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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 11 — May. 24, 2010
  • pp: 11138–11147
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Technique of fiber optics used to localize epidural space in piglets

Chien-Kun Ting and Yin Chang  »View Author Affiliations


Optics Express, Vol. 18, Issue 11, pp. 11138-11147 (2010)
http://dx.doi.org/10.1364/OE.18.011138


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Abstract

Technique of loss-of-resistance in epidural block is commonly used for epidural anesthesia in humans with approximately 90% successful rate. However, it may be one of the most difficult procedures to learn for anesthesia residents in hospital. A two-wavelength (650 nm and 532 nm) fiber-optical method has been developed according to the characteristic reflectance spectra of ex-vivo porcine tissues, which are associated with the needle insertion to localize the epidural space (ES). In an in-vivo study in piglets showed that the reflected lights from ES and its surrounding tissue ligamentum flavum (LF) are highly distinguishable. This indicates that this technique has potential to localize the ES on the spot without the help of additional guiding assistance.

© 2010 OSA

1. Introduction

Epidural technique is one of the neuroaxial block techniques for regional anesthesia, postoperative patient control analgesia, painless labor, and chronic pain relief [2

2. P. R. Bromage, “Epidural Analgesia” (W. B. Saunders, 1978).

,3

3. M. J. Cousins, and B. T. Veering, “Epidural neural block,” in Neural Blockade in Clinical Anesthesia and Management of Pain, 3rd ed., M. J. Cousins, P. O. Bridenbaugh, eds. (Lippincott-Raven, 1998), pp. 243–321.

]. It may also contribute to a decrease in perioperative morbidity [4

4. J. R. Rigg, K. Jamrozik, P. S. Myles, B. S. Silbert, P. J. Peyton, R. W. Parsons, and K. S. CollinsJ. R. RiggK. JamrozikP. S. MylesB. S. SilbertP. J. PeytonR. W. ParsonsK. S. CollinsMASTER Anaethesia Trial Study Group, “Epidural anaesthesia and analgesia and outcome of major surgery: a randomized trial,” Lancet 359(9314), 1276–1282 (2002). [CrossRef] [PubMed]

]. However, the successful rate of epidural block is only approximately 90% due to incorrect catheter placement [5

5. M. Curatolo, A. Orlando, A. M. Zbinden, P. Scaramozzino, and F. S. Venuti, “A multifactorial analysis to explain inadequate surgical analgesia after extradural block,” Br. J. Anaesth. 75(3), 274–281 (1995). [PubMed]

,6

6. P. H. Pan, T. D. Bogard, and M. D. Owen, “Incidence and characteristics of failures in obstetric neuraxial analgesia and anesthesia: a retrospective analysis of 19,259 deliveries,” Int. J. Obstet. Anesth. 13(4), 227–233 (2004). [CrossRef] [PubMed]

], which is dependent on the operator’s experience, patient positioning, body habitués, and spinal anatomy [7

7. G. R. de Filho, H. P. Gomes, M. H. da Fonseca, J. C. Hoffman, S. G. Pederneiras, and J. H. Garcia, “Predictors of successful neuraxial block: a prospective study,” Eur. J. Anaesthesiol. 19(6), 447–451 (2002). [PubMed]

9

9. D. D. Hood and D. M. Dewan, “Anesthetic and obstetric outcome in morbidly obese parturients,” Anesthesiology 79(6), 1210–1218 (1993). [CrossRef] [PubMed]

]. Epidural technique may be one of the most difficult procedures to learn for anesthesia residents in hospitals. It is reported that an average of 60 to 90 epidural placements in practice is necessary to reach a plateau of successful rate [10

10. C. Konrad, G. Schüpfer, M. Wietlisbach, and H. Gerber, “Learning manual skills in anesthesiology: is there a recommended number of cases for anesthetic procedures?” Anesth. Analg. 86(3), 635–639 (1998). [CrossRef] [PubMed]

]. In anatomy, the space of ES is very narrow. In the posterior space its dorsoventral dimension is approximately 5.0-6.0 mm in average in the region of lumbar and decreases in the thoracic region in adult males. To localize the ES normally, the technique of loss-of-resistance (LOR) is usually employed, of which a saline- or air-filled syringe is put on the needle’s end to serve as a tool to detect the ES by pushing piston while the epidural needle reaches the space (after the LF is punctured) with great pressure loss [11

11. A. M. Dogliotti, “Segmental peridural spinal anesthesia: a new method of block anesthesia,” Am. J. Surg. 20, 107–118 (1993). [CrossRef]

]. Punctuation of the dura mater during needle insertion will lead the cerebral spinal fluid (CSF) leakage and decrease the CSF pressure in spine. The consequence could cause the patient to suffer from severe headache. LOR technique particularly relies on the tactile sensation without any objective guidance and is not always reliable, particularly when a false sense of LOR occurs. This leaves the task of determining the ES position to the anesthesiologist’s individual ability. Therefore a way of having objectively reliable guidance for a right needle placement in the ES is desirable. Several techniques or devices have been introduced to improve successful rate of epidural puncture [12

12. T. Nagaro, T. Yorozuya, M. Kamei, N. Kii, T. Arai, and S. Abe, “Fluoroscopically guided epidural block in the thoracic and lumbar regions,” Reg. Anesth. Pain Med. 31(5), 409–416 (2006). [PubMed]

,13

13. B. C. Tsui, P. Tarkkila, S. Gupta, and R. Kearney, “Confirmation of caudal needle placement using nerve stimulation,” Anesthesiology 91(2), 374–378 (1999). [CrossRef] [PubMed]

], including uses of acoustic devices, clinical signs, epidural nerve stimulation [14

14. T. J. Lechner, M. G. van Wijk, A. J. Maas, F. R. van Dorsten, R. A. Drost, C. J. Langenberg, L. J. Teunissen, P. H. Cornelissen, and J. van Niekerk, “Clinical results with the acoustic puncture assist device, a new acoustic device to identify the epidural space,” Anesth. Analg. 96(4), 1183–1187 (2003). [CrossRef] [PubMed]

16

16. B. C. Tsui, C. Guenther, D. Emery, and B. Finucane, “Determining epidural catheter location using nerve stimulation with radiological confirmation,” Reg. Anesth. Pain Med. 25(3), 306–309 (2000). [PubMed]

], ultrasonography [17

17. M. K. Karmakar, X. Li, A. M. Ho, W. H. Kwok, and P. T. Chui, “Real-time ultrasound-guided paramedian epidural access: evaluation of a novel in-plane technique,” Br. J. Anaesth. 102(6), 845–854 (2009). [CrossRef] [PubMed]

], fluoroscopy [12

12. T. Nagaro, T. Yorozuya, M. Kamei, N. Kii, T. Arai, and S. Abe, “Fluoroscopically guided epidural block in the thoracic and lumbar regions,” Reg. Anesth. Pain Med. 31(5), 409–416 (2006). [PubMed]

], computed tomography epidurography and pulsatile pressure waveform detection through the epidural catheter [18

18. Ghia Jn, M. Arora Sk, Castillo, and Mukherji Sk, “Confirmation of location of epidural catheters by epidural pressure waveform and computed tomography cathetergram,” Reg. Anesth. Pain Med. 26(4), 337–341 (2001). [PubMed]

,19

19. P. H. Lennox, H. S. Umedaly, R. P. Grant, S. A. White, B. G. Fitzmaurice, and K. G. Evans, “A pulsatile pressure waveform is a sensitive marker for confirming the location of the thoracic epidural space,” J. Cardiothorac. Vasc. Anesth. 20(5), 659–663 (2006). [CrossRef] [PubMed]

]. However, fluoroscopically guided epidural block and electric stimulation can only be used to confirm correct catheter placement, in which specially designed catheters are required [16

16. B. C. Tsui, C. Guenther, D. Emery, and B. Finucane, “Determining epidural catheter location using nerve stimulation with radiological confirmation,” Reg. Anesth. Pain Med. 25(3), 306–309 (2000). [PubMed]

], and pulsatile pressure waveform and computed tomography epidurography are not feasible in clinical practice. Ultrasound visualization of the spinal column and surrounding structures gives additional anatomical information, which can assist the block easier and safer. It has been shown to have a significant reduction of puncture occurrences in epidural anesthesia by providing the optimal skin puncture site, the ideal direction of needle advancement and the skin-to-ES distance [20

20. T. Grau, R. W. Leipold, R. Conradi, and E. Martin, “Ultrasound control for presumed difficult epidural puncture,” Acta Anaesthesiol. Scand. 45(6), 766–771 (2001). [CrossRef] [PubMed]

]. It also shows to improve the successful rate and safety of a variety of peripheral regional anesthesia techniques in children [17

17. M. K. Karmakar, X. Li, A. M. Ho, W. H. Kwok, and P. T. Chui, “Real-time ultrasound-guided paramedian epidural access: evaluation of a novel in-plane technique,” Br. J. Anaesth. 102(6), 845–854 (2009). [CrossRef] [PubMed]

]. However, this technique relies on a two-man operation; one has to handle the ultrasound probe and the other has to perform the LOR Therefore an ideal method to localize the ES without the assistance of additional hands for guidance is still not available. Thus we herein propose a method of guided epidural block by using two-wavelength optical method which mediated fiber optic technique to differentiate the reflectance spectra in different biological tissues. Studies were carried out in-vitro porcine tissues and in piglets in-vivo.

2. Materials and Methods

Two experiments were carried out for feasibility and practicability to meet the purpose mentioned above. The first one was to identify the characteristic reflectance spectra of the in-vitro biological tissues of piglets that were associated with the tissues on the pathway of needle insertion for anesthesia. The second one was to detect the ES in piglets in-vivo by using the technique of fiber optics with selected particular wavelengths according to the results done in the in-vitro experiment. The standard procedure of placing catheter into the epidural space is briefly described below. Epidural needle set composes of one hollow (epidural) needle (about 9.84 cm in length) and a solid needle (stylet). The latter is normally inserted in the hollow space of the epidural needle. For doing epidural block anesthesia, this eipdural needle is gradually inserted into the interspinous ligament between vertebras. Once the ES is sensed, the stylet needle is pulled out and checked by the technique of LOR. If the LOR is positively confirmed (the ES is located) then a catheter is inserted into the hollowly epidural needle until it is placed in the ES. After that the epidural needle is pulled out along the catheter and the other end of the catheter is connected to a machine or a syringe for further drug delivery.

2.1 Experiment I – in-vitro study

The successive tissue layers on the pathway during the needle insertion to localize the ES are skin, fat, muscle, periosteum (it is a thin layer of dense, irregular connective tissue membrane that covers the outer surface of a bone in all places except at joints) and LF.

The ES is right behind the LF and in front of the dura in the direction of needle insertion. The set up shown in Fig. 1
Fig. 1 Schematic diagram of the set up is shown for measuring the reflectance spectrum of an ex vivo tissue. Details are described in the text.
is to measure the reflectance spectrum of each ex-vivo tissue. The light source was a 75W xenon lamp and its light was coupled into an objective lens by way of relay lenses to illuminate the tissue through the core fibers of a Y-shape optic fiber bundle. The reflected light from the tissue was transmitted to a fiber optic spectrometer (EPP2000, StellarNet Inc. USA) through the surrounding fibers of the bundle. The configuration of the fiber bundle is also shown in Fig. 1 schematically. The computer acquired the spectral data for further analysis. It is noted that the hemoglobin in the in-vitro tissue has already deoxygenated so that its reflectance spectrum may differ from that obtained in-vivo. The spectrum of the xenon lamp is obtained through a barium sulfate reflector which has nearly flat reflectance (reflectance factor = 0.983) in the range of visible wavelength [21

21. S. F. Chen, Y. Chang, and J. C. Wu, “The spatial distribution of macular pigment in humans,” Curr. Eye Res. 23(6), 422–434 (2001). [CrossRef]

]. The relative reflectance spectra of the tissues within particular interested wavelength range from 500 nm to 700 nm are shown in Fig. 2
Fig. 2 Reflectance spectra (500-700 nm) of in-vitro porcine tissues at back spine are displayed. They are corrected with the spectrum of the xenon lamp.
. They are obtained by dividing the spectrum of the xenon lamp. It is noticed that the spectra of muscle and periosteum are nearly overlapped. The spectrum of the dura may represent the ‘spectrum’ of the ES while the needle probe reaches the space. The dashed lines indicate the wavelengths of 532 and 650 nm which are the wavelengths of commercially available solid state lasers. These lines also implicitly reveal that the ratio of the relative reflectance of the LF at 650 nm to 532 nm can be discriminated from the other tissues (The ratios of 650 nm to 532 nm for dura mater and LF are 1.5882 ± 0.1402 and 2.8191 ± 0.2711, respectively, with sample size n = 5. Statistical Wilcoxon Signed Ranks Test showed p = 0.043 with significant difference between the two matters).

2.2 Experiment II – in-vivo study

2.2.1 System setup and optics of the custom-made stylet

An electro-optic control system incorporated with a custom-made stylet needle used in this study is shown in Fig. 3
Fig. 3 Schematic diagram of the system is used to locate ES in piglet in vivo.
, in which the two light sources (solid state lasers) with wavelengths of 650 and 532 nm (5 mW each) are modulated by two counter-phased 3-Hz clocks, which are generated from the control circuit, and their light paths are perpendicularly arranged to form the beam for tissue illumination by way of a 50/50 beam splitter (BS). This light is coupled into a single fiber (Fiber 1) of a fiber bundle, which is embedded in the stylet needle, through a relay lens L. A photodiode (PD) is employed for laser-power monitoring. M is a flat reflective mirror used to guide the light to the PD. The light reflected or backscattered from the tissue is received by a PMT (H5783-20, Hamamatsu, Japan) through the rest of the optic fibers (Fiber 2) of the bundle at the tip of the stylet needle. The PMT signal is amplified and displayed on the screen of an oscilloscope. A PC simultaneously collects and stores the data for further analysis.

The hollow ‘stylet’ needle with 0.9 mm in outer diameter and 0.75 mm in inner diameter was custom made from a fine machine shop so that its size and shape is completely similar to the original one and fits in the hollow space of the epidural needle. A total of 7 fibers are inserted in the hollow tube of the stylet. At the tip of the needle the fibers are glued together and shaped as the needle bevel. The numerical aperture (NA) of the fiber (core diameter = 62.5 um, GGF 625, POFC, Taiwan) is about 0.2792 for 650 nm or 0.2796 for 532 nm (acceptance angle θa ≈16.21° (see Eq. (1), n1 = 1.4574 (core) and n2 = 1.4304 (cladding) for 650 nm; n1 = 1.4610 and n2 = 1.4340 for 532 nm) with estimated attenuation coefficient ≤ 7.2 db/km at 650 nm and 13.6 db/km at 532 nm.

NA0.279=nairsinθa=(n12n22).
(1)

Since the length of the fiber cable is only about 180 cm thus the attenuations for these wavelengths can be neglected. The angle of the bevel referred to the fiber axis is about 20°. Figure 4(a)
Fig. 4 (a) Incident lights from the upper (red) and lower (green) portions of the acceptance angle of the cone form traveling tracks in the fiber core. The exit directions of these lights at the bevel surface of the fiber are shown. (b) A magnified diagram of the dashed box in (a) is shown. See details in the text.
displays a schematic diagram of two light tracks presented in red and green colors in the single fiber indicating the range of incident lights from the fiber axis to the borders of the input cone that travel within the fiber and exit at the other end of the bevel surface. The acceptance angle θa at the front end of the fiber is approximately 16.21°; the refractive angle (or the confinement angle) α is approximately 11.04° for 650 nm and 11.02° for 532 nm by calculation. In order to make the expression simple, the numerical precision in the subsequent text will be presented by two digits and one digit after decimal point for refractive indexes and angles, respectively. Meanwhile the influence of the wavelength to these parameters is also not considered. Thus the calculated critical angle θc [Eq. (2)] for creating total internal reflection in the fiber is about 78.4°.

θc=sin1(n2n1).
(2)

For the rays traveling along the red track in Fig. 4(a) (red/green track is the representative for the lights which incident angles are 0° < θi ≤ 16.2° above/below the fiber axis. In the subsequent description of the text the incident angle = 16.2° is used as an extreme case), the calculated incident angle β on the exit bevel surface is about 59.0°. Thus there will be no light exits from the fiber into the medium if its refractive index is less than 1.25. Fortunately, the refractive indexes of biological tissues are usually greater than this value [22

22. F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989). [CrossRef] [PubMed]

,23

23. M. Sand, T. Gambichler, G. Moussa, F. G. Bechara, D. Sand, P. Altmeyer, and K. Hoffmann, “Evaluation of the epidermal refractive index measured optical coherence tomography,” Skin Res. Technol. 12(2), 114–118 (2006). [CrossRef] [PubMed]

] so that the lights traveling along the red track can be transmitted into the tissues. For the lights traveling along the green track in Fig. 4(a), they will be totally reflected at point B if the refractive index of the tissue is less than 1.43 (since ∠BGH = 160.0°, ∠GHB = α = 11.0°, and ∠GBH = 180.0° - 160.0° - α = 9.0°). According to the published data that the refractive index of most biological tissues are greater than this value [22

22. F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989). [CrossRef] [PubMed]

,23

23. M. Sand, T. Gambichler, G. Moussa, F. G. Bechara, D. Sand, P. Altmeyer, and K. Hoffmann, “Evaluation of the epidermal refractive index measured optical coherence tomography,” Skin Res. Technol. 12(2), 114–118 (2006). [CrossRef] [PubMed]

], thus in most of cases the lights in the green track should be delivered into the tissues. However, if a tissue’s refractive index is less than this value, then a total internal reflection occurs at point B. The consequence is that the reflective light will impinge the interface of the core and the cladding at point I. Figure 4(b) is a magnification of the dashed box in Fig. 4(a), in which ∠ϕ = ∠CBI + 20.0° (external angle of ΔCBI in Fig. 4(a), ∠CBI = ∠GBH) = 29.0°. Thus the incident angle (61.0°) of the light at point I is less than the critical angle θc and there will be no total internal reflection. Therefore the light will refract into the cladding layer (n2) and further hit the boundary at point L with incident angle of 63.2°. This leads to the question: Is there any chance to bring the light back into the core and further emerge into the tissue? The condition to create a total internal reflection at point L is that the refractive index n3 of the connective matter must be less than 1.27 in order to allow the light in the green track that may have a chance to transmit into the tissue (exits at point N). Unfortunately, the connective matter may not be air but the glue at the tip of the needle. No data of refractive index for the hardened glue is available at present but this should not affect the results of this study at all. Some ex-vivo porcine tissues such as muscle and fat have been reported of having refractive indexes of 1.380 ± 0.007/1.460 ± 0.008 (muscle fiber alignment is parallel or perpendicular to the interface of the measuring instrument) and 1.4595 ± 0.0002 respectively [24

24. H. Li and S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35(10), 1793–1795 (1996). [CrossRef] [PubMed]

,25

25. M. Irie, “Evaluation of porcine fat with fiber-optic spectroscopy,” J. Anim. Sci. 77(10), 2680–2684 (1999). [PubMed]

]. Although the data of refractive index for LF is not available at present, it is expected that its value should not be far from that of the muscle. In short summary, most of the lights that enter the fiber can be transmitted into the tissues according to the analysis described above.

2.2.2 Experiment in Piglets

An in vivo animal study was done in a 20 kg piglet. The epidural needle (17 Ga) was used from an epidural catheterization set (EC-05400-E, Arrow® International, USA). The piglet was initially anaesthetized with tiletamine-zolazepam at a dosage of 5 mg/kg and maintained with pentobarbital sodium (15 mg/h/kg, intravenous injection) under mechanically ventilated general anesthesia with electrocardiographic monitoring during operation. Data of reflected lights of 650 nm and 532 nm from muscle, periosteum, LF and ES at lower lumbar were recorded, which was referred to the waveforms shown on the screen of an oscilloscope (GWISTEK, GDS2104, 100 MHz, 4 ch). A total of 5 punctures at the region of lumbar vertebrate were carried out in this study.

3. Results

Typical waveforms obtained from periosteum, muscle, LF and ES in response to the illuminating lights of 650 and 532 nm are shown in Fig. 5
Fig. 5 Responses obtained from periosteum, muscle, LF and ES. High amplitudes in each plot are responses from 650 nm and the lows are from 532 nm.
. The signal of high/low amplitude in each plot indicates that the light is reflected from 650nm/532nm respectively. It shows that the signal of LF has much higher amplitude of 650 nm than those of periosteum, muscle and ES but the magnitudes of 532 nm are nearly the same. From the qualitative point of view, the responsive signals of LF and ES with respect to the two wavelengths provide very clear information for feature-differentiation so that the ES could be accurately located.

In the in-vitro tissue experiment, we found that the 532 nm was a wavelength that could be used to distinguish the ES from the LF. However, in the in-vivo study it does not express in such a way as we expected. This could be due to the different contents of oxyhaemoglobin (HbO2) and deoxyhaemoglobin (Hb) of in-vivo and in-vitro tissues. The absorption spectra [26

26. G. A. Mook, O. W. Van Assendelft, and W. G. Zijlstra, “Wavelength dependency of the spectrophotometric determination of blood oxygen saturation,” Clin. Chim. Acta 26(1), 170–173 (1969). [CrossRef] [PubMed]

] of HbO2 and Hb in the range of 400-700 nm are shown in Fig. 6(a)
Fig. 6 (a) Relative absorption spectra of HbO2 and Hb between 400 nm to 700 nm are shown. (b) Wavelengths between 500 nm to 700 nm are displayed for revealing the absorptions at 532 nm and 650 nm for HbO2 and Hb.
and the wavelength of 436 nm indicates the largest difference in the absorption between the two. Figure 6(b) is an enlarged plot of Fig. 6(a) with wavelength ranged 500~690 nm and particular wavelengths of 532 nm and 650 nm are indicated by dashed lines. It reveals that the 532 nm light can have more absorption in the in-vivo tissues than those of in-vitro and reversed for the 650 nm. This explains why there is not much difference in the responses between tissues at 532 nm since more blood vessels exist in the dura. On the contrary, when HbO2 is plentifully contained in a tissue, it is nearly unabsorbed for 650 nm if scattering factor is ignored. Therefore the amount of the reflected 650 nm light is dependent on the reflectance of the tissue itself. The averaged ratios in magnitude of 650 nm to 532 nm of 5 punctures for LF and ES are 2.92 ± 0.18 and 2.40 ± 0.12 respectively. Although the sample size is small, however, significant difference is shown with p < 0.05 while statistical Wilcoxon Signed Ranks test is applied. It reflects that LF and ES can be clearly differentiated by using this optical method without additional assistance of guidance.

4. Discussion

The criterion of this study is mainly based on the detection of the reflectance spectra of the biological tissues which appear on the pathway during the epidural needle insertion for regional anesthesia in piglets. In the ex-vivo study, it revealed that LF and dura had significant difference in their individual reflectance spectra (Fig. 3), which explicitly implied that the ES could be successfully localized in the further in-vivo study in piglets. Biological tissues are usually inhomogeneous in structure, phenomena of absorption, diffuse- and back-scattering in tissue can occur when irradiation is applied [27

27. J. Reichman, “Determination of absorption and scattering coefficients for nonhomogeneous media. 1: Theory,” Appl. Opt. 12(8), 1811–1815 (1973). [CrossRef] [PubMed]

,28

28. R. L. Longini and R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15(1), 4–10 (1968). [CrossRef]

].

In this study the variability of back-scattering pattern, either in buck tissue [29

29. W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990). [CrossRef]

] or in the size of cellular scale [30

30. L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. Crawford, and M. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998). [CrossRef]

32

32. A. K. Popp, M. T. Valentine, P. D. Kaplan, and D. A. Weitz, “Microscopic origin of light scattering in tissue,” Appl. Opt. 42(16), 2871–2880 (2003). [CrossRef] [PubMed]

], is not considered but the amount of the reflective signal based on the backscattering light in tissue is concerned. Ordinary applications of fiber optics in telecommunication, life science, medicine or industry are very rare to indicate that the output end of the fiber(s) has been shaped with certain fixed angle. This is because the light signal can tremendously reduce in the direction of the fiber axis at the output end. If the output end of the fiber in the stylet needle is designed as a usual way, perpendicular to the fiber axis, then the fiber will face to large resistance during insertion. It had been realized that if the ‘stylet’ was designed with bevel shape at the output end it could result in a loss of light. However, what the concern was the reality for practical use. Although the system has already been successfully demonstrated in the detection of the ES without additional assistance of guidance in this study, the bevel angle (20.0°) of the stylet needle could be a factor that restricts the performance of this technique to certain extent. It is unknown whether this is the optimal angle for the stylet needle to deliver light to and collect light from tissue. Therefore a simulation is carried out with refractive angle γ on the bevel surface vs. variable bevel angle under conditions of various refractive indexes given for a tissue. Since the incident angles from the backscattering or reflected light of a tissue to the receiving optic fiber are unknown in this study the returned light could be dependent upon fiber orientation of the tissue, thus only the exit light (with refractive angle g) in the fiber for tissue illumination is considered in the simulation. The tissue refractive index is assumed to vary from 1.30 to 1.50 with changing step of 0.05. The bevel angle C varies from 10.0° to 90.0° with changing step of 1.0°. Figures 7(a)
Fig. 7 Simulations for refractive angle γ [at point B in Fig. 3(a)] with respect to the various bevel angles at the output end of an optic fiber while the tissue is under the condition of given refractive index. (a) Incident light is at the border of the acceptance angle of 16.2°, of which the refractive light travels along the red track shown in Fig. 3(a). (b) Incident light is at the center of the acceptance angle, 0.0°. (c) Incident light is at the border of the acceptance angle of 16.2°, of which the refractive light travels along the red track shown in Fig. 3(a). (d) A magnification of combined plot for the bevel angle is between 75.0° and 90.0° in plots (a), (b), and (c), which are represented by A, B, and C respectively. From which one can see different behaviors of the lights travel within the red and green tracks, or the upper and the lower portions of the incident light cone that separated by the fiber axis.
, 7(b), and 7(c) are the results of the simulation for the refractive angle γ with respect to the bevel angle C (10.0°~90.0°) at particular incident angle θi = 16.2° [red and green tracks in Fig. 3(a)] or 0°. Figure 7(a) shows that when the tissue’s refractive index is relatively low (say n = 1.30), there will be no light along the red track which can transmit into the tissue unless the bevel angle C is larger than 16.2°. When the bevel angle C increases, the refractive angle γ at the point B on the bevel surface decreases. Until the bevel angle C ≈79.0° (note: the confinement angle α ≈11.0°), the direction of the refractive light transmitting into the tissue is the normal line at point B of the bevel surface. In other words, at this angle, the light traveling along the red track which transmits into the tissue will be no refraction no matter what the refractive index of the tissue is. When the bevel angle C is greater than 79.0°, the refractive light will move to another direction that shows a negative value of γ in the plot. Given various refractive indexes to the tissue, this plot implicitly indicates that this device (‘stylet’ needle) can deliver light into tissue with various refractive angles, which is tissue’s refractive index dependent. If the amount of the backscattering light from a tissue is only counted on the incident angle of an irradiance (this may not be exactly correct but an assumption), then this light that reaches the receiving fiber is also dependent on the refractive angle at the bevel surface. Thus the bevel angle C = 79.0° may not be a good choice to obtain differentiable signals for different tissues even when more light can be delivered to the tissue with this angle.

While the incident angle of the light at the front end of the fiber changes from 16.2° to 0.0°, Fig. 7(b) demonstrates that the slope of each curve in Fig. 7(a) increases with respect to the increment of the tissue refractive index. In other words, it explicitly indicates that more light can be transmitted into the tissue at the same bevel angle C. However, the tissue’s refractive index also limits the light to emerge into the tissue unless that the bevel angle C increases to some degree (such as: for tissue n = 1.30, the starting bevel angle C = 27.0°). Figure 7(c) apparently reveals that the light in the green track transmitted into the tissue is also confined by the bevel angle C. Compared to Fig. 7(a), the light in the green track has more restriction for it to be transmitted into tissue due to tissue’s refractive index and the bevel angle of the fiber. In the same plot, light is unable to transmit into the tissue if the tissue’s refractive index is less than 1.45 for bevel angle C ≤ 16.0°. Figure 7(d) is a combined display for Figs. 7(a), 7(b), and 7(c) (indicated by A, B and C respectively) with the bevel angle C varied from 75.0° to 90.0°. It shows that the refractive angle γ is influenced by the tissue’s refractive index, light incident angle at the front end and the bevel angle C of the fiber. In this study, the refractive indexes of the tissues on the way of the needle insertion can be assumed to be larger than 1.45, thus there is no problem for the light within the acceptance angle to transmit into the tissue while the bevel angle C is 20.0°.

In short summary, according to the results of simulation in Fig. 7, the incident light within the cone of acceptance angle of 16.2° at the front end of the optical fiber its refractive angle (with n = 1.45) varies in the range of 59.3° (red track) and 82.2° (green track) with respect to the plane normal of the bevel surface (Fig. 3) with bevel angle C≈20.0°. In other words, with reference to the fiber axis (direction of needle insertion), the refractive angle γ is within the range of −10.7° (59.3°-70.0°) to 12.2° (82.2°-70.0°). This relative small range of refractive angle γ in this study should benefit to the fiber of receiving the back scattering light from tissues. Another possibility to make the study work with a bevel cut fiber bundle is that upon the needle entering the space, the greatest clear distance is not in the direction of insertion but at an angle to the insertion direction.

The cause of decreased red/green ratio in the epidural space could be more complex than what we expected. The contents of the epidural space include the nerve roots, fat, areolar tissue, lymphatics, and blood vessels [33

33. R. D. Miller, “Miller's Anesthesia,” 7th ed., (Churchill Livingstone, 2009).

]. Additionally, Ellis described this space as “The space projects through each intervertebral canal to lie behind the parietal pleura, whose negative pressure is transmitted to it.” [34

34. H. Ellis, “The anatomy of the epidural space,” Anaesth. Intensive Care Med. 7(11), 402–404 (2006). [CrossRef]

]. Thus two hypotheses could explain the decreased red/green ratio in the space: (1) the puncture introduced by the needle leads to a spread of light before scattering due to relatively large refractive index change. Because the light spread is wavelength dependent, thus it could cause a decrease in light coupled back into the fiber; (2) a relative large absorption (such as 532 nm in HbO2) or forward scattering for particular wavelength occurs in these tissues and results in a reduced red/green ratio.

Conclusion

In this study, the stylet used in traditional epidural anesthesia was redesigned. By which the ES localization by traditional LOR technique can be potentially replaced by this optical technique. This technique can provide additional observable signal for the operator to distinguish LF and ES so that the successful rate of catheter placement could be better than the traditional way.

Acknowledgments

This work was supported by Grant NSC95-2622-E-010-001-CC3 of the National Science Council, Taiwan and a grant from Ministry of Education, Aim for the Top University Plan. We are also grateful to Dr. Kuang-Yi Chang for his advice on statistical methodology.

References and links

1.

C. K. Ting, M. Y. Tsou, P. T. Chen, K. Y. Chang, M. S. Mandell, K. H. Chan, and Y. Chang, “A new technique to assist epidural needle placement: fiberoptic-guided insertion using two wavelengths,” Anesthesiology 112(5), 1128–1135 (2010). [CrossRef] [PubMed]

2.

P. R. Bromage, “Epidural Analgesia” (W. B. Saunders, 1978).

3.

M. J. Cousins, and B. T. Veering, “Epidural neural block,” in Neural Blockade in Clinical Anesthesia and Management of Pain, 3rd ed., M. J. Cousins, P. O. Bridenbaugh, eds. (Lippincott-Raven, 1998), pp. 243–321.

4.

J. R. Rigg, K. Jamrozik, P. S. Myles, B. S. Silbert, P. J. Peyton, R. W. Parsons, and K. S. CollinsJ. R. RiggK. JamrozikP. S. MylesB. S. SilbertP. J. PeytonR. W. ParsonsK. S. CollinsMASTER Anaethesia Trial Study Group, “Epidural anaesthesia and analgesia and outcome of major surgery: a randomized trial,” Lancet 359(9314), 1276–1282 (2002). [CrossRef] [PubMed]

5.

M. Curatolo, A. Orlando, A. M. Zbinden, P. Scaramozzino, and F. S. Venuti, “A multifactorial analysis to explain inadequate surgical analgesia after extradural block,” Br. J. Anaesth. 75(3), 274–281 (1995). [PubMed]

6.

P. H. Pan, T. D. Bogard, and M. D. Owen, “Incidence and characteristics of failures in obstetric neuraxial analgesia and anesthesia: a retrospective analysis of 19,259 deliveries,” Int. J. Obstet. Anesth. 13(4), 227–233 (2004). [CrossRef] [PubMed]

7.

G. R. de Filho, H. P. Gomes, M. H. da Fonseca, J. C. Hoffman, S. G. Pederneiras, and J. H. Garcia, “Predictors of successful neuraxial block: a prospective study,” Eur. J. Anaesthesiol. 19(6), 447–451 (2002). [PubMed]

8.

J. Sprung, D. L. Bourke, J. Grass, J. Hammel, E. Mascha, P. Thomas, and I. Tubin, “Predicting the difficult neuraxial block: a prospective study,” Anesth. Analg. 89(2), 384–389 (1999). [CrossRef] [PubMed]

9.

D. D. Hood and D. M. Dewan, “Anesthetic and obstetric outcome in morbidly obese parturients,” Anesthesiology 79(6), 1210–1218 (1993). [CrossRef] [PubMed]

10.

C. Konrad, G. Schüpfer, M. Wietlisbach, and H. Gerber, “Learning manual skills in anesthesiology: is there a recommended number of cases for anesthetic procedures?” Anesth. Analg. 86(3), 635–639 (1998). [CrossRef] [PubMed]

11.

A. M. Dogliotti, “Segmental peridural spinal anesthesia: a new method of block anesthesia,” Am. J. Surg. 20, 107–118 (1993). [CrossRef]

12.

T. Nagaro, T. Yorozuya, M. Kamei, N. Kii, T. Arai, and S. Abe, “Fluoroscopically guided epidural block in the thoracic and lumbar regions,” Reg. Anesth. Pain Med. 31(5), 409–416 (2006). [PubMed]

13.

B. C. Tsui, P. Tarkkila, S. Gupta, and R. Kearney, “Confirmation of caudal needle placement using nerve stimulation,” Anesthesiology 91(2), 374–378 (1999). [CrossRef] [PubMed]

14.

T. J. Lechner, M. G. van Wijk, A. J. Maas, F. R. van Dorsten, R. A. Drost, C. J. Langenberg, L. J. Teunissen, P. H. Cornelissen, and J. van Niekerk, “Clinical results with the acoustic puncture assist device, a new acoustic device to identify the epidural space,” Anesth. Analg. 96(4), 1183–1187 (2003). [CrossRef] [PubMed]

15.

M. P. Lewis, P. Thomas, L. F. Wilson, and R. C. Mulholland, “The ‘whoosh’ test,” Anaesthesia 47(1), 57–58 (1992). [CrossRef] [PubMed]

16.

B. C. Tsui, C. Guenther, D. Emery, and B. Finucane, “Determining epidural catheter location using nerve stimulation with radiological confirmation,” Reg. Anesth. Pain Med. 25(3), 306–309 (2000). [PubMed]

17.

M. K. Karmakar, X. Li, A. M. Ho, W. H. Kwok, and P. T. Chui, “Real-time ultrasound-guided paramedian epidural access: evaluation of a novel in-plane technique,” Br. J. Anaesth. 102(6), 845–854 (2009). [CrossRef] [PubMed]

18.

Ghia Jn, M. Arora Sk, Castillo, and Mukherji Sk, “Confirmation of location of epidural catheters by epidural pressure waveform and computed tomography cathetergram,” Reg. Anesth. Pain Med. 26(4), 337–341 (2001). [PubMed]

19.

P. H. Lennox, H. S. Umedaly, R. P. Grant, S. A. White, B. G. Fitzmaurice, and K. G. Evans, “A pulsatile pressure waveform is a sensitive marker for confirming the location of the thoracic epidural space,” J. Cardiothorac. Vasc. Anesth. 20(5), 659–663 (2006). [CrossRef] [PubMed]

20.

T. Grau, R. W. Leipold, R. Conradi, and E. Martin, “Ultrasound control for presumed difficult epidural puncture,” Acta Anaesthesiol. Scand. 45(6), 766–771 (2001). [CrossRef] [PubMed]

21.

S. F. Chen, Y. Chang, and J. C. Wu, “The spatial distribution of macular pigment in humans,” Curr. Eye Res. 23(6), 422–434 (2001). [CrossRef]

22.

F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989). [CrossRef] [PubMed]

23.

M. Sand, T. Gambichler, G. Moussa, F. G. Bechara, D. Sand, P. Altmeyer, and K. Hoffmann, “Evaluation of the epidermal refractive index measured optical coherence tomography,” Skin Res. Technol. 12(2), 114–118 (2006). [CrossRef] [PubMed]

24.

H. Li and S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35(10), 1793–1795 (1996). [CrossRef] [PubMed]

25.

M. Irie, “Evaluation of porcine fat with fiber-optic spectroscopy,” J. Anim. Sci. 77(10), 2680–2684 (1999). [PubMed]

26.

G. A. Mook, O. W. Van Assendelft, and W. G. Zijlstra, “Wavelength dependency of the spectrophotometric determination of blood oxygen saturation,” Clin. Chim. Acta 26(1), 170–173 (1969). [CrossRef] [PubMed]

27.

J. Reichman, “Determination of absorption and scattering coefficients for nonhomogeneous media. 1: Theory,” Appl. Opt. 12(8), 1811–1815 (1973). [CrossRef] [PubMed]

28.

R. L. Longini and R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15(1), 4–10 (1968). [CrossRef]

29.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990). [CrossRef]

30.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. Crawford, and M. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998). [CrossRef]

31.

A. H. Hielscher, J. R. Mourant, and I. J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,” Appl. Opt. 36(1), 125–135 (1997). [CrossRef] [PubMed]

32.

A. K. Popp, M. T. Valentine, P. D. Kaplan, and D. A. Weitz, “Microscopic origin of light scattering in tissue,” Appl. Opt. 42(16), 2871–2880 (2003). [CrossRef] [PubMed]

33.

R. D. Miller, “Miller's Anesthesia,” 7th ed., (Churchill Livingstone, 2009).

34.

H. Ellis, “The anatomy of the epidural space,” Anaesth. Intensive Care Med. 7(11), 402–404 (2006). [CrossRef]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: March 1, 2010
Revised Manuscript: April 13, 2010
Manuscript Accepted: April 19, 2010
Published: May 11, 2010

Virtual Issues
Vol. 5, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Chien-Kun Ting and Yin Chang, "Technique of fiber optics used to localize epidural space in piglets," Opt. Express 18, 11138-11147 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11138


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References

  1. C. K. Ting, M. Y. Tsou, P. T. Chen, K. Y. Chang, M. S. Mandell, K. H. Chan, and Y. Chang, “A new technique to assist epidural needle placement: fiberoptic-guided insertion using two wavelengths,” Anesthesiology 112(5), 1128–1135 (2010). [CrossRef] [PubMed]
  2. P. R. Bromage, “Epidural Analgesia” (W. B. Saunders, 1978).
  3. M. J. Cousins, and B. T. Veering, “Epidural neural block,” in Neural Blockade in Clinical Anesthesia and Management of Pain, 3rd ed., M. J. Cousins, P. O. Bridenbaugh, eds. (Lippincott-Raven, 1998), pp. 243–321.
  4. J. R. Rigg, K. Jamrozik, P. S. Myles, B. S. Silbert, P. J. Peyton, R. W. Parsons, K. S. Collins, and MASTER Anaethesia Trial Study Group, “Epidural anaesthesia and analgesia and outcome of major surgery: a randomized trial,” Lancet 359(9314), 1276–1282 (2002). [CrossRef] [PubMed]
  5. M. Curatolo, A. Orlando, A. M. Zbinden, P. Scaramozzino, and F. S. Venuti, “A multifactorial analysis to explain inadequate surgical analgesia after extradural block,” Br. J. Anaesth. 75(3), 274–281 (1995). [PubMed]
  6. P. H. Pan, T. D. Bogard, and M. D. Owen, “Incidence and characteristics of failures in obstetric neuraxial analgesia and anesthesia: a retrospective analysis of 19,259 deliveries,” Int. J. Obstet. Anesth. 13(4), 227–233 (2004). [CrossRef] [PubMed]
  7. G. R. de Filho, H. P. Gomes, M. H. da Fonseca, J. C. Hoffman, S. G. Pederneiras, and J. H. Garcia, “Predictors of successful neuraxial block: a prospective study,” Eur. J. Anaesthesiol. 19(6), 447–451 (2002). [PubMed]
  8. J. Sprung, D. L. Bourke, J. Grass, J. Hammel, E. Mascha, P. Thomas, and I. Tubin, “Predicting the difficult neuraxial block: a prospective study,” Anesth. Analg. 89(2), 384–389 (1999). [CrossRef] [PubMed]
  9. D. D. Hood and D. M. Dewan, “Anesthetic and obstetric outcome in morbidly obese parturients,” Anesthesiology 79(6), 1210–1218 (1993). [CrossRef] [PubMed]
  10. C. Konrad, G. Schüpfer, M. Wietlisbach, and H. Gerber, “Learning manual skills in anesthesiology: is there a recommended number of cases for anesthetic procedures?” Anesth. Analg. 86(3), 635–639 (1998). [CrossRef] [PubMed]
  11. A. M. Dogliotti, “Segmental peridural spinal anesthesia: a new method of block anesthesia,” Am. J. Surg. 20, 107–118 (1993). [CrossRef]
  12. T. Nagaro, T. Yorozuya, M. Kamei, N. Kii, T. Arai, and S. Abe, “Fluoroscopically guided epidural block in the thoracic and lumbar regions,” Reg. Anesth. Pain Med. 31(5), 409–416 (2006). [PubMed]
  13. B. C. Tsui, P. Tarkkila, S. Gupta, and R. Kearney, “Confirmation of caudal needle placement using nerve stimulation,” Anesthesiology 91(2), 374–378 (1999). [CrossRef] [PubMed]
  14. T. J. Lechner, M. G. van Wijk, A. J. Maas, F. R. van Dorsten, R. A. Drost, C. J. Langenberg, L. J. Teunissen, P. H. Cornelissen, and J. van Niekerk, “Clinical results with the acoustic puncture assist device, a new acoustic device to identify the epidural space,” Anesth. Analg. 96(4), 1183–1187 (2003). [CrossRef] [PubMed]
  15. M. P. Lewis, P. Thomas, L. F. Wilson, and R. C. Mulholland, “The ‘whoosh’ test,” Anaesthesia 47(1), 57–58 (1992). [CrossRef] [PubMed]
  16. B. C. Tsui, C. Guenther, D. Emery, and B. Finucane, “Determining epidural catheter location using nerve stimulation with radiological confirmation,” Reg. Anesth. Pain Med. 25(3), 306–309 (2000). [PubMed]
  17. M. K. Karmakar, X. Li, A. M. Ho, W. H. Kwok, and P. T. Chui, “Real-time ultrasound-guided paramedian epidural access: evaluation of a novel in-plane technique,” Br. J. Anaesth. 102(6), 845–854 (2009). [CrossRef] [PubMed]
  18. Ghia Jn, M. Arora Sk, Castillo, and Mukherji Sk, “Confirmation of location of epidural catheters by epidural pressure waveform and computed tomography cathetergram,” Reg. Anesth. Pain Med. 26(4), 337–341 (2001). [PubMed]
  19. P. H. Lennox, H. S. Umedaly, R. P. Grant, S. A. White, B. G. Fitzmaurice, and K. G. Evans, “A pulsatile pressure waveform is a sensitive marker for confirming the location of the thoracic epidural space,” J. Cardiothorac. Vasc. Anesth. 20(5), 659–663 (2006). [CrossRef] [PubMed]
  20. T. Grau, R. W. Leipold, R. Conradi, and E. Martin, “Ultrasound control for presumed difficult epidural puncture,” Acta Anaesthesiol. Scand. 45(6), 766–771 (2001). [CrossRef] [PubMed]
  21. S. F. Chen, Y. Chang, and J. C. Wu, “The spatial distribution of macular pigment in humans,” Curr. Eye Res. 23(6), 422–434 (2001). [CrossRef]
  22. F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989). [CrossRef] [PubMed]
  23. M. Sand, T. Gambichler, G. Moussa, F. G. Bechara, D. Sand, P. Altmeyer, and K. Hoffmann, “Evaluation of the epidermal refractive index measured optical coherence tomography,” Skin Res. Technol. 12(2), 114–118 (2006). [CrossRef] [PubMed]
  24. H. Li and S. Xie, “Measurement method of the refractive index of biotissue by total internal reflection,” Appl. Opt. 35(10), 1793–1795 (1996). [CrossRef] [PubMed]
  25. M. Irie, “Evaluation of porcine fat with fiber-optic spectroscopy,” J. Anim. Sci. 77(10), 2680–2684 (1999). [PubMed]
  26. G. A. Mook, O. W. Van Assendelft, and W. G. Zijlstra, “Wavelength dependency of the spectrophotometric determination of blood oxygen saturation,” Clin. Chim. Acta 26(1), 170–173 (1969). [CrossRef] [PubMed]
  27. J. Reichman, “Determination of absorption and scattering coefficients for nonhomogeneous media. 1: Theory,” Appl. Opt. 12(8), 1811–1815 (1973). [CrossRef] [PubMed]
  28. R. L. Longini and R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15(1), 4–10 (1968). [CrossRef]
  29. W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990). [CrossRef]
  30. L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. Crawford, and M. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998). [CrossRef]
  31. A. H. Hielscher, J. R. Mourant, and I. J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,” Appl. Opt. 36(1), 125–135 (1997). [CrossRef] [PubMed]
  32. A. K. Popp, M. T. Valentine, P. D. Kaplan, and D. A. Weitz, “Microscopic origin of light scattering in tissue,” Appl. Opt. 42(16), 2871–2880 (2003). [CrossRef] [PubMed]
  33. R. D. Miller, “Miller's Anesthesia,” 7th ed., (Churchill Livingstone, 2009).
  34. H. Ellis, “The anatomy of the epidural space,” Anaesth. Intensive Care Med. 7(11), 402–404 (2006). [CrossRef]

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