Khabaz, K. | bioRxiv Science

bioRxiv2022

e-cone and d-cone singularities drive submucosal collagen fiber remodeling in intestinal anastomotic surgery

Following resection of a diseased segment of intestine, a reconnection (anastomotic) geometry is chosen to reduce postoperative stress and optimize outcomes. As proper healing of an intestinal anastomosis is strongly affected by its mechanobiology, much attention has been devoted to the conical structures formed along the suture lines, where stress-focusing is expected. However, geometric considerations reveal that in addition to the obvious loci of stress-focusing, additional remote locations of stress-focusing may form. We identify conical structures that inevitably form within regions of otherwise uninterrupted tissue. In this work we use geometric analysis, finite element modeling (FEM), and in-vivo experiments to investigate these emergent stress-focusing structures, their mechanical stresses, and the resulting submucosal collagen fiber re-orientation, as these naturally arise in the side-to-side small bowel anastomosis (SBA), the most common configuration performed in patients. FEM predicts the appearance of remote high-stress regions. Allowing for tissue remodeling, our simulations also predict an increased dispersion of submucosal collagen fibers in these regions. In-vivo experiments performed on ten-week-old male C57BL/6 mice assigned the creation of side-to-side SBA or sham-laparotomy corroborate this result. Anastomoses were analyzed at sacrifice on post-operative day (POD) 14 and 88 with histologic-sectioning, staining, high magnification imaging, and submucosal collagen fiber orientation ({kappa}) mapping. The mean and variance of{kappa} , a measure of collagen fiber dispersion, at POD-14 far from the anastomosis show similar values to those obtained for sham-operated mice, while the FEM-predicted loci of stress-focusing display statistically significant higher values. The values at POD-88 at all loci show no statistically-significant difference, and agree with those of the sham-operated mice at POD-14.

bioengineering↗

bioRxiv2022

Aortic Shape Space Topology

Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature ({delta}K) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing{delta} K forming the hallmark of aortic disease. Divergent{delta} K is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8 {+/-}1.7%. The analysis of{delta} K can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes.

bioengineering↗