Inferring inflammation spread rates in inflammatory bowel diseases using traveling wave solutions
Abstract
Ulcerative Colitis (UC) is an inflammatory bowel disease (IBD) characterized by continuous inflammation leading to bleeding and ulcer lesions, typically starting in the rectum. Although colonoscopy enables clinicians to visualize the colon and assess disease severity using endoscopic scores, it focuses only on the most severe lesions and neglects their spatial distribution along the colon. Moreover, it does not provide any information on the speed at which inflammation propagates, a key indicator for improving diagnosis and patient follow-up. In this paper, we propose a novel method to infer the inflammation propagation speed in UC from colonoscopy videos. We model the spatial distribution of lesions as a traveling wave solution of a Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) reaction-diffusion equation. Taking advantage of the uniqueness of the traveling wave profile up to spatial translation, we estimate the inflammation propagation speed by fitting this profile to the observed lesion distribution. We further derive the invasion time, defined as the time until the entire colon becomes inflamed (pancolitis). We evaluated our approach on an in-house dataset of colonoscopy videos from UC patients. Our method demonstrates strong agreement between the ground-truth lesion profiles and the estimated profiles. Regarding inflammation propagation speed, we found that bleeding lesions propagate faster than ulcer lesions among patients with the same disease type, resulting in shorter invasion times until pancolitis. Our approach provides a new perspective for understanding the pathogenesis of IBDs and highlights the importance of accounting for the spatial distribution of endoscopic lesions in precise disease assessment.
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BibTeX
@misc{alali2026inferring,
title = {{Inferring inflammation spread rates in inflammatory bowel diseases using traveling wave solutions}},
author = {Safaa Al-Ali and Yoram Bouhnik and John Chaussard and Sébastien Li-Thiao-Té and Eric Ogier-Denis and Alice Percy-Du-Sert and Carmen Stefanescu and Xavier Treton and Hatem Zaag},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05616896v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Inferring inflammation spread rates in inflammatory bowel diseases using traveling wave solutions
AU - Safaa Al-Ali
AU - Yoram Bouhnik
AU - John Chaussard
AU - Sébastien Li-Thiao-Té
AU - Eric Ogier-Denis
AU - Alice Percy-Du-Sert
AU - Carmen Stefanescu
AU - Xavier Treton
AU - Hatem Zaag
PY - 2026
DA - 2026/09/25
PB - HAL
UR - https://hal.science/hal-05616896v2
AB - Ulcerative Colitis (UC) is an inflammatory bowel disease (IBD) characterized by continuous inflammation leading to bleeding and ulcer lesions, typically starting in the rectum. Although colonoscopy enables clinicians to visualize the colon and assess disease severity using endoscopic scores, it focuses only on the most severe lesions and neglects their spatial distribution along the colon. Moreover, it does not provide any information on the speed at which inflammation propagates, a key indicator for improving diagnosis and patient follow-up. In this paper, we propose a novel method to infer the inflammation propagation speed in UC from colonoscopy videos. We model the spatial distribution of lesions as a traveling wave solution of a Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) reaction-diffusion equation. Taking advantage of the uniqueness of the traveling wave profile up to spatial translation, we estimate the inflammation propagation speed by fitting this profile to the observed lesion distribution. We further derive the invasion time, defined as the time until the entire colon becomes inflamed (pancolitis). We evaluated our approach on an in-house dataset of colonoscopy videos from UC patients. Our method demonstrates strong agreement between the ground-truth lesion profiles and the estimated profiles. Regarding inflammation propagation speed, we found that bleeding lesions propagate faster than ulcer lesions among patients with the same disease type, resulting in shorter invasion times until pancolitis. Our approach provides a new perspective for understanding the pathogenesis of IBDs and highlights the importance of accounting for the spatial distribution of endoscopic lesions in precise disease assessment.
ER -