Terahertz Mie scattering in tissue: diffuse polarimetric imaging and Monte Carlo validation in highly attenuating media models

Abstract

Significance: Changes in the structure of tissue occur in many disease processes, such as the boundaries of cancerous tumors and burn injuries. Spectroscopic and polarimetric alterations of terahertz light caused by Mie scattering patterns have the potential to be a diagnostic marker.

Aim: We present an analysis of Monte Carlo simulation of Mie scattering of polarized terahertz light from cancerous tumor budding, compare the simulation with experimental results obtained in phantom models, and present an analysis of a polarization-sensitive terahertz scan of an ex vivo porcine burn injury.

Approach: Using a Monte Carlo simulation, we modeled the changes in diffuse intensity and degree of polarization of broadband off-specular terahertz light due to scattering particles in highly attenuating tissue. We extracted the Mueller matrix of the tissue using this model and analyzed the Lu-Chipman product decomposition matrices. We compared this model with experimental data from four phantoms consisting of polypropylene particles of varying sizes embedded in gelatin. Finally, we induced a full-thickness burn injury in ex vivo porcine skin samples and compared experimental data captured over burned and healthy regions of the tissue.

Results: Simulation revealed contrast in the Stokes vectors and Mueller Matrix elements for varying scattering particle sizes. Experimental phantom results showed contrast between different sizes of scattering particles in degree of polarization and diffuse intensity in agreement with Monte Carlo simulation results. Finally, we demonstrated a similar diffused imaging signal contrast between burned and healthy regions of ex vivo porcine skin.

Conclusion: Polarimetric terahertz imaging has the potential to detect structural changes due to biological disease processes.

Keywords: Mie scattering; degree of polarization; diffused scattering; terahertz time-domain spectroscopic imaging; terahertz time-domain spectroscopy and polarimetry; tumor budding.

Fig. 1

(a) Diagram of the experimental setup. E = emitter, D = detector, L1 = TPX lens with 50-mm focal length, L2 = PTFE lens with 100-mm focal length, WGP = wire-grid polarizer, and P = phantom. (b) HDPE container used for holding scattering material (SM). (c)–(d) Angular distribution of coherent and incoherent power measured from LDPE scattering material. Measurements from 160 deg to 180 deg were made with the addition of a beam-splitter in the beam path.

Fig. 2

(a) Artistic representation of relevant spherical tissue structure sizes compared to terahertz wavelengths. (b) Mie scattering parameter for particle sizes 50 to $500\mu \mathrm{m}$. (c) Representative optical microscopy images of fabricated phantoms.

Fig. 3

Measured refractive indexes and absorption coefficients of gelatin and polypropylene. Refractive indexes and absorption coefficients of water and skin are included for comparison. Refractive index and absorption coefficient values between water and skin were adopted as our simulation input.

Fig. 4

Flowchart indicating the simulation input parameters and the interface between the Mie Calculator and Polarized Light Monte Carlo model.

Fig. 5

Calculated scattering efficiency and asymmetric factor for relevant particle sizes.

Fig. 6

Spatial map of the simulated Stokes vector, IQUV, for phantoms A and D at 0.6 THz.

Fig. 7

Simulated Mueller Matrix for phantoms A and D at 0.6 THz.

Fig. 8

(a) Experimental setup for diffuse phantom scattering measurements. Simulated (b) and measured (c) diffuse scattered intensity from phantoms A–D are shown. Experimental results are obtained at only one detection angle, as shown in sub-figure (a). The degree of polarization (DOP) is compared between simulation (d) and experimental (e) diffuse scattered beams for different phantoms.

Fig. 9

(a) Visual image of an ex vivo porcine skin burn scanned at a diffuse angle to produce DOP (b) and diffused scattered intensity (c) maps at 0.6 THz.

Fig. 10

Simulated diffuse reflectance ($R_d$), linear DOP, and circular DOP from 0 to 2 THz.