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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 19 — Sep. 20, 2004
  • pp: 4596–4601
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Particle aggregation monitoring by speckle size measurement; application to blood platelets aggregation

Y. Piederriere, J. Le Meur, J. Cariou, J.F. Abgrall, and M.T. Blouch  »View Author Affiliations


Optics Express, Vol. 12, Issue 19, pp. 4596-4601 (2004)
http://dx.doi.org/10.1364/OPEX.12.004596


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Abstract

We report on a new method based on speckle size analysis and devoted to particle aggregation measurements. The experimental measurements give the speckle size variation during a salt aggregation process of polystyrene microspheres. The measurements are taken at a fixed monomer concentration, varying the salt concentration. Moreover, we applied this technique to follow blood platelet aggregation, usually monitored with a visible light transmittance photometer (aggregometer). Aggregation process was induced by ADP (adenosine diphosphate) addition, then we measured the speckle size variation versus time at two different ADP concentrations.

© 2004 Optical Society of America

1. Introduction

Numerous works about colloidal aggregation were produced in the last few years. These researches used different techniques as low angle static light scattering. This well-known method is particularly interesting and gives information about reaction kinetics (associated evolution of clusters sizes) and fractal morphology of the aggregates [1

1. J.P. Wilcoxon, J.E. Martin, and D.W. Shaefer, “Aggregation in colloidal gold,” Phys. Rev. A 39, 2675–2688 (1989). [CrossRef] [PubMed]

,2

2. M. Carpinetti, F. Ferri, M. Giglio, E. Paganini, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990). [CrossRef]

]. Dynamics Light Scattering (DLS) is another interesting method because of its ability to provide data on the size and shape of particles [3

3. Y. Georgalis, E.B. Starikov, B. Hollenbach, R. Lurz, Eberhard Scherzinger, W. Sger, H. Lehrach, and E. Wanker, “Huntingtin aggregation monitored by dynamic light scattering,” Proc. Natl. Acad. Sci. 95, 6118–6121 (1998). [CrossRef] [PubMed]

,4

4. D. Majolino, F. Mallamace, P. Migliardo, N. Micali, and C. Vasi, “Elastic and quasielastic light-scattering studies of the aggregation phenomena in water solutions of polystyrene particles,” Phys. Rev. A 40, 4665–4674 (1989). [CrossRef] [PubMed]

] from dynamical speckle analysis [5

5. D.A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A 14, 192–215 (1997). [CrossRef]

].

Speckle or laser light-induced granularity can be observed either in free space (objective speckle) or on the image plane of a diffuse object illuminated with a coherent source (subjective speckle) [6

6. J.W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser speckle and related phenomena, Vol.9 in series Topics in Applied Physics, J.C. Dainty, Ed., (Springer-Verlag, Berlin, Heidelberg New York Tokyo, 1984).

]. The speckle effect through a coherent light source-illuminated medium results from random fluctuations of refractive index. Photons travel along random optical paths; the random dephasing of associated wavelets produce random interferences that induce a statistical distribution of light intensity.

Speckle parameters (size, contrast, intensity, polarization,…) can bring information on scattering media. For example, spatial characteristics such as the speckle size can be used to measure the roughness of surfaces [7

7. P. Lehmann, “Surface-roughness measurement based on the intensity correlation function of scattered light under speckle-pattern illumination,” Appl. Opt. 38, 1144–1152 (1999). [CrossRef]

,8

8. G. Da Costa and J. Ferrari, “Anisotropic speckle patterns in the light scattered by rough cylindrical surfaces,” Appl. Opt. 36, 5231–5237 (1997). [CrossRef] [PubMed]

,9

9. R. Berlasso, F. Perez Quintian, M.A. Rebollo, C.A. Raffo, and N.G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. 39, 5811–5819 (2000). [CrossRef]

] or to determine the thickness of a Teflon plate [10

10. A. Sadhwani, K.T. Schomaker, G.J. Tearney, and N.S. Nishioka, “Determination of Teflon thickness with laser speckle. I. Potential for burn depth diagnosis,” Appl. Opt. 35, 5727–5735 (1996). [CrossRef] [PubMed]

].

The study reported here was aimed at following the kinetics of aggregation process from speckle size measurements.

Thus, we first investigated polystyrene-microsphere aggregation induced by different salt additions and characterized the two limiting regimes of aggregation kinetics [2

2. M. Carpinetti, F. Ferri, M. Giglio, E. Paganini, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990). [CrossRef]

]: the slow aggregation regime that it is named Reaction-Limited Cluster Aggregation (RLCA) and the fast aggregation regime that it is named Diffusion Limited Cluster Aggregation (DLCA). The sticking probability between particles determines the behavior as follows: a sticking probability equal to one leads to the DLCA, whereas values noticeably smaller than 1 give rise to RLCA. The chosen salt concentration assures fast or slow aggregation.

Secondly we realized a biomedical application for blood platelet aggregation monitoring. Platelet aggregation is of paramount importance to stop a hemorrhage after a vessel injury. So the clinical evaluation of the status of aggregation platelet is necessary in the diagnosis of imbalance. A visible light transmittance photometer (aggregometer) is classically used to follow the aggregation process because of the changes induced in scattering characteristics, and then in transmitted light [11

11. Y. Ozaki, “Measurement of platelet aggregation and attempts for standardization,” Sysmex J. Int. 8, 15–22 (1998).

]. Nevertheless this method can be limited by the photometer geometry or multiple scattering [12

12. P. Latimer, “Blood platelet aggrgometer: predicted effects of aggregation, photometer geometry, and multiple scattering,” Appl. Opt. 22, 1136–1143 (1983). [CrossRef] [PubMed]

]. This led us to propose, here, a new method based on speckle size measurement to assess the aggregation process.

2. Methodology and speckle size measurement

During an aggregation process, the two parameters N and d vary, and then both produce an increase of the speckle size: the sticking between particle induces an increase of d and a decrease of N.

To estimate the speckle size, we calculated the normalized autocovariance function of the intensity speckle pattern obtained in the observation plane (x,y). This function corresponds to the normalized autocorrelation function of the intensity; it has a zero base and its width provides a reasonable measurement of the “average width” of a speckle [6

6. J.W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser speckle and related phenomena, Vol.9 in series Topics in Applied Physics, J.C. Dainty, Ed., (Springer-Verlag, Berlin, Heidelberg New York Tokyo, 1984).

]. If I (x 1, y 1) and I(x 2,x 2)are the intensities of two points in the observation plane (x,y), the intensity autocorrelation function is defined by Eq. (1) [6

6. J.W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser speckle and related phenomena, Vol.9 in series Topics in Applied Physics, J.C. Dainty, Ed., (Springer-Verlag, Berlin, Heidelberg New York Tokyo, 1984).

]:

RI(Δx,Δy)=Ix1y1Ix2y2
(1)

where Δx = x 1 - x 2 and Δy = y 1-y 2. ⟨ ⟩ corresponds to a spatial average. If x 2 = 0, y 2 = 0, x 1 = x and y 1 = y, we can write:

RI(Δx,Δy)=RIxy
(2)

The normalized autocovariance function of the intensity, cI (x,y), is given by Eq. (3):

cIxy=RIxyIxy2Ixy2Ixy2
(3)

As implied by the Wiener-Khintchine theorem, the autocorrelation function of the intensity is given by the Inverse Fourier Transform (FT -1) of the Power Spectral Density (PSD) of the intensity:

PSDIυxυy=FT[Ixy]2
(4)

FT is the Fourier Transform.

cI (x, y) calculated from the intensity distribution measured of the speckle is:

cIxy=FT1[FT[Ixy]2]Ixy2Ixy2Ixy2
(5)

cI (x, 0) and cI (0, y) are the horizontal and the vertical profile of cI (x, y), respectively. Let us term dx the width of cI (x,0) so that cI (dx/2,0) = 0.5 and dy the width of cI(0,y) such as cI (0, dy/2) = 0.5.

Figure 1 illustrates the experimental set up. The 7-mW HeNe laser used emits a 1.12-mm-wide polarized (linear) beam at I0/e2 with I0 being the maximum laser intensity, at the 632.8 nm wavelength with a coherence length of about 20 cm. The light intensity is monitored by a half wave plate L associated to a polarizer P1. The length L of the fluid sample is 1 cm.

Fig. 1. Experimental set-up (top view).

A CCD camera records the medium-produced speckle field. The CCD imager contains 788×268 pixels that are 8 μm×8 μm in size. When a newly acquired image is digitized, the analog-to-digital converter assigns an intensity value (gray level) in the range of 1 to 1024 (10-bit precision).

To record the speckle, one should be aware of the Brownian motion of particles in the medium. These movement induce a random agitation of the speckle (“boiling speckle”). Consequently, the image acquisition time must be very short. So, the time exposure of our CCD camera could vary from 60.10-3 to 10-4 s. However, in order to keep a correct signal-to-noise ratio, in our experiments image acquisition took 0.001 s.

Another consideration of importance in recording the speckle data is the speckle size on the CCD array: the speckles must be large as compared to the pixel size so as to resolve variations in speckle intensity [15

15. Terri L. Alexander, James E. Harvey, and Arthur R. Weeks, “Average speckle size as a function of intensity threshold level: comparison of experimental measurements with theory,” Appl. Opt. 33, 8240–8250 (1994). [CrossRef] [PubMed]

]. Moreover, each image needs to contain many speckles for meaningful statistical evaluation. These conditions were met by choosing the distance D (D = 36 cm) between the sample and the CCD camera.

3. Polystyrene microsphere aggregation

We will first illustrate on polystyrene microsphere aggregation how this process can be monitored by speckle size measurements. The polystyrene microspheres used had a diameter of 0.535 μm and were from Polyscience Inc.; they were provided to us in a deionized water solution and their number per cubed meter, N0, is known. The undiluted solution contains N 0 =3.147 * 1017 m-3. By dilution in deionized water, we adjusted the parameter N and so the scattering coefficient. μs determined by Beer-Lambert Law application: μs = 6.23c, where c is the concentration of the initial solution. Furthermore, we employed deionized water to avoid the possible effect of particle aggregation due to electrostatic interaction. The refractive indices were 1.59 and 1.33 for the spheres and medium, respectively.

As the scattering coefficient must be high enough to get a small initial speckle size and allow it to greatly vary during aggregation. It is worth recalling that the speckle size decreases when the scattering coefficient is increasing. So the density of particles was chosen so that μs = 4 cm-1, and the initial speckle size measured about 46 μm. For our experimental configuration, the speckle size cannot exceed about 220 μm. dy 220 μm when μs 0 cm-1 and this speckle size limit depends on the intensity distribution of the laser beam size [13

13. Y. Piederriere, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express 12, 176–188 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176 [CrossRef] [PubMed]

]. The salt used to induce aggregation was MgCl2. Figure 2 illustrates dy evolution versus the time, t, for several salt concentrations.

Fig.2. dy versus t during aggregation process at several salt concentrations with the respective linear fitting curves:
[MgCl2]=3mM: dy = 0.9t + 46.5
[MgCl2]=45mM: dy = 1.6t + 64.1
[MgCl2]=300mM: dy = 0.3t + 127.2

Finally these curves show that speckle size measurement can allow one to characterize an aggregation process and distinguish between a RLCA and a DLCA (weak and strong salt concentrations, respectively).

4. Blood platelets aggregation

In this section we will apply such a speckle size measurement to the monitoring of a blood platelet aggregation process. The samples, platelet suspensions in plasma, were prepared from whole blood after centrifugation to remove the larger red and white cells. To induce the aggregation, we added ADP (ADP denotes adenosine diphosphate) to the samples previously heated at 37°C. The measured scattering coefficient was 11 cm-1 and the speckle size before aggregation dy = 100 μm. Large diffusers induce a large speckle size [13

13. Y. Piederriere, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express 12, 176–188 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176 [CrossRef] [PubMed]

], so compared to the polystyrene microsphere, dy is higher even though μs is higher (platelet size is about 4 μm and polystyrene microsphere size is 0.535 μm).

Figure 3 depicts dy versus t at two ADP concentrations: 25 μM and 10 μM.

It shows that, at the higher ADP concentration, the speckle size is strongly increased for one minute after ADP addition; this corresponds to a fast aggregation (elevation of dy from 100 to 135 μm). Afterwards, one should note the slow increase of the speckle size concomitant with the slowing down of the aggregation process.

At the weaker ADP concentration, despite the first fast aggregation the speckle size extends only to 111 μm; this goes along with the formation of smaller aggregate. Moreover, after the first minute, there is a reduction of the speckle size followed with a stabilization at 107 μm after t = 1.5 min.

So, the obtained curves show clearly different behavior according to the ADP concentration.

Fig.3. dy versus the time t during platelet aggregation process obtained for two ADP concentration

5. Conclusion

In this study we experimentally showed that aggregation process can be monitored by speckle size measurement because of the changes undergone by scatters-size and -density. So such a speckle size measurement allowed us to characterize the fast and the slow aggregation processes, respectively denoted DLCA and RLCA, during a salt-induced aggregation of polystyrene microspheres.

Our method was also applied to the monitoring of blood platelet aggregation further to ADP addition. Among the two ADP concentrations used, the higher one permitted us to demonstrate that aggregation was fast during the first minute after ADP addition, and then slow. The lower ADP concentration induced a different aggregation; it produced smaller aggregates before a stabilization of the process.

Aggregometers are currently used in medicine to monitor platelet aggregation, but according to some investigations like the ones by P. Latimer [12

12. P. Latimer, “Blood platelet aggrgometer: predicted effects of aggregation, photometer geometry, and multiple scattering,” Appl. Opt. 22, 1136–1143 (1983). [CrossRef] [PubMed]

] the effects of the photometers geometry (angle of the incident laser beam, detector size) and multiple scattering may spoil the analysis. Thus, speckle measurement may be an alternative method.

Finally the real-time, cheap method presented here sounds very promising for getting data on blood platelet aggregation and in general on the aggregate systems.

References and links

1.

J.P. Wilcoxon, J.E. Martin, and D.W. Shaefer, “Aggregation in colloidal gold,” Phys. Rev. A 39, 2675–2688 (1989). [CrossRef] [PubMed]

2.

M. Carpinetti, F. Ferri, M. Giglio, E. Paganini, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990). [CrossRef]

3.

Y. Georgalis, E.B. Starikov, B. Hollenbach, R. Lurz, Eberhard Scherzinger, W. Sger, H. Lehrach, and E. Wanker, “Huntingtin aggregation monitored by dynamic light scattering,” Proc. Natl. Acad. Sci. 95, 6118–6121 (1998). [CrossRef] [PubMed]

4.

D. Majolino, F. Mallamace, P. Migliardo, N. Micali, and C. Vasi, “Elastic and quasielastic light-scattering studies of the aggregation phenomena in water solutions of polystyrene particles,” Phys. Rev. A 40, 4665–4674 (1989). [CrossRef] [PubMed]

5.

D.A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A 14, 192–215 (1997). [CrossRef]

6.

J.W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser speckle and related phenomena, Vol.9 in series Topics in Applied Physics, J.C. Dainty, Ed., (Springer-Verlag, Berlin, Heidelberg New York Tokyo, 1984).

7.

P. Lehmann, “Surface-roughness measurement based on the intensity correlation function of scattered light under speckle-pattern illumination,” Appl. Opt. 38, 1144–1152 (1999). [CrossRef]

8.

G. Da Costa and J. Ferrari, “Anisotropic speckle patterns in the light scattered by rough cylindrical surfaces,” Appl. Opt. 36, 5231–5237 (1997). [CrossRef] [PubMed]

9.

R. Berlasso, F. Perez Quintian, M.A. Rebollo, C.A. Raffo, and N.G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. 39, 5811–5819 (2000). [CrossRef]

10.

A. Sadhwani, K.T. Schomaker, G.J. Tearney, and N.S. Nishioka, “Determination of Teflon thickness with laser speckle. I. Potential for burn depth diagnosis,” Appl. Opt. 35, 5727–5735 (1996). [CrossRef] [PubMed]

11.

Y. Ozaki, “Measurement of platelet aggregation and attempts for standardization,” Sysmex J. Int. 8, 15–22 (1998).

12.

P. Latimer, “Blood platelet aggrgometer: predicted effects of aggregation, photometer geometry, and multiple scattering,” Appl. Opt. 22, 1136–1143 (1983). [CrossRef] [PubMed]

13.

Y. Piederriere, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express 12, 176–188 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176 [CrossRef] [PubMed]

14.

H.C. Van de Hulst, Light scattering by small particles (New York, Dover, 1981).

15.

Terri L. Alexander, James E. Harvey, and Arthur R. Weeks, “Average speckle size as a function of intensity threshold level: comparison of experimental measurements with theory,” Appl. Opt. 33, 8240–8250 (1994). [CrossRef] [PubMed]

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation
(170.1470) Medical optics and biotechnology : Blood or tissue constituent monitoring
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(290.5850) Scattering : Scattering, particles

ToC Category:
Research Papers

History
Original Manuscript: July 26, 2004
Revised Manuscript: August 23, 2004
Published: September 20, 2004

Citation
Yann Piederrière, J. Le Meur, J. Cariou, J. Abgrall, and M. Blouch, "Particle aggregation monitoring by speckle size measurement; application to blood platelets aggregation," Opt. Express 12, 4596-4601 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-19-4596


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References

  1. J.P. Wilcoxon, J.E. Martin, D.W. Shaefer, �??Aggregation in colloidal gold,�?? Phys. Rev. A 39, 2675-2688 (1989). [CrossRef] [PubMed]
  2. M. Carpinetti, F. Ferri, M. Giglio, E. Paganini, U. Perini, �??Salt-induced fast aggregation of polystyrene latex,�?? Phys. Rev. A 42, 7347-7354 (1990). [CrossRef]
  3. Y. Georgalis, E.B. Starikov, B. Hollenbach, R. Lurz, Eberhard Scherzinger, W. Sger, H. Lehrach, E. Wanker, �??Huntingtin aggregation monitored by dynamic light scattering,�?? Proc. Natl. Acad. Sci. 95, 6118-6121 (1998). [CrossRef] [PubMed]
  4. D. Majolino, F. Mallamace, P. Migliardo, N. Micali, C. Vasi, �??Elastic and quasielastic light-scattering studies of the aggregation phenomena in water solutions of polystyrene particles,�?? Phys. Rev. A 40, 4665-4674 (1989). [CrossRef] [PubMed]
  5. D.A. Boas and A. G. Yodh, �??Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,�?? J. Opt. Soc. Am. A 14, 192-215 (1997). [CrossRef]
  6. J.W. Goodman, �??Statistical Properties of Laser Speckle Patterns,�?? in Laser speckle and related phenomena, Vol. 9 in series Topics in Applied Physics, J.C. Dainty, Ed., (Springer-Verlag, Berlin, Heidelberg New York Tokyo, 1984).
  7. P. Lehmann, �??Surface-roughness measurement based on the intensity correlation function of scattered light under speckle-pattern illumination,�?? Appl. Opt. 38, 1144-1152 (1999). [CrossRef]
  8. G. Da Costa and J. Ferrari, �??Anisotropic speckle patterns in the light scattered by rough cylindrical surfaces,�?? Appl. Opt. 36, 5231-5237 (1997). [CrossRef] [PubMed]
  9. R. Berlasso, F. Perez Quintian, M.A. Rebollo, C.A. Raffo and N.G. Gaggioli, �??Study of speckle size of light scattered from cylindrical rough surfaces,�?? Appl. Opt. 39, 5811-5819 (2000). [CrossRef]
  10. A. Sadhwani, K.T. Schomaker, G.J. Tearney and N.S. Nishioka, �??Determination of Teflon thickness with laser speckle. I. Potential for burn depth diagnosis,�?? Appl. Opt. 35, 5727-5735 (1996). [CrossRef] [PubMed]
  11. Y. Ozaki, �??Measurement of platelet aggregation and attempts for standardization,�?? Sysmex J. Int. 8, 15-22 (1998).
  12. P. Latimer, �??Blood platelet aggrgometer: predicted effects of aggregation, photometer geometry, and multiple scattering,�?? Appl. Opt. 22, 1136-1143 (1983). [CrossRef] [PubMed]
  13. Y. Piederriere, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, J. Lotrian, �??Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,�?? Opt. Express 12, 176-188 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176</a> [CrossRef] [PubMed]
  14. H.C. Van de Hulst, Light scattering by small particles (New York, Dover, 1981).
  15. Terri L. Alexander, James E. Harvey, and Arthur R. Weeks, �??Average speckle size as a function of intensity threshold level: comparison of experimental measurements with theory,�?? Appl. Opt. 33, 8240-8250 (1994). [CrossRef] [PubMed]

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