## Impact of model parameters on Monte Carlo simulations of backscattering Mueller matrix images of colon tissue |

Biomedical Optics Express, Vol. 2, Issue 7, pp. 1836-1851 (2011)

http://dx.doi.org/10.1364/BOE.2.001836

Acrobat PDF (1818 KB)

### Abstract

Polarimetric imaging is emerging as a viable technique for tumor detection and staging. As a preliminary step towards a thorough understanding of the observed contrasts, we present a set of numerical Monte Carlo simulations of the polarimetric response of multilayer structures representing colon samples in the backscattering geometry. In a first instance, a typical colon sample was modeled as one or two scattering “slabs” with monodisperse non absorbing scatterers representing the most superficial tissue layers (the mucosa and submucosa), above a totally depolarizing Lambertian lumping the contributions of the deeper layers (muscularis and pericolic tissue). The model parameters were the number of layers, their thicknesses and morphology, the sizes and concentrations of the scatterers, the optical index contrast between the scatterers and the surrounding medium, and the Lambertian albedo. With quite similar results for single and double layer structures, this model does not reproduce the experimentally observed stability of the relative magnitudes of the depolarizing powers for incident linear and circular polarizations. This issue was solved by considering bimodal populations including large and small scatterers in a single layer above the Lambertian, a result which shows the importance of taking into account the various types of scatterers (nuclei, collagen fibers and organelles) in the same model.

© 2011 OSA

## 1. Introduction

*polarization*due to interaction with the sample. As such, it may provide different and complementary information with respect to the usual imaging based on

*intensity*measurements. Among many other topics, the detection and measurement of weak optical activity in samples of biomedical interest is being actively investigated [1

1. I. A. Vitkin, R. D. Laszlo, and C. L. Whyman, “Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light,” Opt. Express **10**(4), 222–229 (2002). [PubMed]

6. M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. **14**(1), 014029 (2009). [CrossRef] [PubMed]

9. H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. **40**(3), 400–412 (2001). [CrossRef] [PubMed]

10. I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. **92**(6), 915–923 (2002). [CrossRef]

11. S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE **6842**, 68420I, 68420I-7 (2008). [CrossRef]

6. M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. **14**(1), 014029 (2009). [CrossRef] [PubMed]

12. M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications **2**, 07018 (2007). [CrossRef]

13. 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]

14. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express **18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

*et al*. demonstrated that the Mueller matrix imaging can differentiate between normal and tumoral cell suspensions [15

15. A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, and I. J. Bigio, “Diffuse backscattering Mueller matricesof highly scattering media,” Opt. Express **1**(13), 441–453 (1997). [CrossRef] [PubMed]

16. M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE **3911**, 210–216 (2000). [CrossRef]

17. M. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE **4257**, 82–89 (2001). [CrossRef]

18. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express **13**(12), 4420–4438 (2005). [CrossRef] [PubMed]

20. A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE **7895**, 78950E (2011). [CrossRef]

14. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express **18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

20. A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE **7895**, 78950E (2011). [CrossRef]

22. A. Pierangelo, A. De Martino, M. Anastasiadou, P. Validire, B. Huynh, H. Cohen, and L. Schwartz, “Multispectral Mueller imaging of *ex-vivo* tissue,” in *Proceedings of the European 1st NanoCharM Workshop on Polarization-Based Optical Techniques Applied to Biology and Medicine* (nanocharm.org, 2009), pp. 32–38, http://www.nanocharm.org/images/stories/Library/Proceedings/1st%20Workshop/1stWorkshopProceedings.pdf.

23. 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. M. Crawford, and M. S. 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]

25. K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. **126**, 265–279, discussion 303–311 (2004). [CrossRef] [PubMed]

26. D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. **50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

26. D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. **50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

26. D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. **50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

14. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express **18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

27. B. Kaplan, G. Ledanois, and B. Drévillon, “Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation,” Appl. Opt. **40**(16), 2769–2777 (2001). [CrossRef] [PubMed]

## 2. Materials and methods

### 2.1. Typical backscattering Mueller matrix images of ex-vivo colon samples

**18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

*diagonal*, which means that the sample behaves as a

*pure depolarizer*, without any significant diattenuation or retardation. This sample comprises both healthy (bottom left) and tumoral (top right) regions. At this stage (exophytic growth in the mucosa, with the underlying tissues still untouched) the tumor is less depolarizing than the healthy part. The contrast between the two regions is clearly enhanced in the polarimetric images M*

_{22}and M*

_{33}with respect to the intensity image M

_{11}(at the top left corner), showing the potential of the technique for early tumor detection. At subsequent stages, the behavior of the polarimetric response is more complex, as shown in [19

19. A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “*Ex-vivo* characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express **19**(2), 1582–1593 (2011). [CrossRef] [PubMed]

20. A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE **7895**, 78950E (2011). [CrossRef]

_{22}and M*

_{33}are almost identical and larger than M*

_{44}.

**18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

### 2.2. Modeling the backscattering from ex vivo colon tissue with Monte Carlo method

#### 2.2.1. Ex-vivo colon tissue structure

28. J.-M. André, M. Catala, J.-J. Morère, E. Escudier, G. Katsanis, and J. Poirier, “Histologie: les tissus,” (Faculté de Médicine, Université Pierre et Marie Curie, PAES) (2007–2008), http://www.chups.jussieu.fr/polys/histo/histoP1/histoP1.pdf/.

**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

24. G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. **38**(31), 6628–6637 (1999). [CrossRef] [PubMed]

**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

29. S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. **61**(2), 482–490 (1996). [CrossRef] [PubMed]

#### 2.2.2. The proposed model of colon optical response

*ex-vivo*colon samples we have represented such samples as multi-layered scattering structures. In a first step we assumed that the mucosa and the submucosa layers consist of a surrounding medium with mono-dispersed scattering spheres. Due to very small thickness of the muscularis mucosa and the similarity between the muscularis mucosa and submucosa optical properties, the muscularis mucosa will be included in the submucosa layer in our model. All underlying layers were lumped into a totally depolarizing Lambertian substrate. In a second step, we considered the layers with bimodal populations representing both the collagen spheres and the sub-cellular organelles - the most important scatterers - within each layer.

**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

*r*, and optical index

*n*

_{s}were embedded in an extra cellular matrix with optical index

*n*. The photon mean free path

_{m}*MFP*was defined as 1/

*Nσ*, where

*N*is the number density of scatterers and

*σ*is the scattering cross-section [30]. The number density

*N*was calculated from the volume fraction

*F*of the scatterers (i.e. the volume occupied by scatterers per cubic centimeter of sample) as

*N*=

*F/V*, where

_{r}*r*.

*h*, see Fig. 3a ). The lateral walls of cylinder were assumed to be totally absorbing. The bottom of cylinder was either absorbing or Lambertian substrate. The diffuse illumination (

*λ*= 633 nm) was propagated along the axis of the cylinder.

*r*of the scattering spheres, their number density

*N*, which determines the photon mean free path

*MFP*, the optical index contrast,

*m*=

*n*

_{s}/

*n*

_{m}; and the layer thickness

*h*. For the layer with bimodal population, the radii, number density and optical index contrast of the two types of scatterers are different;

_{i}*r*

_{1},

*r*

_{2},

*MFP*,

_{1}*MFP*,

_{2}*m*

_{1}and

*m*

_{2}.

*θ*of the scattered light, while being uniformly distributed over the azimuthal angle

*ϕ*. More precisely the intensity

*I(θ,ϕ)*(W sr

^{−1}) backscattered into a solid angle dΩ around the angles (

*θ,ϕ*) is given by:

*Z*

_{0}is the illumination power (W) incident on the Lambertian and

*a*its albedo. This is a first approximation of the response of the underlying layers, based on the assumption of a complete randomization of the polarization and emerging direction of the backscattered photons due to a large number of scattering events.

27. B. Kaplan, G. Ledanois, and B. Drévillon, “Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation,” Appl. Opt. **40**(16), 2769–2777 (2001). [CrossRef] [PubMed]

## 3. Results and discussion

### 3.1. Multilayered structures with monodisperse scatterers within each layer

#### 3.1.1. Single layer (mucosa) on top of a Lambertian

**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

*r*= 200 nm) at 12% volume fraction in physiological liquid (

*MFP*= 53.7 µm,

*m*= 1.46/1.38,

*h*= 0.5 mm). The submucosa tissue was modeled as a suspension of large collagen spheres (

_{1}*r*= 1.75 µm), at 50% volume fraction in physiological liquid (

*MFP*= 19.69 µm,

*m*= 1.38/1.36,

*h*= 0.7 mm). No absorption (either from the medium or from the spheres) was taken into account so far.

_{2}*a*was chosen in order to account for the absorption by the mucosa and submucosa layers and the global contribution from the deeper layers. We considered reasonable to vary albedo

*a*values between 0 and 0.3.

*a*= 0) the simulated Mueller matrix of the sample obeys the relation:

**18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

*a*had to be increased to 0.3 to make all the diagonal matrix elements equal, which is not yet what is observed in experiments, namely a M*

_{44}element being significantly smaller than both M*

_{22}and M*

_{33}. As a result, the single layer model with the nominal values of the parameters for the mucosa is certainly not adequate.

*MFP*from 53.7 µm to 161.11 µm (or a reduction of

*µ*from 186.20 to 62.07 cm

_{s}= 1/MFP^{−1}). Increasing the

*MFP*is equivalent to shortening the thickness of the scattering medium, thus reducing: the number of scattering events. A transition from Mie to Rayleigh scattering regimes is observed when

*µ*

_{s}decreases, with a threshold at

*µ*

_{s}= 0.95 cm

^{−1}(see Fig. 3c). This result suggests that multiple scattering may induce a Mie regime when the number of scattering events is large enough, even for “small” scatterers, for which a Rayleigh regime would be expected and is indeed observed at lower concentrations.

*h*, between 0.2 and 1.5 mm (Fig. 3d). For this study, the volume fraction of the collagen spheres (with radius 200 nm), was fixed at 6%, corresponding to a

*MFP*of 107.4 µm, so that the experimental criterion was held among the diagonal elements of the Mueller matrix. Moreover, the Lambertian albedo

*a*was set equal to 0.3 to account for the absorption by the medium of the mucosa tissue phantom and the global contribution (absorption and scattering) to the reflected intensity from the layers beneath the mucosa. Figure 3d shows a transition from Rayleigh to Mie regimes when

*h*increases, a result consistent with the previously discussed evolution of the scattering regime with

*µ*

_{s}. When layer thickness

*h*increases, the average number of scattering events increases too, leading to the same trend as that observed when scattering coefficient

*µ*

_{s}increases.

*r*= 200 nm) at 12% volume fraction in physiological liquid (

*MFP*= 53.7 µm,

*m*= 1.46/1.38,

*h*= 0.5 mm) obtained by varying one model parameter (

_{1}*r*,

*MFP*,

*h*) at time, for reasonable values of the parameters obey to the relation in Eq. (2) typical of Mie scattering, while the occurrence of Mie scattering is never seen experimentally, lead the conclusion that the proposed model of colon tissue is not realistic. It is therefore natural to explore the polarimetric response of more complex structures, which might provide better models of the complex colon tissue structure.

_{1}#### 3.1.2. Double layer structure (submucosa and mucosa) on top of the Lambertian

_{ii}. In contrast, the histograms (2) and (3) of the diagonal Mueller matrix elements, calculated with Lambertian albedos equal to 0.1 and 0.3 respectively, are typical of the Mie scattering regime. Moreover, the absolute values of the IM*

_{ii}I are practically identical to those shown on Fig. 3 for the same parameters of the mucosa scatterers.

#### 3.1.3. Influence of the layer shapes: simulations of budding tumors

*r*= 200 nm,

*m*= 1.46/1.38,

*MFP*= 107.41 µm,

*h*= 0.5 mm;

*a*= 0) while preserving its thickness and optical properties, as in [31

31. G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. **43**(2), 113–122 (1996). [CrossRef] [PubMed]

*d*= 0.5 cm (which is one half of the diameter

_{s}*d*of the whole sample). We performed the simulations for different heights

*h*

_{s}of the bump (0.5 mm, 1 mm, 2 mm) to mimic the incremental growth of the colon tissue deformation. As shown on the right panel of Fig. 5, these morphological changes do not reverse the scattering regime, they only modify the absolute values of the diagonal elements of the Mueller matrix.

*R*= 0.25 cm;

_{s}*h*= 0.5 mm, 1 mm, 2 mm). In Fig. 6c the exophytic growth is described as radially symmetric expansion of the mucosa tissue that invades the deeper layer while also developing in height (

_{s}*R*= 0.75 mm,

_{s}*h*= 0.5 mm;

_{s}*R*= 1.25 mm,

_{s}*h*= 1 mm,

_{s}*R*= 2.25 mm

_{s}*h*= 2 mm).

_{s}### 3.2. Multilayered structures with bimodal populations of scatterers

*r*

_{1}= 200 nm,

*n*

_{2}= 1.46) and nuclei-like spheres (

*R*

_{2}= 3 µm,

*n*

_{2}= 1.4) or sub-organelles/protein (

*r*

_{2}= 50 nm) in physiological liquid (optical index contrast

*m(λ)*=

*n*

_{s}

*(λ)*/

*n*

_{m,}

*n*

_{m}= 1.38; absorption coefficient

*µ*

_{a}(

*λ*)) filling the cylinder described above (diameter 1 cm; depth,

*h*), with diffuse illumination at different wavelengths

*λ*= 500, 550, 600, 633, 650, 700 nm propagating along the axis of the cylinder. We kept the totally depolarizing Lambertian substrate with typical albedo value of 0.3 to model the contribution of the layers beneath the mucosa layer.

*µ*

_{s}of the scattering medium was calculated as the sum of the scattering parameters

*µ*

_{si}=

*N*

_{i}

*σ*

_{i}of the embedded monodisperse media. The overall mean free path of the medium is thus

27. B. Kaplan, G. Ledanois, and B. Drévillon, “Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation,” Appl. Opt. **40**(16), 2769–2777 (2001). [CrossRef] [PubMed]

#### 3.2.1. Preliminary studies with bimodal populations for λ = 633 nm

32. M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. **28**(3), 237–243 (2001). [CrossRef] [PubMed]

*MFP*decrease from 55.49 to 53.39 µm (

*r*

_{1}= 200 nm,

*r*

_{2}= 50 nm,

*m*= 1.058,

*λ*= 633nm) and compared to the simulation without the sub-organelles (monodisperse phantom tissue,

*MFP*= 53.7 µm). The insertion of the sub-organelles modified the scattering regime of the phantom tissue already at 0.003% of volume fraction (

*MFP*= 53.7 µm,

*µ*= 186.206 cm

_{s}^{−1}) as it is shown in Fig. 7 . This trend is certainly due to a rapid increase of the Rayleigh type contribution due to the small spheres to the backscattered light. Increasing the concentration of the small spheres enhances the Rayleigh type contribution over the Mie type contribution due to the large spheres and strengthens the Rayleigh-like nature of the backscattering from the phantom tissue with bimodal population. It manifests itself as growing divergence between the |M

_{22}*|, |M

_{33}*| and |M

_{44}*| values in Fig. 7.

_{22}|, |M*

_{33}| and |M*

_{44}| elements, we performed the series of simulations for different layer thicknesses with volume fractions kept constant at 12% for the medium (radius 200 nm) scatterers while the volume fraction for the small (radius 50 nm) scatterers was varied from 0% to 1%. Figure 8 shows the diagonal element values versus layer thickness ranging from 0.5 to 10 mm.

_{44}coefficient takes negative values as the concentration of the small spheres overpass 0.01% volume fraction, which explains the kink in the curve of |M

_{44}*| in Fig. 7.

#### 3.2.2. Wavelength dependent polarimetric response

*µ*is the scattering coefficient,

_{s}*µ*

_{a}is the absorption coefficient. The value of scattering albedo

*β*used in Lambert-Beer law [33

33. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express **13**(12), 4420–4438 (2005). [CrossRef] [PubMed]

37. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. **37**(31), 7392–7400 (1998). [CrossRef] [PubMed]

## 4. Conclusion

*µ*, layer thickness

_{s}*h*), implying that the monodisperse single layer (mucosa) model is not adequate for complex colon tissue. Simulated backscattering Mueller matrix images of the double layer (mucosa and submucosa) model with monodisperse (radius 200 nm) mucosa and monodisperse (radius 1.75 µm) submucosa layers illustrated that adding to the model the monodisperse single submucosa layer does not impact the regime of scattering of the monodisperse single mucosa layer. As a result, the single layer (mucosa) model constitutes a valid simplification of colon tissue.

## Appendix A

38. A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE **4162**, 265–268 (2000). [CrossRef]

39. A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength: a simple approximation,” Proc. SPIE **5068**, 393–395 (2003). [CrossRef]

*λ*is expressed in nm. The medium refractive index was kept constant (

*n*

_{m}= 1.38).

40. “Research in Biomedical Optics,” MIT spectroscopy, http://web.mit.edu/spectroscopy/research/biomedicaloptics.html.

41. H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, and M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm,” Appl. Opt. **30**(31), 4507–4514 (1991). [CrossRef] [PubMed]

42. R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers,” Opt. Lett. **27**(4), 246–248 (2002). [CrossRef] [PubMed]

43. L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. **10**(4), 235–243 (1995). [CrossRef]

*bvr*is the effective blood vessel radius in mm and

*C*is the concentration of hemoglobin expressed in mg/mL, α is the degree of oxygen saturation of hemoglobin,

_{Hb}^{−1}mole

^{−1}L [44

44. S. Prahl, “Optical Absorption of Hemoglobin” (Oregon Medical Laser Center, Portland, OR) (1999) http://omlc.ogi.edu/spectra/hemoglobin/.

*C*is normally equal to 150 mg/ml. We set the value of 70% for α [26

_{Hb}**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

*bvr*, since the diameter of capillary is varied between 5 and 7 µm [29

29. S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. **61**(2), 482–490 (1996). [CrossRef] [PubMed]

40. “Research in Biomedical Optics,” MIT spectroscopy, http://web.mit.edu/spectroscopy/research/biomedicaloptics.html.

_{Hb}which approximated 2% [26

**50**(6), 1071–1093 (2005). [CrossRef] [PubMed]

*β*-carotene (in cm

^{−1}) is given by:

*C*is the concentration of

_{β-car}*β*-carotene [mg/ml] and

## References and links

1. | I. A. Vitkin, R. D. Laszlo, and C. L. Whyman, “Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light,” Opt. Express |

2. | X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt. |

3. | M. F. G. Wood, X. Guo, and I. A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt. |

4. | N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. |

5. | N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. |

6. | M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. |

7. | V. V. Tuchin, L. Wang, and D. A. Zimnyakov, |

8. | V. V. Tuchin, |

9. | H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. |

10. | I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. |

11. | S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE |

12. | M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications |

13. | 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. |

14. | M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express |

15. | A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, and I. J. Bigio, “Diffuse backscattering Mueller matricesof highly scattering media,” Opt. Express |

16. | M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE |

17. | M. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE |

18. | J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express |

19. | A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “ |

20. | A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE |

21. | V. Sankaran, J. T. Walsh Jr, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. |

22. | A. Pierangelo, A. De Martino, M. Anastasiadou, P. Validire, B. Huynh, H. Cohen, and L. Schwartz, “Multispectral Mueller imaging of |

23. | 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. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. |

24. | G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. |

25. | K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. |

26. | D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. |

27. | B. Kaplan, G. Ledanois, and B. Drévillon, “Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation,” Appl. Opt. |

28. | J.-M. André, M. Catala, J.-J. Morère, E. Escudier, G. Katsanis, and J. Poirier, “Histologie: les tissus,” (Faculté de Médicine, Université Pierre et Marie Curie, PAES) (2007–2008), http://www.chups.jussieu.fr/polys/histo/histoP1/histoP1.pdf/. |

29. | S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. |

30. | H. C. van de Hulst, |

31. | G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. |

32. | M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. |

33. | J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express |

34. | J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part II,” Opt. Express |

35. | R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijistra, A. C. M. Dassel, and J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. |

36. | A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. |

37. | A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. |

38. | A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE |

39. | A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength: a simple approximation,” Proc. SPIE |

40. | “Research in Biomedical Optics,” MIT spectroscopy, http://web.mit.edu/spectroscopy/research/biomedicaloptics.html. |

41. | H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, and M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm,” Appl. Opt. |

42. | R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers,” Opt. Lett. |

43. | L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. |

44. | S. Prahl, “Optical Absorption of Hemoglobin” (Oregon Medical Laser Center, Portland, OR) (1999) http://omlc.ogi.edu/spectra/hemoglobin/. |

45. | H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. |

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(260.5430) Physical optics : Polarization

(290.4020) Scattering : Mie theory

(290.4210) Scattering : Multiple scattering

(110.5405) Imaging systems : Polarimetric imaging

**ToC Category:**

Optics of Tissue and Turbid Media

**History**

Original Manuscript: April 15, 2011

Revised Manuscript: May 31, 2011

Manuscript Accepted: May 31, 2011

Published: June 3, 2011

**Citation**

Maria-Rosaria Antonelli, Angelo Pierangelo, Tatiana Novikova, Pierre Validire, Abdelali Benali, Brice Gayet, and Antonello De Martino, "Impact of model parameters on Monte Carlo simulations of backscattering Mueller matrix images of colon tissue," Biomed. Opt. Express **2**, 1836-1851 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-7-1836

Sort: Year | Journal | Reset

### References

- I. A. Vitkin, R. D. Laszlo, and C. L. Whyman, “Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light,” Opt. Express 10(4), 222–229 (2002). [PubMed]
- X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt. 11(4), 041105 (2006). [CrossRef] [PubMed]
- M. F. G. Wood, X. Guo, and I. A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt. 12(1), 014029 (2007). [CrossRef] [PubMed]
- N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13(4), 044036 (2008). [CrossRef] [PubMed]
- N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105(10), 102023 (2009). [CrossRef]
- M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009). [CrossRef] [PubMed]
- V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, Berlin, 2006).
- V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed., SPIE Press Monograph Vol. PM166 (SPIE, Bellingham, WA, 2007).
- H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40(3), 400–412 (2001). [CrossRef] [PubMed]
- I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. 92(6), 915–923 (2002). [CrossRef]
- S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE 6842, 68420I, 68420I-7 (2008). [CrossRef]
- M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007). [CrossRef]
- 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]
- M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express 18(10), 10200–10208 (2010). [CrossRef] [PubMed]
- A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, and I. J. Bigio, “Diffuse backscattering Mueller matricesof highly scattering media,” Opt. Express 1(13), 441–453 (1997). [CrossRef] [PubMed]
- M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000). [CrossRef]
- M. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001). [CrossRef]
- J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13(12), 4420–4438 (2005). [CrossRef] [PubMed]
- A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19(2), 1582–1593 (2011). [CrossRef] [PubMed]
- A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE 7895, 78950E (2011). [CrossRef]
- V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7(3), 300–306 (2002). [CrossRef] [PubMed]
- A. Pierangelo, A. De Martino, M. Anastasiadou, P. Validire, B. Huynh, H. Cohen, and L. Schwartz, “Multispectral Mueller imaging of ex-vivo tissue,” in Proceedings of the European 1st NanoCharM Workshop on Polarization-Based Optical Techniques Applied to Biology and Medicine (nanocharm.org, 2009), pp. 32–38, http://www.nanocharm.org/images/stories/Library/Proceedings/1st%20Workshop/1stWorkshopProceedings.pdf .
- 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. M. Crawford, and M. S. 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]
- G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. 38(31), 6628–6637 (1999). [CrossRef] [PubMed]
- K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004). [CrossRef] [PubMed]
- D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. 50(6), 1071–1093 (2005). [CrossRef] [PubMed]
- B. Kaplan, G. Ledanois, and B. Drévillon, “Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation,” Appl. Opt. 40(16), 2769–2777 (2001). [CrossRef] [PubMed]
- J.-M. André, M. Catala, J.-J. Morère, E. Escudier, G. Katsanis, and J. Poirier, “Histologie: les tissus,” (Faculté de Médicine, Université Pierre et Marie Curie, PAES) (2007–2008), http://www.chups.jussieu.fr/polys/histo/histoP1/histoP1.pdf/ .
- S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. 61(2), 482–490 (1996). [CrossRef] [PubMed]
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
- G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996). [CrossRef] [PubMed]
- M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. 28(3), 237–243 (2001). [CrossRef] [PubMed]
- J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13(12), 4420–4438 (2005). [CrossRef] [PubMed]
- J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part II,” Opt. Express 13(25), 10392–10405 (2005). [CrossRef] [PubMed]
- R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijistra, A. C. M. Dassel, and J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32(4), 426–434 (1993). [CrossRef] [PubMed]
- A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996). [CrossRef] [PubMed]
- A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37(31), 7392–7400 (1998). [CrossRef] [PubMed]
- A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–268 (2000). [CrossRef]
- A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength: a simple approximation,” Proc. SPIE 5068, 393–395 (2003). [CrossRef]
- “Research in Biomedical Optics,” MIT spectroscopy, http://web.mit.edu/spectroscopy/research/biomedicaloptics.html .
- H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, and M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm,” Appl. Opt. 30(31), 4507–4514 (1991). [CrossRef] [PubMed]
- R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers,” Opt. Lett. 27(4), 246–248 (2002). [CrossRef] [PubMed]
- L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995). [CrossRef]
- S. Prahl, “Optical Absorption of Hemoglobin” (Oregon Medical Laser Center, Portland, OR) (1999) http://omlc.ogi.edu/spectra/hemoglobin/ .
- H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.