrossRef] [PubMed]
M. Giannini, C. J. Soares, and R. M. de Carvalho, “Ultimate tensile strength of tooth structures,” Dent. Mater. 20(4), 322–329 (2004). [CrossRef] [PubMed]
L. A. Chernov, Wave propagation in a random medium, (Dover Publications, 1967).
K. Franjic, F. Talbot, and R. J. D. Miller, (to be submitted)
B. Braun, F. X. Kärtner, G. Zhang, M. Moser, and U. Keller, “56-ps passively Q-switched diode-pumped microchip laser,” Opt. Lett. 22(6), 381–383 (1997). [CrossRef] [PubMed]
D. Kraemer, M. L. Cowan, R. Z. Hua, K. Franjic, and R. D. Miller, “High-power femtosecond infrared laser source based on noncollinear optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 24(4), 813–818 (2007). [CrossRef]

Adunas, G.
Albagli, D.
Aronson, R.
Arridge, S. R.
Barbiellini, B.
Beard, P. C.
Bellin, C.
Bille, J. F.
Braun, B.
Bruner, B. D.
Buslaps, T.
Chugh, B.
Clokie, C. M. L.
Cloutier, M.
Copeland, M.
Cowan, M. L.
Cox, B. T.
Cui, F. Z.
Dark, M. L.
Davidson, J.
de Carvalho, R. M.
Dibdin, G. H.
Diebold, G. J.
Dingus, R. S.
Doukas, A. G.
Duhn, C.
Dunn, K. L.
Dwyer, J. R.
Dyer, P. E.
Edwards, G.
Eisenmann, L.
Elsaesser, T.
Esenaliev, R. O.
Featherstone, J. D. B.
Feld, M. S.
Feng, H. L.
Flotte, T. J.
Franjic, K.
Fratzl, P.
Fried, D.
Ge, J.
Gerstman, B. S.
Giannini, M.
Gilmore, R. S.
Girard, B.
Gould, G.
Grenoble, D. E.
Grill, W.
Guo, M. S.
Halle, B.
Hazemann, J. L.
Hibst, R.
Horvath, C.
Hua, R. Z.
Huse, N.
Hutson, M. S.
Huttman, G.
Itzkan, I.
Ivanov, B.
Jacques, S. L.
Jansen, E. D.
Jayasinghe, A.
Johnson, B.
Jordan, R. E.
Juhasz, T.
Kalinichev, A. G.
Kara, S.
Karabutov, A. A.
Karasev, M. E.
Kärtner, F. X.
Katz, J. L.
Kaxiras, E.
Keller, U.
Khan, M. I.
Klaushofer, K.
Kollias, N.
Kozub, J.
Kozub, J. A.
Kraemer, D.
Kulevskii, L. A.
Kulevsky, L. A.
Kurtz, R.
Letokhov, V. S.
Lindner, J.
Liu, D. L. D.
Loesel, F. H.
Logan, R.
Lukashev, A. V.
Maciunas, R.
Mackanos, M. A.
Marzari, N.
Mast, T. D.
McCormack, S. M.
Mendenhall, M.
Meng, S.
Meredith, N.
Mikhalevich, V. G.
Mikic, B. B.
Miller, R. D.
Miller, R. J. D.
Moser, M.
Murty, K. L.
Nachman, A. I.
Nibbering, E. T. J.
Niemz, M. H.
Nishioka, N. S.
Noack, J.
Oday, D.
Oraevsky, A. A.
Ossoff, R.
Paltauf, G.
Perelman, L. T.
Persson, E.
Peterlik, H.
Pioch, T.
Podymova, N. B.
Pruss, A.
Raksi, F.
Ramos, M. M. D.
Reinisch, L.
Rodin, A. M.
Roschger, P.
Scammon, R. J.
Schäfer, T.
Schmidt-Kloiber, H.
Schwarzer, D.
Sehgal, C. M.
Seka, W.
Setchell, D. J.
Shori, R.
Shori, R. K.
Shukla, A.
Sit, P. H. L.
Siwick, B. J.
Soares, C. J.
Solon, L. R.
Souriau, L. P.
Spooner, G.
Stafsudd, O. M.
Stoneham, A. M.
Störkel, U.
Suarez, C.
Sun, J. M.
Sun, T.
Swanson, S. A. V.
Tabei, M.
Testemale, D.
Thompson, R.
Toker, G. R.
Tribble, J.
Venugopalan, V.
Verde, A. V.
Vodopyanov, K. L.
Vogel, A.
Vöhringer, P.
von Rosenberg, C.
Waag, R. C.
Wagner, W.
Walsh, J. T.
Walston, A. A.
Wang, X. M.
Werkhaven, J.
Wilson, B. C.
Wilson, D. J.
Xiao, Y. W.
Yablon, A. D.
Zhang, G.
Zuerlein, M.

Adv. Drug Deliv. Rev.

A. G. Doukas and N. Kollias, “Transdermal drug delivery with a pressure wave,” Adv. Drug Deliv. Rev. 56(5), 559–579 (2004). [CrossRef] [PubMed]

Annu. Rev. Phys. Chem.

R. J. D. Miller, “Vibrational energy relaxation and structural dynamics of heme proteins,” Annu. Rev. Phys. Chem. 42(1), 581–614 (1991). [CrossRef] [PubMed]

Appl. Phys. B

A. Vogel, J. Noack, G. Huttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005). [CrossRef]
R. O. Esenaliev, A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Laser-Ablation of Aqueous-Solutions with Spatially Homogeneous and Heterogeneous Absorption,” Appl. Phys. B 59(1), 73–81 (1994). [CrossRef]
A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).

Appl. Phys.Mater. Sci

G. Paltauf and H. Schmidt-Kloiber, “Photoacoustic cavitation in spherical and cylindrical absorbers,” Appl. Phys.Mater. Sci . 68, 525–531 (1999). [CrossRef]

Appl. Surf. Sci.

D. Fried, M. Zuerlein, J. D. B. Featherstone, W. Seka, C. Duhn, and S. M. McCormack, “IR laser ablation of dental enamel: mechanistic dependence on the primary absorber,” Appl. Surf. Sci. 127(1-2), 852–856 (1998). [CrossRef]

Biomaterials

J. Ge, F. Z. Cui, X. M. Wang, and H. L. Feng, “Property variations in the prism and the organic sheath within enamel by nanoindentation,” Biomaterials 26(16), 3333–3339 (2005). [CrossRef] [PubMed]

Biophys. J.

S. Meng and E. Kaxiras, “Mechanisms for ultrafast nonradiative relaxation in electronically excited eumelanin constituents,” Biophys. J. 95(9), 4396–4402 (2008). [CrossRef] [PubMed]

Caries Res.

G. H. Dibdin, “The Water in Human Dental Enamel and Its Diffusional Exchange Measured by Clearance of Tritiated Water from Enamel Slabs of Varying Thickness,” Caries Res. 27(2), 81–86 (1993). [CrossRef] [PubMed]

Chem. Rev.

A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103(2), 577–644 (2003). [CrossRef] [PubMed]
G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 (2003). [CrossRef] [PubMed]

Dent. Mater.

M. Giannini, C. J. Soares, and R. M. de Carvalho, “Ultimate tensile strength of tooth structures,” Dent. Mater. 20(4), 322–329 (2004). [CrossRef] [PubMed]

IEEE J. Quantum Electron.

F. H. Loesel, M. H. Niemz, J. F. Bille, and T. Juhasz, “Laser-induced optical breakdown on hard and soft tissues and its dependence on the pulse duration: Experiment and model,” IEEE J. Quantum Electron. 32(10), 1717–1722 (1996). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

R. K. Shori, A. A. Walston, O. M. Stafsudd, D. Fried, and J. T. Walsh, “Quantification and modeling of the dynamic changes in the absorption coefficient of water at λ=2.94 μm,” IEEE J. Sel. Top. Quantum Electron. 7(6), 959–970 (2001). [CrossRef]

IEEE T. Ultrason. Ferr.

T. D. Mast, L. P. Souriau, D. L. D. Liu, M. Tabei, A. I. Nachman, and R. C. Waag, “A k-space method for large-scale models of wave propagation in tissue,” IEEE T. Ultrason. Ferr. 48(2), 341–354 (2001). [CrossRef]

J. Acoust. Soc. Am.

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: Application to biomedical photoacoustics,” J. Acoust. Soc. Am. 121(6), 3453–3464 (2007). [CrossRef] [PubMed]
C. M. Sehgal, “Quantitative relationship between tissue composition and scattering of ultrasound,” J. Acoust. Soc. Am. 94(4), 1944–1952 (1993). [CrossRef] [PubMed]
M. I. Khan, T. Sun, and G. J. Diebold, “Photoacoustic Waves Generated by Absorption of Laser-Radiation in Optically Thin Cylinders,” J. Acoust. Soc. Am. 94(2), 931–940 (1993). [CrossRef]

J. Biomed. Mater. Res.

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J. Chem. Phys.

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Laser selective cutting of biological tissues by impulsive heat deposition through ultrafast vibrational excitations

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Abstract

1. Introduction: laser tissue ablation

2. Experimental studies of dental enamel ablation under IHDVE conditions

2.1 Dental enamel as a model tissue

2.2 The laser system

2.3 Scanning electron microscopy

3. Theoretical considerations and numerical modeling

3.1 Vibrational relaxation in the condensed phase

3.2. Enhancement of the photomechanical ablation effect in biological tissues through ultrafast vibrational excitations

3.3 Propagation of high-frequency high-power ultrasound in tissue structures

3.4 Simplified numerical modeling of IHDVE generated acoustic fields in tissues using a k-space propagation method

4. Summary and conclusions

Acknowledgements

References and links

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Zh. Eksp. Teor. Fiz.

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Laser selective cutting of biological tissues by impulsive heat deposition through ultrafast  vibrational excitations