Universal temperature-dependent normalized

0 downloads 0 Views 910KB Size Report
We studied the temperature dependence of Gruneisen parameter in blood and ... method is based on high temperature sensitivity of the Gruneisen parameter in.
PROGRESS IN BIOMEDICAL OPTICS AND IMAGING Vol. 16 No. 21

Photons Plus Ultrasound: Imaging and Sensing 2015 Alexander A. Oraevsky Lihong V. Wang Editors 8–10 February 2015 San Francisco, California, United States Sponsored by SPIE Cosponsored by Seno Medical Instruments, Inc. (United States) Published by SPIE

Volume 9323

Proceedings of SPIE, 1605-7422, V. 9323 SPIE is an international society advancing an interdisciplinary approach to the science and application of light.

Photons Plus Ultrasound: Imaging and Sensing 2015, edited by Alexander A. Oraevsky, Lihong V. Wang Proc. of SPIE Vol. 9323, 932301 · © 2015 SPIE · CCC code: 1605-7422/15/$18 doi: 10.1117/12.2192869 Proc. of SPIE Vol. 9323 932301-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/27/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

Universal temperature-dependent normalized optoacoustic response of blood Elena V. Petrova, Anton Liopo, Alexander A. Oraevsky, Sergey A. Ermilov

TomoWave Laboratories Inc., 6550 Mapleridge St., Suite 124, Houston, TX 77081, USA ABSTRACT We found and interpreted the universal temperature-dependent optoacoustic (photoacoustic) response (ThOR) in blood; the normalized ThOR is invariant with respect to hematocrit at the hemoglobin’s isosbestic point. The unique compartmentalization of hemoglobin, the primary optical absorber at 805 nm, inside red blood cells (RBCs) explains the effect. We studied the temperature dependence of Gruneisen parameter in blood and aqueous solutions of hemoglobin and for the first time experimentally observed transition through the zero optoacoustic response at temperature T0, which was proved to be consistent for various blood samples. On the other hand, the hemoglobin solutions demonstrated linear concentration function of the temperature T 0. When this function was extrapolated to the average hemoglobin concentration inside erythrocytes, the temperature T 0 was found equivalent to that measured in whole and diluted blood. The obtained universal curve of blood ThOR was validated in both transparent and light scattering media. The discovered universal optoacoustic temperature dependent blood response provides foundation for future development of non-invasive in vivo temperature monitoring in vascularized tissues and blood vessels. Keywords: optoacoustic imaging, photoacoustic tomography, ThOR, Gruneisen parameter, hemoglobin, red blood cell, non-invasive temperature monitoring.

1. INTRODUCTION Real-time non-invasive temperature monitoring in live tissue is a challenging problem in thermal treatments of cancer1-7. Due to significant thermal sensitivity of the photoacoustic effect in live tissues, optoacoustic (OA) imaging technology has a great potential of becoming a competitive modality for non-invasive temperature measurements during hypo- and hyperthermal therapies8. However, variations of tissue composition and its complex structure significantly complicate calibration of in vivo OA response as a function of temperature. The optoacoustic thermometry method is based on high temperature sensitivity of the Gruneisen parameter in biological tissues. OA signal amplitude VOA can be expressed as9: VOA ΓaF, where Γ – thermoelastic efficiency or Gruneisen parameter of light-absorbing material, a – optical absorption coefficient, F – local optical fluence. Gruneisen parameter integrates three components9: volumetric thermal expansion (β), speed of sound for longitudinal waves (V), and specific (per mass) heat capacity at constant pressure (Cp): Γ = βV2/Cp. All the components of Gruneisen parameter are generally temperature dependent, making Γ, and the whole optoacoustic response temperature dependent as well. It was shown10 that significant temperature dependence of the Gruneisen parameter for water is mostly caused by the thermal expansion that is changing with heating or cooling. Our recent studies revealed that temperature-dependent optoacoustic response (ThOR) of aqueous solutions transits through its nil point at the temperature of zero thermal expansion or maximum density11. The existence of a unique temperature of nil ThOR allows normalization of the calibration curve with respect to optical fluence and absorbance that can be reversed for use in thermometry applications. We proposed a general equation11 for normalized ThOR that includes two material-specific parameters T0 and ΔTmax allowing experimental image data to be fitted with a second order polynomial function3,5:

Photons Plus Ultrasound: Imaging and Sensing 2015, edited by Alexander A. Oraevsky, Lihong V. Wang Proc. of SPIE Vol. 9323, 93231Y · © 2015 SPIE · CCC code: 1605-7422/15/$18 doi: 10.1117/12.2083594 Proc. of SPIE Vol. 9323 93231Y-1

̅̅̅̅ = − 4∆𝑇𝑚𝑎𝑥3 (𝑇 − 𝑇0 )(𝑇 − 𝑇1 ) + 𝑂𝐴 (𝑇 ) 1 −𝑇0

𝑇−𝑇0 𝑇1 −𝑇0

.

̅̅̅̅ is the normalized optoacoustic intensity; T – temperature (C), T1 –normalization temperature,(𝑂𝐴 ̅̅̅̅(𝑇1 ) = Where 𝑂𝐴 1). In biological applications, it is prudent to select T1 as a normal physiological temperature, for humans T1 = 37C; T0 is the temperature of zero optoacoustic response; Tmax is a maximum thermal nonlinearity of ThOR in the temperature range [T0 T1]. If Tmax = 0, the function becomes linear, identical to the one described in our previous studies of the aqueous cupric sulfate in the smaller temperature range. 12,13 Recently, we showed that hemoglobin has similar impact on the temperature of the maximum density as ionic salts11. In the case of hemoglobin compartmentalized inside red blood cells, the effect could be further augmented by other components of the erythrocyte’s cytoplasm. Reduced molecular mobility of water depresses the maximum solution density, and therefore also the point of zero optoacoustic response, towards lower temperatures, the phenomenon known as the Despretz’s law.14 This effect is also similar to lowering of freezing temperatures of solutions in comparison with pure liquids—the cryoscopic effect.15 In this work, we looked for a method of calibration for non-invasive temperature mapping in live tissues considering blood to be a dominant endogenous optical absorber during OA imaging. We measured ThOR of whole and diluted blood to simulate variations in hematocrit. Laser wavelength 805 nm was used to confine temperaturedependent absorbance of hemoglobin. The found results demonstrate that the blood’s ThOR could be used for accurate calibration and non-invasive temperature monitoring in various biomedical applications.

2. MATERIALS AND METHODS The experimental setup allows optoacoustic 2D-imaging of liquid samples under controlled decrease of ambient temperature. The setup (Fig.1a) utilizes a 128-channel real-time (up to 10 frames per second, 1536 samples/channel, 40 MHz sampling rate) two-dimensional laser optoacoustic imaging system (LOIS, TomoWave Laboratories, Houston TX) with a linear ultrasound probe, which was previously developed for breast cancer imaging16. Ti-Sapphire output of the laser unit (Spectra Wave, TomoWave Laboratories, Houston, TX) was tuned to 805 nm. The system produced 6 ns, 16 mJ per pulse laser radiation with pulse repetition rate of 10 Hz. Two optical fiber bundles were used to deliver light overlapping in the imaging plane at the location of the samples. Apertures of the rectangular outputs were 1.5×50 mm2 each and produced cumulative laser fluence of 2mJ/cm2 at a distance of 20 mm from the ultrasound probe. The probe and fiber optic outputs were hermetically sealed to enable operation in liquid environment.

a

Ti:Sapphire laser

(1)

Optical fiber

Sync

(2)

128 ch DAQ

Temperature reading

II

(2)

2D- ultrasound probe Thermocouples

(3)

-+ Phantom Thermostat solution Cooling system w /temperature control

(a)

(b)

Figure 1: Schematics of the experimental setup for 2D imaging of temperature-dependent OA response (a). Linear ultrasound probe – 1, light bar illuminators – 2, and multi-tube phantom frame with tubes oriented orthogonally to the imaging plane – 3 are placed into a tank with acoustically coupling liquid (b).

Proc. of SPIE Vol. 9323 93231Y-2

Controlled cooling was achieved by placing the phantom/probe assembly into a chest freezer (CF-1510, Avanti, Miami, FL) set at a temperature of -30C. The temperature of samples was measured and logged by digital thermometer (HH806AU, Omega, Stamford, CT) with precision of 0.1C. A 1.5 L tank with the test unit was filled with coupling solution and was subject to 0.2C/min cooling rate. Our test unit (Fig.1b) contained up to 7 tubes filled with sample solutions. Samples were located at two levels of depth – 15 and 22 mm from the linear ultrasound probe and, therefore, experienced different laser fluence. The tubes were positioned orthogonally to the imaging plane, so that their cross sections could be observed on reconstructed optoacoustic images. PTFE tubes (Sub-Lite-Wall Tubing, Zeus, Orangeburg, SC) of inner diameter 0.635 mm and wall thickness 0.051 mm were filled with studied solutions and blood. The studied samples of porcine blood were obtained from a local slaughterhouse on the day of experiments. Sodium heparin (Alfa Aesar, Ward Hill, MA) solution of 0.1 mL of 2000 USP in phosphate buffered saline (PBS) at pH 7.4 (Sigma-Aldrich, St. Louis, MO) was used to prevent coagulation. The same PBS was used to dilute samples of whole blood. The acoustic coupling medium consisted of NaCl 20wt%. We acquired optoacoustic images of the samples every 30 s while temperature was slowly decreased. Reconstructed optoacoustic images had total size of 5050 mm2. Each frame was reconstructed using 2D filtered back projection of measured integrated signals. To increase SNR and remove low-frequency optoacoustic artifacts created by light distribution within background, we performed digital post processing of optoacoustic signals with zero-phase infinite impulse response band pass filter (1-5 MHz sixth order Butterworth) using built-in filtfilt function in Matlab (Mathworks, Natick, MA). The filter was preferred over its second order counterpart due to better artifact removal performance. It also bested its tenth order analogue due to smaller amplitude of introduced post-filter ringing. As optoacoustic signals generated by tubes of 0.635 mm diameter had the main lobe of their spectrum within the bandwidth of utilized probe (1.5-6 MHz at -6dB), the detected waveforms preserved their original N-shaped features, and it was not necessary to perform deconvolution of the probe’s impulse response. To evaluate ThOR of the blood samples we measured median image intensity in a manually selected region of interest (ROI) containing the image of a particular tube. Earlier we demonstrated that such method enables highprecision quantification of OA response13. We reconstructed OA images taking into account temperature changes of speed of sound in the coupling liquid. The temperature dependence of speed of sound in silicone lens was neglected based on measurements performed in separate studies. Spectrophotometer (Evolution 201, Thermo Scientific, Waltham, MA) was employed to measure absorbance spectra of hemoglobin solutions.

3. RESULTS Temperature dependent optoacoustic response (ThOR) was measured in blood samples before and after dilution simulating four erythrocyte volume fractions (hematocrit) and found to be identical after normalization at 37C (Fig. 2a-b). Testing whole blood samples, we were able to decrease their temperatures up to -15C without spontaneous freezing and found that around -13C OA images of the samples inverted their contrast from positive to negative (Fig. 2b). Opposite to blood, hemoglobin’s ThOR shows concentration dependence (Fig.2c). The temperature T0 of the zero Gruneisen parameter is getting depressed for higher concentrations (Fig. 2d). When extrapolated to the concentration of hemoglobin inside RBCs (5.5 mM), it results in T0 = -12.3C, which is equal to T0 measured in blood samples within the experimental error. While concentration dependence of ThOR in solutions of hemoglobin appears to be in controversy with concentration independence of blood’s ThOR, both agree when considering a microenvironment of a single erythrocyte. It is known, that RBC’s membrane is sensitive to temperature changes17,18. It can also be disrupted under osmotic stress18. Therefore, we validated the integrity of erythrocytes during our cooling experiments. To evaluate potential RBCs’ damage induced by deep cooling and, in addition, nanosecond laser illumination we measured optical absorption spectra of supernatant blood plasma before and after ThOR measurements. If erythrocyte membrane is injured, release of hemoglobin, which is compartmentalized within RBCs, affects absorbance spectrum of plasma17. We analyzed three types of samples: control (sample remained at room temperature), deep cooling only, and deep cooling accompanied by laser illumination. The cooling was applied at the same rate 0.2C/min as in the ThOR measurements. Fig.3a shows photographs of the vials: (1) a control sample of blood; (2) blood after cooling to -16C under continuous Q-switched 805 nm laser illumination. The erythrocyte suspension on the bottom is separated from the plasma on the top. Supernatant is visually clear in both cases; its absorbance spectra is shown in Fig.3b. Within the experimental error, the spectra of all the samples were identical before and after the treatment that confirms the integrity of RBC membranes during our ThOR evaluation experiments.

Proc. of SPIE Vol. 9323 93231Y-3

Blood 100% 100% 75% 50% 25%

-16 -8

0 8 16 24 32 Temperature [oC]

40

Normalized OA image intensity

OA image intensity [a.u.]

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.02

1.0 0.8 0.6 0.4 0.2 -0.2

-16 -8

Hb (1.860 mM) Hb (1.085 mM) Hb (0.186 mM)

0.6

o

0.4 0.2

T0 is depressed

0.0 -0.2 -10

0

0 8 16 24 32 40 Temperature [oC] (b)

T0 ( C)

Norm. OA image intensity

0.8

T0

0.0

(a)

1.0

Blood 100% 100% 75% 50% 25%

10 20 30 o Temperature ( C)

40

4 2 0 -2 -4 -6 -8 -10 -12 -14 0

(c)

1 2 3 4 5 Hb concentration (mM) (d)

Fig.2. (a) Temperature dependence of OA image intensity (ThOR) for the whole blood (100%) and blood diluted by phosphate buffered saline (PBS) at pH 7.4. Percentiles indicate fraction of the whole blood in diluted samples. The insets illustrate the same volume of blood samples with different concentration of erythrocytes (hematocrit). (b) ThORs normalized at 37C become identical regardless of blood sample dilution. 2D images (insets) show a cross-section of blood-filled tube and illustrate the inversion of contrast upon transition through the zero value of Gruneisen parameter. (c) ThOR of hemoglobin solutions as it varies with concentration. Increase of Hb concentration depresses the nil Gruneisen temperature T 0. (d) The concentration function of T0 for hemoglobin dissolved in PBS is approximated by a linear fit: -2.8*CHb + 3.1. The picture of erythrocyte indicates intracellular concentration of hemoglobin and the measured T 0 of blood.

Proc. of SPIE Vol. 9323 93231Y-4

6

1.0

(1) (2)

Absorbance

0.8

Control probe After deep cooling Deep cooling + Laser

0.6 0.4 0.2 0.0 300 400 500 600 700 800 900 1000 1100 Wavelength [nm]

(a)

(b)

Fig. 3. (a) Blood samples in 1.5 mL tubes have clear plasma at the tops and RBCs suspension at the bottoms before (1) and after (2) the procedure. (b) Absorbance spectra of plasma from the tested blood samples illustrate absence of RBCs’ hemolysis after just cooling as well as cooling with laser irradiation. The utilized laser wavelength is indicated by the arrow. Microscopic examination of erythrocytes before and after deep cooling with a Q-switched laser excitation further proved that RBCs’ remained intact during measurements of ThoR in blood (Fig. 4). Erythrocytes had no visible alteration of shapes and volumes after cooling to -16C.

(a)

(b)

(c)

Fig.4. Light microscopy images (40x) of RBCs in diluted blood samples before the procedure (a), after the deep cooling only (b), and after deep cooling and laser irradiation (c). Finally, the transparent acoustically coupling medium was replaced by optically scattering medium to study behavior of the blood ThOR in conditions close to live tissue. As a medium we employed fat free milk, since it was previously shown to have optical scattering properties close to those of biological tissues19. The experiment was performed at the temperature range from 30 to 5C to avoid freezing of the milk. The curves of temperature dependence for OA image intensity in scattering medium replicate the previous result in transparent medium (Fig.5).

Proc. of SPIE Vol. 9323 93231Y-5

o

Temperature [ C]

Norm. OA image intensity

23 1.0 0.8 In scattering medium: Blood sample 1 Blood sample 2 Blood sample 3 Blood sample 3 In transparent medium: Averaged function

0.6 0.4 0.2 0.0

0

5

10

15

20

25

30

35

22 21 20 19 18

In milk surrounding: Sample 1 Sample 2 Sample 3 Sample 3 In transparent soln: Aver func

17 16 15 14 0.70

o

Temperature [ C]

0.75

0.80

0.85

0.90

0.95

1.00

Norm. OA image intensity

(a)

(b)

Fig.5. (a) Temperature-dependent optoacoustic response of blood in scattering medium in comparison to averaged ThOR function in transparent surrounding. OA image intensity was normalized at 27C. (b) The inverse plot of temperature vs normalized optoacoustic response, zoomed in within ΔT=10C, could be used for temperature mapping in live tissues. Maximum error of individual readings does not exceed ±1.5C (b).

4. DISCUSSION The identical behavior of normalized ThOR in whole and diluted blood was observed experimentally and explained by unique compartmentalization of hemoglobin within individual erythrocytes. The implemented dilution of blood changed the apparent concentration of hemoglobin (hematocrit) as it happens in a live organism across the entire vascular network18. In aqueous solutions elevated concentrations of proteins or salts cause the depression of the maximum density temperature according to the Despretz law14 and the equivalent shift of the ThOR parameter T01113 . However, in blood the concentration dependence of T0 does not exist (Fig.2b), the phenomenon related to heterogeneous composition of blood. Since the dominant chromophore, hemoglobin, is isolated within erythrocyte, we expect that normalized OA response will be determined by the hemoglobin concentration inside RBCs, which is known to be very stable17. Thus, the normalized blood ThOR depends on concentration of hemoglobin within erythrocyte only and does not vary with blood dilution. Based on our recent work11, the phenomenon can also be explicated in terms of the Gruneisen parameter’s dependence on temperature. In aqueous solutions, the nil optoacoustic response is achieved at the temperature of maximum density (T0) due to the fact that thermal expansion becomes thermal contraction. Similar to electrolytes13, hemoglobin solutions exhibit linear concentration function of the temperature T 0 (Fig.2c). When this function was extrapolated to the average hemoglobin concentration inside erythrocytes (Fig.2d), the temperature T0 was found to be consistent with that measured in blood, whole and diluted alike. The proposed hypothesis explaining universal behavior of ThOR in blood requires solid integrity of RBCs in order to keep all hemoglobin enclosed within intracellular environment. Dilution of blood by PBS pH 7.4 preserves the entireness of erythrocytes. Nonetheless, temperature changes could provoke disruption of RBC’s membrane. Two tests were performed to clarify this point (Figs. 3,4). (i) Absorbance spectra of plasma supernatant did not change following cooling and laser irradiation as it was applied during ThOR measurements. (ii) Optical microscopy images did not reveal any physical damage or deformation of individual RBCs. At the same time, it is known that, for example, cryoablation does induce disruptive effects in cell membranes via cyclic local application of freezing followed by fast or slow thawing18. Therefore, the rate of temperature change could be an important parameter limiting application of the optoacoustic thermometry based on the universal ThOR of blood. Red blood cells, as well as hemoglobin molecules, could also become damaged at temperatures higher than 42C17. Thus, the proposed temperature monitoring technique should be cautiously applied with correction to the rate of hemolysis during hyperthermia treatments like high-frequency ultrasound (HiFU), radio frequency (RF), and laser ablations.

Proc. of SPIE Vol. 9323 93231Y-6

Another point for discussion is the involvement of the erythrocyte’s microenvironment in generation of optoacoustic response from blood samples. Does it come only from intracellular hemoglobin-rich cytoplasm or hemoglobin-free blood plasma surrounding RBCs also contributes to the phenomenon? Our findings suggest that contribution of RBC’s surrounding medium to whole blood’s OA response is negligible. Considering potential biomedical applications of the universal blood ThOR for non-invasive thermometry in tissue, we emphasize that the phenomenon was reproducible both in transparent liquid and in light scattering medium (Fig.5). The precision of the calibration curve was improving towards low temperatures and reached 0.1C at 0C. A single-reading temperature accuracy in light scattering medium was 1.5C.

5. CONCLUSION As a result of these studies, we conclude that normalized temperature-dependent OA response of blood is universal and independent on blood hematocrit when obtained using laser illumination at the isosbestic point of hemoglobin (805 nm). The phenomenon is explained by the unique compartmentalization of the dominant absorbing agent hemoglobin within red blood cells. The phenomenon was observed in both optically transparent and scattering media. The normalization of the optoacoustic image intensity confines uncertainties introduced by spatial fluctuations of the laser fluence and optical absorption. In the future, the obtained calibration curve of the blood ThOR could be employed for important applications of in vivo optoacoustic temperature monitoring.

ACKNOWLEDGMENTS This work was supported in part by National Institutes of Health (National Cancer Institute) grant 1R43CA17714801A1. The authors greatly thank all members of the R&D and Engineering teams from TomoWave Laboratories, Inc.

REFERENCES [1] Esenaliev, R. O., Oraevsky, A. A., Larin, K. V., Larina I. V., Motamedi, M., “Real-time optoacoustic monitoring of temperature in tissues,” Proc. SPIE 3601, 268-275 (1999). [2] Shah, J., Park, S., Aglyamov, S., Larson, T., Ma, L., Sokolov, K., Johnston, K., Milner, T., Emelianov, S. Y., "Photoacoustic imaging and temperature measurement for photothermal cancer therapy," Journal of biomedical optics 13, 034024 (2008). [3] Pramanik, M., Wang, L. V., "Thermoacoustic and photoacoustic sensing of temperature," Journal of biomedical optics 14, 054024 (2009). [4] Nikitin, S. M., Khokhlova, T. D., Pelivanov, I. M., "Temperature dependence of the optoacoustic transformation efficiency in ex vivo tissues for application in monitoring thermal therapies," Journal of biomedical optics 17, 061214 (2012). [5] Brinkmann, R., Koinzer, S., Schlott, K., Ptaszynski, L., Bever, M., Baade, A., Luft, S., Miura, Y., Roider, J., Birngruber, R., “Real-time temperature determination during retinal photocoagulation on patients,” Journal of biomedical optics 17, 061219 (2012). [6] Chen, Y.-S., Frey, W., Walker, C., Aglyamov, S., Emelianov, S., “Sensitivity enhanced nanothermal sensors for photoacoustic temperature mapping,” Journal of biophotonics 6, 534-542 (2013). [7] Serebryakov, V. A., Boiko, E. V., Yan, A. V., “Real-time optoacoustic monitoring of the temperature of the retina during laser therapy,” Journal Opt. Technol. 81, 312-321 (2014). [8] Ke H., Tai, S, Wang, L. V., “Photoacoustic thermography of tissue,” Journal of biomedical optics 19, 026003 (2014). [9] Oraevsky, A. A., Karabutov,A. A., "Optoacoustic tomography," in [Biomedical Photonics Handbook], T. VoDinh, ed., CRC, 34/31-34/34 (2003). [10] Gusev, V. E., Karabutov, A. A., [Laser Optoacoustics], AIP, 11-18 (1993). [11] Petrova, E. V., Oraevsky A. A., Ermilov, S. A., “Red blood cell as a universal optoacoustic sensor for noninvasive temperature monitoring,” Applied physics letters 105, 094103 (2014). [12] Petrova, E. V., Ermilov, S. A., Su, R., Nadvoretsky, V. V., Conjusteau, A., Oraevsky, A. A., “Temperature dependence of Gruneisen parameter in optically absorbing solutions measured by 2D optoacoustic imaging,” Proceeding SPIE 8943, 89430S (2014).

Proc. of SPIE Vol. 9323 93231Y-7

[13] Petrova, E., Ermilov, S., Su, R., Nadvoretskiy, V., Conjusteau, A., Oraevsky, A., “Using optoacoustic imaging for measuring the temperature dependence of Grüneisen parameter in optically absorbing solutions,” Optics Express, 25077-25090 (2013). [14] Despretz, C. M., “Recherches sur le maximum de densite de l’eau pure, et des dissolutions aqueuses,” Annales de chimie et de physique 70, 5 (1839). [15] Dill, K., Bromberg, S., [Molecular Driving Forces], Garland Science, New York, 651 (2003). [16] Nadvoretskiy,V., Ermilov, S., Brecht, H. P., Su, R., and Oraevsky, A., "Image processing and analysis in a dualmodality optoacoustic/ultrasonic system for breast cancer diagnosis," Proc. SPIE 7899, 789909 (2011). [17] Gershfeld, N. L., Murayama, M., “Thermal instability of red blood cell membrane bilayers: temperature dependence of hemolysis,” Journal of membrane biology 101, 67 (1988). [18] Zhmakin, A. I., [Fundamentals of cryobiology: physical phenomena and mathematical models], Springer, 276 (2010). [19] Waterworth, M.D., Tarte, B. J., Joblin, A. J., van Doorn, T., Niesler, H. E., “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas Phys. Eng. Sci. Med. 18, 39-44 (1995).

Proc. of SPIE Vol. 9323 93231Y-8