Estimation of optical properties of neuroendocrine pancreas tumor with double-integrating-sphere system and inverse Monte Carlo model

Abstract

The investigation of laser-tissue interaction is crucial for diagnostics and therapeutics. In particular, the estimation of tissue optical properties allows developing predictive models for defining organ-specific treatment planning tool. With regard to laser ablation (LA), optical properties are among the main responsible for the therapy efficacy, as they globally affect the heating process of the tissue, due to its capability to absorb and scatter laser energy. The recent introduction of LA for pancreatic tumor treatment in clinical studies has fostered the need to assess the laser-pancreas interaction and hence to find its optical properties in the wavelength of interest. This work aims at estimating optical properties (i.e., absorption, μ _a , scattering, μ _s , anisotropy, g, coefficients) of neuroendocrine pancreas tumor at 1064 nm. Experiments were performed using two popular sample storage methods; the optical properties of frozen and paraffin-embedded neuroendocrine tumor of the pancreas are estimated by employing a double-integrating-sphere system and inverse Monte Carlo algorithm. Results show that paraffin-embedded tissue is characterized by absorption and scattering coefficients significantly higher than frozen samples (μ _a of 56 cm⁻¹ vs 0.9 cm⁻¹, μ _s of 539 cm⁻¹ vs 130 cm⁻¹, respectively). Simulations show that such different optical features strongly influence the pancreas temperature distribution during LA. This result may affect the prediction of therapeutic outcome. Therefore, the choice of the appropriate preparation technique of samples for optical property estimation is crucial for the performances of the mathematical models which predict LA thermal outcome on the tissue and lead the selection of optimal LA settings.

Appendix

The power deposition in tissue causes temperature increase that can be estimated by the bioheat equation [28, 29]:

$$ \rho \cdot c\frac{\partial T\left(x,y,z,t\right)}{\partial t}=\nabla \left(k\nabla T\left(x,y,z,t\right)\right)+{Q}_b+{Q}_{\begin{array}{l}l\\ {}\end{array}} $$

(3)

where ρ is the density [kg m⁻³], c is the specific heat [J kg⁻¹ K⁻¹] and k is the heat conductivity [W m⁻¹ K⁻¹] of tissue. T(x,y,z,t) is the tissue temperature, function of spatial coordinates x, y, and z and of time, t [s]. Tissue is assumed to be homogeneous and isotropic to make the heat transfer analysis more feasible and to maintain generality. Other terms in Eq. 3 are as follows:Q _b [W m⁻³], the heat absorption due to blood perfusion per volume unit in the tissue:

$$ {Q}_b={\rho}_b\cdot {c}_b\cdot {w}_b\left(T\left(x,y,z,t\right)-{T}_b\right) $$

(4)

where ρ _b is the density [kg m⁻³], c _b the specific heat [J kg⁻¹ K⁻¹], w _b the perfusion rate per volume unit [s⁻¹], and T _b the temperature of blood;Q _l [W m⁻³], the laser heat source term, related to tissue optical properties according to the Lambert-Beer law:

$$ {Q}_l={\mu}_{\mathrm{eff}}\cdot {P}_d\cdot {e}^{-{\mu}_{\mathrm{eff}}\cdot z} $$

(5)

The effective attenuation coefficient, μ _eff, determines the amount of laser energy converted into heat due to light penetration and depends on μ _a , μ _s , and g (Eq. 6):

$$ {\mu}_{\mathrm{eff}}=\sqrt{3{\mu}_a\left({\mu}_a+{\mu}_s\left(1-g\right)\right)} $$

(6)

Constant values are as follows: for pancreas, ρ = 1040 kg m⁻³, c = 3590 J kg⁻¹ K⁻¹, and k = 0.5417 W m⁻¹ K⁻¹; for blood, ρ _b  = 1060 kg m⁻³, c _b  = 3640 J kg⁻¹ K⁻¹, and w _b  = 0.03 s⁻¹.Laser settings are as follows: laser power density (P _d) 8 W cm⁻² and treatment time 200 s. Simulations are implemented in Comsol Multiphysics® environment, considering a 3D cylindrical geometry. Initial tissue and blood temperature, as well as boundary conditions, are 310 K.