Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. II. Quantitative examinations of the steady-state theory

Collagen Complexity Spatially Defines Microregions of Total Tissue Pressure in Pancreatic Cancer

The poor efficacy of systemic cancer therapeutics in pancreatic ductal adenocarcinoma (PDAC) is partly attributed to deposition of collagen and hyaluronan, leading to interstitial hypertension collapsing blood and lymphatic vessels, limiting drug delivery. The intrinsic micro-regional interactions between hyaluronic acid (HA), collagen and the spatial origins of mechanical stresses that close off blood vessels was investigated here. Multiple localized pressure measurements were analyzed with spatially-matched histochemical images of HA, collagen and vessel perfusion. HA is known to swell, fitting a linear elastic model with total tissue pressure (TTP) increasing above interstitial fluid pressure (IFP) directly with collagen content. However, local TTP appears to originate from collagen area fraction, as well as increased its entropy and fractal dimension, and morphologically appears to be maximized when HA regions are encapsulated by collagen. TTP was inversely correlated with vascular patency and verteporfin uptake, suggesting interstitial hypertension results in vascular compression and decreased molecular delivery in PDAC. Collagenase injection led to acute decreases in total tissue pressure and increased drug perfusion. Large microscopic variations in collagen distributions within PDAC leads to microregional TPP values that vary on the hundred micron distance scale, causing micro-heterogeneous limitations in molecular perfusion, and narrows viable treatment regimes for systemically delivered therapeutics.

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. V. Steady-state fluorescence

As Part V in our series, this paper examines steady-state fluorescence photon diffusion in a homogenous medium that contains a homogenous distribution of fluorophores, and is enclosed by a "concave" circular cylindrical applicator or is enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to predict by analytics and examine with the finite-element method the changing characteristics of the fluorescence-wavelength photon-fluence rate and the ratio (sometimes called the Born ratio) of it versus the excitation-wavelength photon-fluence rate, with respect to the source-detector distance. The analysis is performed for a source and a detector located on the medium-applicator interface and aligned either azimuthally or longitudinally in both concave and convex geometries. When compared to its steady-state counterparts on a semi-infinite medium-applicator interface with the same line-of-sight source-detector distance, the fluorescence-wavelength photon-fluence rate reduces faster along the longitudinal direction and slower along the azimuthal direction in the concave geometry, and conversely in the convex geometry. However, the Born ratio increases slower in both azimuthal and longitudinal directions in the concave geometry and faster in both directions in the convex geometry, respectively, when compared to that in the semi-infinite geometry.

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. IV. Frequency-domain analysis

Part IV examines frequency-domain photon diffusion in a homogeneous medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to assess by analogical and finite-element methods the changes of AC amplitude, modulation depth, and phase with respect to the line-of-sight source-detector distance for a source and a detector located along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts along a straight line on a semi-infinite medium-applicator interface, for the same line-of-sight source-detector distance, it is found that: (1) the decay-rate of AC photon fluence is smaller along the azimuthal direction and greater along the longitudinal direction on the concave interface, (2) the decay-rate of AC photon fluence is greater along the azimuthal direction and smaller along the longitudinal direction on the convex interface, (3) the modulation depth along both azimuthal and longitudinal directions decays more slowly on the concave interface and faster on the convex interface, and (4) the phase along both azimuthal and longitudinal directions increases more slowly on the concave interface and faster on the convex interface.

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. III. Synthetic study of continuous-wave photon fluence rate along unique spiral paths

This is Part III of the work that examines photon diffusion in a scattering-dominant medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator. In Part II of this work Zhang et al. [J. Opt. Soc. Am. A, 66 (2011)] predicted that, on the tissue-applicator interface of either "concave" or "convex" geometry, there exists a unique set of spiral paths, along which the steady-state photon fluence rate decays at a rate equal to that along a straight line on a planar semi-infinite interface, for the same line-of-sight source-detector distance. This phenomenon of steady-state photon diffusion is referred to as "straight-line-resembling-spiral paths" (abbreviated as "spiral paths"). This Part III study develops analytic approaches to the spiral paths associated with geometry of a large radial dimension and presents spiral paths found numerically for geometry of a small radial dimension. This Part III study also examines whether the spiral paths associated with a homogeneous medium are a good approximation for the medium containing heterogeneity. The heterogeneity is limited to an anomaly that is aligned azimuthally with the spiral paths and has either positive or negative contrast of the absorption or scattering coefficient over the background medium. For a weak-contrast anomaly the perturbation by it to the photon fluence rate along the spiral paths is found by applying a well-established perturbation analysis in cylindrical coordinates. For a strong-contrast anomaly the change by it to the photon fluence rate along the spiral paths is computed using the finite-element method. For the investigated heterogeneous-medium cases the photon fluence rate along the homogeneous-medium associated spiral paths is macroscopically indistinguishable from, and microscopically close to, that along a straight line on a planar semi-infinite interface.

Diffuse photon remission along unique spiral paths on a cylindrical interface is modeled by photon remission along a straight line on a semi-infinite interface

We demonstrate that, for a long cylindrical applicator that interfaces concavely or convexly with a scattering-dominant medium, a unique set of spiral-shaped directions exist on the tissue-applicator interface, along which the diffuse photon remission is essentially modeled by the photon remission along a straight line on a semi-infinite interface. This interesting phenomenon, which is validated in steady state in this work by finite-element and Monte Carlo methods, may be particularly useful for simplifying deeper-tissue sensing in endoscopic imaging geometry.