## Genetic algorithms and MCML program for recovery of optical properties of homogeneous turbid media |

Biomedical Optics Express, Vol. 4, Issue 3, pp. 433-446 (2013)

http://dx.doi.org/10.1364/BOE.4.000433

Acrobat PDF (929 KB)

### Abstract

In this paper, we present and validate a new method for optical properties recovery of turbid media with slab geometry. This method is an iterative method that compares diffuse reflectance and transmittance, measured using integrating spheres, with those obtained using the known algorithm MCML. The search procedure is based in the evolution of a population due to selection of the best individual, i.e., using a genetic algorithm. This new method includes several corrections such as non-linear effects in integrating spheres measurements and loss of light due to the finite size of the sample. As a potential application and proof-of-principle experiment of this new method, we use this new algorithm in the recovery of optical properties of blood samples at different degrees of coagulation.

© 2013 OSA

## 1. Introduction

*μ*,

_{a}*μ*and

_{s}*g*. The absorption and the scattering coefficients,

*μ*and

_{a}*μ*, give the probability per unit path length of photon being absorbed or scattered, respectively. The anisotropy coefficient,

_{s}*g*, is defined as the average cosine of the photon scattering angle. Different values of the optical parameters give an insight of the structure and component concentration of the biological sample under study. For example, normal human whole blood consist of about 55 vol % plasma (90% water, 10% proteins) and 45 vol % cells (99% red blood cells “erythrocytes”, 1% leukocytes and thrombocyte), giving a high absorption coefficient and a strong forward scattering, due to the big size of the red blood cells [2

2. A. Roggan, K. Dorschel, G. Muller, M. Friebel, and A. Hahn, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. **4**, 36–46 (1999). [CrossRef] [PubMed]

4. P. Kubelka, “New contributions to the optics of intensely light-scattering materials,” J. Opt. Soc. Am. **38**, 448–457 (1948). [CrossRef] [PubMed]

9. P. S. Mudgett and L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. **10**, 1485–1502 (1971). [CrossRef] [PubMed]

10. S. A. Prahl, I. A. Vitkin, B. C. Wilson, and R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. **37**, 1203–1217 (1992). [CrossRef] [PubMed]

11. M. S. Patterson, B. Chance, and B. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurements of tissue optical properties,” Appl. Opt. **28**, 2331–2336 (1989). [CrossRef] [PubMed]

12. M. S. Patterson, E. Schwarts, and B. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” Proc. SPIE **1065**, 115–122, (1989). [CrossRef]

13. S. K. Jacques and S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. **6**, 494–503 (1987). [CrossRef] [PubMed]

14. G. Yoon, F. Liu, and R. R. Alfano, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. **28**, 2250–2255 (1989). [CrossRef] [PubMed]

15. S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. **32**, 559–568 (1993). [CrossRef] [PubMed]

15. S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. **32**, 559–568 (1993). [CrossRef] [PubMed]

17. A. Roggan, G. Muller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. **11**, 34021 (2006). [CrossRef] [PubMed]

20. A. M. K. Nilsson, R. Berg, and S. Andersson-Engels, “Measurements of the optical properties of tissue in conjunction with photodynamic therapy,” Appl. Opt. **34**, 4609–4619 (1995). [CrossRef] [PubMed]

19. J. S. Dam, T. Dalgaard, P. E. Fabricius, and S. Andersson-Engels, “Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements,” Appl. Opt. **39**, 1202–1209 (2000). [CrossRef]

21. I. V. Yaroslavsky, A. N. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Inverse hybrid technique for determining the optical properties of turbid media from integrating-sphere measurements,” Appl. Opt. **34**, 6797–6809 (1996) [CrossRef]

22. M. Hammer, A. Roggan, D. Schweitzer, and G. Mller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. **40**, 963–978 (1995). [CrossRef] [PubMed]

20. A. M. K. Nilsson, R. Berg, and S. Andersson-Engels, “Measurements of the optical properties of tissue in conjunction with photodynamic therapy,” Appl. Opt. **34**, 4609–4619 (1995). [CrossRef] [PubMed]

19. J. S. Dam, T. Dalgaard, P. E. Fabricius, and S. Andersson-Engels, “Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements,” Appl. Opt. **39**, 1202–1209 (2000). [CrossRef]

21. I. V. Yaroslavsky, A. N. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Inverse hybrid technique for determining the optical properties of turbid media from integrating-sphere measurements,” Appl. Opt. **34**, 6797–6809 (1996) [CrossRef]

22. M. Hammer, A. Roggan, D. Schweitzer, and G. Mller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. **40**, 963–978 (1995). [CrossRef] [PubMed]

21. I. V. Yaroslavsky, A. N. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Inverse hybrid technique for determining the optical properties of turbid media from integrating-sphere measurements,” Appl. Opt. **34**, 6797–6809 (1996) [CrossRef]

22. M. Hammer, A. Roggan, D. Schweitzer, and G. Mller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. **40**, 963–978 (1995). [CrossRef] [PubMed]

*et al.*optical properties of blood are required for the calculation of the light distribution in blood-perfused tissues, for example, in optical tomography, fluorescence diagnosis, photodynamic therapy, and laser-induced thermotherapy [23

23. M. Meinke, G. Muller, J. Helfmann, and M. Friebel, “Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range,” J. Biomed. Opt. **12**, 014024 (2007). [CrossRef] [PubMed]

2. A. Roggan, K. Dorschel, G. Muller, M. Friebel, and A. Hahn, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. **4**, 36–46 (1999). [CrossRef] [PubMed]

17. A. Roggan, G. Muller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. **11**, 34021 (2006). [CrossRef] [PubMed]

23. M. Meinke, G. Muller, J. Helfmann, and M. Friebel, “Optical properties of platelets and blood plasma and their influence on the optical behavior of whole blood in the visible to near infrared wavelength range,” J. Biomed. Opt. **12**, 014024 (2007). [CrossRef] [PubMed]

28. D. J. Faber, M. C. Aalders, E. G. Mik, B. A. Hooper, M. J. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. **93**(2), 028102 (2004). [CrossRef] [PubMed]

*g*. For this, a recovery algorithm for

*g*could be sensitive to the formation of clots in human blood.

*R*, and diffuse transmittance,

_{d}*T*, using a system of two integrating spheres. Due to the non-linear effects introduced by the spheres, the experimental values are affected and do not correspond to real reflectance and transmittance measurements. The algorithm presented takes into account this effects by correcting the experimental values measured with the two integrating spheres set-up [30

_{d}30. T. Moffitt, Y. C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. **11**, 041103 (2006). [CrossRef] [PubMed]

31. L.-H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biol. **47**, 131–146 (1995). [CrossRef]

## 2. Materials and methods

### 2.1. Sample preparation

*μ*m diameter) and different concentrations. The polystyrene microspheres have a small standard deviations in size (around 5%). The samples were put in glass cuvettes of 2 mm thickness. It was considered that the refractive index for these samples is 1.33.

### 2.2. Experimental setup

36. B. Morales, S. V. y Montiel, and J. A. D. Atencio, “Behavior of optical properties of coagulated blood sample at 633 nm wavelength,” Proc. SPIE **7897**, 78970S (2011). [CrossRef]

37. B. Morales, S. A. Prahl, J. A. D. Atencio, and S. V. y Montiel, “Validation of ga-mcml algorithm against iad program,” Proc. SPIE **8011**, 80118O (2011). [CrossRef]

*e*

^{2}of the peak intensity was 0.88 mm, and the beam divergence was about 0.92 mrad. The laser beam was directed into the entrance port of integrating sphere 1, whose exit port was coupled with the entrance port of integrating sphere 2; the sample was situated between the two integrating spheres, as seen in Fig. 1. The exit port of integrating sphere 2 was covered with a cap with a reflective surface identical to the integrating spheres coat.

38. S. Prahl, Inverse Adding-Doubling for Optical Property Measurements (2007), http://omlc.ogi.edu/software/iad/index.html.

*R*is the current detected by detector 1 with the sample in the port between the two spheres,

_{s}*R*

_{0}is the current detected by detector 1 with open port, and a standard reflective surface at the exit port of integrating sphere 1,

*T*is the current detected by detector 2 with the sample at sample port and a reflective surface at exit port of integrating sphere 2, and

_{s}*T*

_{0}is the current detected by detector 2 with no sample and with a reflective surface at the exit port of the second integrating sphere.

*R*is the correction factor for the stray light measured by detector 1 with no sample and the exit sample port uncovered and sphere 2 removed.

_{dark}*T*is the correction for detector 2 measured with no sample or light entering the two integrating sphere system.

_{dark}### 2.3. Genetic algorithm and MCML program

36. B. Morales, S. V. y Montiel, and J. A. D. Atencio, “Behavior of optical properties of coagulated blood sample at 633 nm wavelength,” Proc. SPIE **7897**, 78970S (2011). [CrossRef]

37. B. Morales, S. A. Prahl, J. A. D. Atencio, and S. V. y Montiel, “Validation of ga-mcml algorithm against iad program,” Proc. SPIE **8011**, 80118O (2011). [CrossRef]

31. L.-H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biol. **47**, 131–146 (1995). [CrossRef]

#### 2.3.1. GA-MCML code

31. L.-H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Biol. **47**, 131–146 (1995). [CrossRef]

39. J. H. Torres, A. J. Welch, I. Çilesiz, and M. Motamedi, “Tissue optical property measurements: overestimation of absorption coefficient with spectrophotometric techniques,” Lasers Surg. Med. **14**, 249–257 (1994). [CrossRef] [PubMed]

40. G. de Vries, J. F. Beek, G. W. Lucassen, and M. van Gemert, “The effect of light losses in double integrating spheres on optical properties estimation,” IEEE J. Sel. Top. Quantum Electron. **5**, 944–947 (1999). [CrossRef]

#### 2.3.2. Genetic algorithms

*x*is [

_{j}*a*,

_{j}*b*] and the required precision is

_{j}*q*places after the decimal point, the range of the domain of the variable should be divided into at least (

*b*−

_{j}*a*) × 10

_{j}*size ranges. The required bits (*

^{q}*m*) for a variable is calculated as follows:

_{j}*x*is computed as follows: where

_{j}*decimal*(

*substring*) represents the decimal value of

_{j}*substring*for variable

_{j}*x*.

_{j}*p*) is defined as the ratio of the number of offspring produced in each generation to the population size (

_{c}*pop*–

*size*). This ratio controls the expected number

*p*×

_{c}*pop*–

*size*of chromosomes that undergo a crossover operation. Mutation is a background operator which produces spontaneous random changes in some individuals. In a genetic algorithm, mutation serves the role of either replacing the genes lost from the population during the selection process or providing the genes that were not present in the initial population, exploring new possibilities of solutions [33]. The mutation rate (

*p*) is defined as the percentage of the total number of genes muted in the whole population and controls the rate at which new genes are introduced into the population for trial. If it is too low, many genes that would have been useful are never tried out; but if it is too high, there will be much random perturbation and the algorithm will lose the ability to learn from the history of the search.

_{m}*k*= 1, 2,...,

*pop – size*and to evaluate the fitness function

*f*(

**x**

*). In our case, the fitness function represents the relative error between the experimental measurements and the simulated ones using MCML.*

^{k}*g*was selected to be [0, 1], for

*μ*was [0, 200] and for

_{s}*μ*was [0,10] for the GA-MCML validation and for the blood experiments was [0.95, 1] for

_{a}*g*, [0, 4000] for

*μ*and [0,100] for

_{s}*μ*. A Boltzmann function was selected as the fitness function. GA-MCML also includes a cut fitness value. If the best element of a given generation has a fitness value greater than the cut value, the program is terminated. In the case of the validation of the method we use 10,000 photons in the MCML simulation and 30 generations in the genetic algorithm. For the optical properties of blood at different grades of coagulation we use 30,000 photons and 30 generations in the MCML simulation and in the genetic algorithm evolution respectively. In both cases no cut fitness value was used.

_{a}#### 2.3.3. Integrating spheres corrections

15. S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. **32**, 559–568 (1993). [CrossRef] [PubMed]

41. J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. **32**, 399–410 (1993). [CrossRef] [PubMed]

42. J. W. Pickering, C. J. M. Moes, H. J. C. M. Sterenborg, S. A. Prahl, and M. J. C. van Gemert, “Two integrating sphere with an intervening scattering sample,” J. Opt. Soc. Am **9**, 621–631 (1992). [CrossRef]

38. S. Prahl, Inverse Adding-Doubling for Optical Property Measurements (2007), http://omlc.ogi.edu/software/iad/index.html.

30. T. Moffitt, Y. C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. **11**, 041103 (2006). [CrossRef] [PubMed]

**32**, 559–568 (1993). [CrossRef] [PubMed]

38. S. Prahl, Inverse Adding-Doubling for Optical Property Measurements (2007), http://omlc.ogi.edu/software/iad/index.html.

*R*and

_{d}*T*. The latter would require a complete modification of the MCML code, so, at first approximation, we use

_{d}## 3. GA-MCML validation

**32**, 559–568 (1993). [CrossRef] [PubMed]

*μ*m diameter and MS059 for the microspheres of 0.59

*μ*m diameter at different concentrations. PBMS stands for a phantom with scattering agent embedded and PBMSA for a phantom not only with scattering agent embedded but also with an absorption agent. Columns two and three indicate the reflectance and transmittance values experimentally obtained by using a system of two integrating spheres. Column four is the thickness of the sample and the last column shows the anisotropy factor used in the recovery of the optical properties, obtained using Mie theory.

37. B. Morales, S. A. Prahl, J. A. D. Atencio, and S. V. y Montiel, “Validation of ga-mcml algorithm against iad program,” Proc. SPIE **8011**, 80118O (2011). [CrossRef]

## 4. Results and discussion

*g*) to a range from 0.95 to 1 based on previous reported values of this parameter for blood samples [2

2. A. Roggan, K. Dorschel, G. Muller, M. Friebel, and A. Hahn, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. **4**, 36–46 (1999). [CrossRef] [PubMed]

17. A. Roggan, G. Muller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. **11**, 34021 (2006). [CrossRef] [PubMed]

25. P. Starukhin, S. Ulyanov, E. Galanzha, and V. Tuchin, “Blood-flow measurements with a small number of scattering events,” Appl. Opt. **39**, 2823–2830 (2000). [CrossRef]

28. D. J. Faber, M. C. Aalders, E. G. Mik, B. A. Hooper, M. J. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. **93**(2), 028102 (2004). [CrossRef] [PubMed]

35. T. Vo-Dinh, *Biomedical Photonics* (CRC Press, 2003). [CrossRef]

*μ*and scattering coefficient

_{a}*μ*were chosen as the free variables. The goal of this first step was to find a suitable value for

_{s}*μ*. The second step was to recover the anisotropy factor (

_{a}*g*) and the scattering coefficient (

*μ*) from two experimentally measured quantities: the diffuse reflectance and the diffuse transmittance using the absorption coefficient (

_{s}*μ*) recovered from the first step. GA-MCML error was estimated using the mean value and standard deviation of several runs of the GA-MCML program.

_{a}*μ*found in this work for different concentration of anti-coagulant range from 6 to about 16

_{a}*cm*

^{−1}which is in agreement with those reported in the literature [2

**4**, 36–46 (1999). [CrossRef] [PubMed]

25. P. Starukhin, S. Ulyanov, E. Galanzha, and V. Tuchin, “Blood-flow measurements with a small number of scattering events,” Appl. Opt. **39**, 2823–2830 (2000). [CrossRef]

28. D. J. Faber, M. C. Aalders, E. G. Mik, B. A. Hooper, M. J. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. **93**(2), 028102 (2004). [CrossRef] [PubMed]

*g*is the key parameter, because it contains information on the clustering of the erythrocytes.

*et al.*by computing the anisotropy factor using the T-matrix theory of a red blood cell volume equivalent spheroid [43

43. A. M. Nilsson, P. Alsholm, A. Karlsson, and S. Andersson-Engels, “T-matrix computations of light scattering by red blood cells,” Appl. Opt. **37**, 2735–2748 (1998). [CrossRef]

*μ*decreases by increasing the concentration of anticoagulant. The points corresponding to 7.5%, 10% and 12.5% had an almost constant scattering coefficient, having an almost linear decreasing at lower and higher anticoagulant concentration (AC). Regarding to the data at 10% of anticoagulant, the first point differs by 38.11% and the final point differs by 213.28%.

_{s}24. A. M. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, and M. J. C. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. **65**, 366–373 (1997). [CrossRef] [PubMed]

27. H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, and B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous nir light,” Phys. Med. Biol. **40**, 1983–1993 (1995). [CrossRef] [PubMed]

**93**(2), 028102 (2004). [CrossRef] [PubMed]

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

*μ*, where the scattering coefficient describes a medium containing many scattering particles at a concentration described as a volume density

_{s}*ρ*. The scattering coefficient is the cross-sectional area per unit volume of medium

_{s}*μ*=

_{s}*ρ*[3]. We are considering

_{s}σ_{s}*σ*constant, i.e. during the coagulation process, the size of the scattering shadow does not change. But, in the first part, neither

_{s}*σ*nor

_{s}*ρ*are constant because the light hits a bigger obstacle by decreasing the anticoagulant concentration (AC) and the total volume is changing. Then, the second part is the only part that is probably linear.

_{s}## 5. Conclusions

## Acknowledgments

## References and links

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38. | S. Prahl, Inverse Adding-Doubling for Optical Property Measurements (2007), http://omlc.ogi.edu/software/iad/index.html. |

39. | J. H. Torres, A. J. Welch, I. Çilesiz, and M. Motamedi, “Tissue optical property measurements: overestimation of absorption coefficient with spectrophotometric techniques,” Lasers Surg. Med. |

40. | G. de Vries, J. F. Beek, G. W. Lucassen, and M. van Gemert, “The effect of light losses in double integrating spheres on optical properties estimation,” IEEE J. Sel. Top. Quantum Electron. |

41. | J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. |

42. | J. W. Pickering, C. J. M. Moes, H. J. C. M. Sterenborg, S. A. Prahl, and M. J. C. van Gemert, “Two integrating sphere with an intervening scattering sample,” J. Opt. Soc. Am |

43. | A. M. Nilsson, P. Alsholm, A. Karlsson, and S. Andersson-Engels, “T-matrix computations of light scattering by red blood cells,” Appl. Opt. |

44. | C. F. Bohren and D. R. Huffman, |

45. | W. F. Cheong, S. A. Prahl, and A. J. Welch, “Review of the optical properties of a biological tissues,” IEEE J. Quantum Electron. |

**OCIS Codes**

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.5280) Medical optics and biotechnology : Photon migration

(290.7050) Scattering : Turbid media

**ToC Category:**

Optics of Tissue and Turbid Media

**History**

Original Manuscript: October 19, 2012

Revised Manuscript: November 29, 2012

Manuscript Accepted: December 22, 2012

Published: February 15, 2013

**Citation**

Beatriz Morales Cruzado, Sergio Vázquez y Montiel, and José Alberto Delgado Atencio, "Genetic algorithms and MCML program for recovery of optical properties of homogeneous turbid media," Biomed. Opt. Express **4**, 433-446 (2013)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-3-433

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