In vivo measurement of the shape of the tissue-refractive-index correlation function and its application to detection of colorectal field carcinogenesis

Abstract

Polarization-gated spectroscopy is an established method to depth-selectively interrogate the structural properties of biological tissue. We employ this method in vivo in the azoxymethane (AOM)-treated rat model to monitor the morphological changes that occur in the field of a tumor during early carcinogenesis. The results demonstrate a statistically significant change in the shape of the refractive-index correlation function for AOM-treated rats versus saline-treated controls. Since refractive index is linearly proportional to mass density, these refractive-index changes can be directly linked to alterations in the spatial distribution patterns of macromolecular density. Furthermore, we found that alterations in the shape of the refractive-index correlation function shape were an indicator of both present and future risk of tumor development. These results suggest that noninvasive measurement of the shape of the refractive-index correlation function could be a promising marker of early cancer development.

Fig. 1

Endoscopic images of a normal saline control (a) and an AOM-treated rat with a tumor (b).

Fig. 2

Extraction of the index correlation-function shape ($m$) from the copolarized intensity (top row) and crosspolarized intensity (bottom row). (a) For $g>0.85$, the intensity is a function of and independent of $g$. A power law can be fit to this dependence for different $m$ as shown in (b). The exponent of the power law has a linear relationship with $m$ as shown in (c). (d–f) are analogous to (a–c) but for the crosspolarized intensity rather than copolarized intensity.

Fig. 3

Depth-selective extraction of index correlation shape ($m$) from a dual-layer Monte Carlo model. The top layer has $m=1.1$ and bottom layer an $m$ of 1.7. The $m$ values from the copolarized and crosspolarized signals are recorded as the optical thickness ($\tau$) of the top layer is varied. For $5<\tau <15$, the copolarized $m$ parameter is sensitive to the top layer and the crosspolarized $m$ parameter is sensitive to the bottom layer.

Fig. 4

Length-scale sensitivity of index correlation function shape ($m$) measurement. (a) Percent between measured and input $m$ values after correlation function was truncated at a particular $r_{\min }$ value. (b) Percent error between measured and input $m$ values after index correlation function was perturbed at various $r_{\max }$ values according to Eq. (9).

Fig. 5

The shape of the index correlation function is sensitive to concurrent and future risk of neoplasia in the AOM-treated rat. (a) Comparison of the $m$ values from the copolarized and crosspolarized signals for saline versus all AOM-treated rats shows a statistical significant increase in $m$ ($P$ $\text{value}=0.007$ and 0.003). (b). Comparison of the shape of index correlation function shape between saline and AOM-treated rats. (c). Comparison of $m$ values between saline controls and AOM-treated rats who had and had not developed tumors at the 18-week measurement point. The $m$ value is highest for rats harboring a tumor but is also significant for AOM rats that had not yet developed a tumor. Solid circle points are group means and error bars are 95% CI.