Mechanophysiology of endometriosis: a non-dimensional physiomarker to detect retrograde flow

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Patankar doi: https://doi.org/10.1101/2024.05.13.593987 Guy Elisha 1 Department of Mechanical Engineering Northwestern University , Evanston, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Guy Elisha Neelesh A. Patankar 1 Department of Mechanical Engineering Northwestern University , Evanston, IL, USA 2 Department of Engineering Sciences and Applied Mathematics, Northwestern University , Evanston, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Neelesh A. Patankar For correspondence: n-patankar{at}northwestern.edu Abstract Full Text Info/History Metrics Preview PDF Abstract Endometriosis affects a significant portion of fertile-age women, often leading to infertility and a substantial decline in quality of life. Despite its prevalence, current diagnostic methods are limited, focusing on assessing the presence or absence of endometrial lesion, rather than the origin of the disorder. Thus, resulting in underdiagnosis. A potential mechanics-based metric for diagnosing endometriosis is proposed here by leveraging the retrograde menstruation hypothesis. By examining the interplay between uterine and fallopian tube peristalses, a non-dimensional physiomarker is introduced to signify the onset of retrograde flow. The analysis reveals that increased uterine contractile activity, coupled with decreased fallopian tube contractile activity, correlates with retrograde flow, suggesting a predisposition to endometriosis. This mechanophysiology-based approach offers a promising avenue for origin based diagnosis, with the proposed non-dimensional physiomarker – the endometriosis number – serving as a potential indicator of endometrial cell migration and the onset of endometriosis. 1 Introduction Endometriosis is estimated to affect roughly 10% of fertile-age women, accounting for up to 50% of female infertility cases, and can have a debilitating effect on women’s lives [ 1 , 2 ]. The severe pain interferes with daily activities, relationships, and livelihood [ 3 ]. The disorder is characterized by the endometrium tissue, which is normally inside the uterus, growing outside the uterine cavity. During healthy menstrual cycle, the endometrium tissue inside the uterus thickens, breaks down, and is shed as menstrual blood. During endometriosis, the same process occurs, but the tissue also grows in places outside the uterus covering the ovaries and fallopian tubes. Consequently, after shedding, the blood cannot exit the body [ 4 ]. Despite its prevalence, endometriosis is under-researched and it often goes undiagnosed [ 5 , 6 ]. Accurate diagnosis of endometriosis requires invasive techniques, contributing to a lack of diagnosis [ 3 , 7 ]. In recent years, there have been repeated calls for finding more efficient diagnostic approaches [ 3 , 7 ]. Agarwal et al.[ 3 ] proposed that diagnosing endometriosis should prioritize symptoms and their origins over assessing the presence or absence of endometrial lesions. However, there is no procedure to quantify or measure the origin of endometriosis. In this work, we explore a potential mechanics-based metric to diagnose endometriosis targeting the origin. Retrograde menstruation hypothesis is a widely accepted plausible explanation for the development of endometriosis [ 8 , 9 ]. It suggests that during menstruation, some menstrual blood containing endometrial cells flows backward through the fallopian tubes into the pelvic cavity instead of being expelled from the body. These endometrial cells then implant and grow in various pelvic locations, leading to the development of endometriosis. Here we focus on finding a diagnostic metric for endometriosis motivated by the success of mechanics-based tools and criteria to diagnose and assess disease progression in other organs [ 11 , 12 ]. Mechanics-based approaches to investigate the physiology (mechanophysiology) of both the uterus and the fallopian tubes have been reported in the past [13, 14, 15, 16, 17, 18, 19]. Studies so far have treated the uterus and fallopian tubes as separate entities, without exploring potential emergent outcomes due to their interconnected influence. Here, we explore if the competition between uterine peristalsis and fallopian tubes’ peristalsis gives insights into when flow becomes retrograde (from the cervix to the fundus into the fallopian tubes, see Fig. 1 ). By doing so, we come up with a non-dimensional physiomarker (a physics-based metric) which marks the critical condition for the onset of retrograde flow. Download figure Open in new tab Figure 1: Uterine cavity and the fallopian tubes intersect around the fundus. The directions of the muscle contractions waves of the uterus and the fallopian tubes are marked with arrows, both directing towards the fundus during potential retrograde flow. Images reproduced with permission from [ 10 ]. Labels and arrows were added to the original image. 2 Mathematical analysis 2.1 Uterus Let a u represent the mean half-height of the uterus channel and λ u denote the uterus peristaltic wavelength. According to Eytan et al. [ 13 ] and Aranda et al. [ 20 ], it holds that a u /λ u << 1. Additionally, uterine Reynolds number ( Re u ) satisfies where c u is the uterine peristaltic wave speed and ν u denotes kinematic viscosity of the uterine fluid. Thus, uterine flow is almost inertialess. Given these assumptions, we utilize the solution for a peristaltic flow inside a two-dimensional planar channel geometry derived by Shapiro et al. [ 21 ] given by where μ u represents the dynamic viscosity of the uterine fluid, Δ P λu denotes the uterine pressure rise per wavelength, and ϕ u = b u /a u indicates the uterine amplitude ratio, where b u stands for the half-amplitude of the uterine peristaltic wave. Additionally, signifies the dimensionless time-averaged flowrate in the uterus, where represents the time-averaged volumetric flowrate at each cross-section along the uterus, and w u denotes the width of the uterine channel [ 21 ]. The pressure rise over the entire uterus length is expressed by where Δ P Lu signifies the pressure at the junction of the uterus and the fallopian tubes (the fundus), f u is the uterus peristaltic frequency, and N u indicates the number of wavelengths in the uterine length. Note that we assume that the pressure at the entrance of the uterus (the cervix) is zero. 2.2 Fallopian Tubes Similarly, to express the pressure rise over the length of a fallopian tube (Δ P Lf ), we again assume that a f /λ f << 1 and Re → 0 ( a f and λ f denote the radius of the fallopian tube and the fallopian tube peristaltic wavelength, respectively). It follows from Shapiro et al. [ 21 ] that where μ f represents the dynamic viscosity of the fallopian tube fluid, f f is the fallopian tube peristaltic frequency, N f indicates the number of wavelengths in the length of the fallopian tube, signifies the time-averaged volumetric flowrate at each cross-section along the fallopian tube, ϕ f = b f /a f indicates the fallopian tube amplitude ratio, and b f stands for the half-amplitude of the fallopian tube peristaltic wave. Note that Eq. (4) represents the flow through one fallopian tube, but the system consists of two tubes intersecting with the uterus. Furthermore, by convention, the traveling contraction in the fallopian tube is in the opposite direction to the one of the uterus ( Fig. 1 ). Hence, the net flow in the fallopian tubes from the fundus toward the ovaries is given by . Finally, it is assumed that the pressure at the ovarian end of the fallopian tubes (in the pelvic cavity) is zero. 2.3 Critical Condition At the junction of the uterus and the fallopian tubes, it is required that Δ P Lu = Δ P Lf and to satisfy steady-state momentum and mass conservation equations. These conditions when imposed in Eqs. (3) and (4) give the solutions for the volumetric flow rate and pressure drop as depicted in Fig. 2a . If the solution for the volumetric flow rate is such that , then the flow is retrograde; there is no retrograde flow if . Download figure Open in new tab Figure 2: (a) A sketch of lines representing the pressure rise over the length of the uterus (Δ P Lu ) and the fallopian tubes (Δ P Lf ) as a function of their respective time-averaged volumetric flowrates ( and ). The intersection of the two lines, for specific parameters in Eqs. (3) and (4) , gives the solution for the volumetric flowrate and the pressure drop (Δ P = Δ P Lu = Δ P Lf ). If the solution is such that (e.g. red and black lines) then the flow is retrograde. Alternately, if (e.g. red and green lines) then there is no retrograde flow. (b) Graph showing the dimensionless endometriosis number ψ vs. ϕ , derived from Eq. (7) , along with possible range for clinical values for ψ and ϕ (orange rectangle). The graph separates the ϕ – ψ space into retrograde and no retrograde scenarios. We can establish a critical condition for retrograde flow using Fig 2a . Consider parameters such that the uterine peristaltic flow is represented by the red line ( Eq. 3 ) in Fig 2a . Now consider three different scenarios for fallopian tube peristaltic flows represented by the green, blue, and black lines ( Eq. 4 ) in Fig 2a . It is seen that if the fallopian tube peristalsis is represented by the black line then the flow will be retrograde because it intersects the red uterine flow line for , whereas if the fallopian tube peristalsis is represented by the green line then the flow won’t be retrograde ( Fig 2a ). It is evident that the blue line case is the borderline scenario between retrograde and no retrograde flow because when it intersects with the red uterine peristalsis line. This shows that, no retrograde flow will take place if where the equality represents the critical condition. We substitute Eqs. (3) and (4) into Eq. (5) to derive for no retrograde flow. We define a non-dimensional number and assume that ϕ u ≈ ϕ f (= ϕ ). Thus, the no retrograde flow condition can be expressed in terms of parameter ψ , such that By setting up this inequality, we find an endometriosis number ψ as a potential physiomarker , which is based on measurable physical quantities on a patient specific basis. It can be used to quantify the critical condition for the onset of retrograde flow potentially causing endometriosis. The plot of the equation above is displayed in Fig. 2b and is discussed in greater details in the following section. Notice that where τ u and τ f are the scales of viscous shear stresses on the walls of the uterus and the fallopian tubes, respectively. To ensure that there is no retrograde flow, the fallopian tubes’ viscous resistance must be greater than that of the uterus. 3 Discussion The graph plotted in Fig. 2b , obtained from Eq. (7) , delineates a space wherein distinct scenarios of retrograde flow and no retrograde flow can be distinguished. Thus, by extracting physical measurements of a particular individual, such as contraction frequency and tube thickness (referenced in Table 1 ), we can compute ψ and ϕ , and thereby determine the presence or absence of retrograde flow. View this table: View inline View popup Download powerpoint Table 1: List parameters and their values gathered from prior clinical studies We gather the necessary parameter values for calculating ψ and ϕ from prior clinical studies, detailed in Table 1 , and make the assumption that μ u = μ f . We find that the clinically plausible range for the endometriosis number ψ is approximately within 0.01 to 150. Smaller ψ values (ranging between 0 to 50) are far more common. Moreover, empirical data indicates that ϕ → 0 since a >> b . Hence, Eq. (7) simplifies to ψ > 7.1, indicating that retrograde flow manifests when ψ > 7.1. This conclusion remains consistent when examining various combinations of ψ and ϕ plotted in Fig. 2b . Importantly, we deduce that retrograde flow presence is solely dictated by the endometriosis number ψ . Leyendecker et al. [ 33 ] reported significant increase in the peristaltic activity (frequency) of the uterus in infertile female diagnosed with endometriosis. Kunz and Leyendecker [ 34 ] and Kissler et. al [ 35 ] observed hypercontractile activity of the uterus in certain patients, noting that this condition may be involved in the development of endometriosis. Xia et al. [ 29 ] have recorded an opposite trend in the fallopian tube. They noticed that the fallopian tubes’ contraction frequency of controls was higher than the ones of patients with endometriosis. These findings align with our results, as the endometriosis number ψ and the critical condition for retrograde flow depend on uterine and fallopian tube contraction activity. Our analysis shows that an increase in the uterine contractile activity and a decrease in the fallopian tubes’ contractile activity favor retrograde flow. To compute the patient-specific value of the endometriosis number, measurements from both the uterus and fallopian tubes are required. Uterine thickness (2 a u ) and contraction properties ( λ u , c u , f u , N u ) can be assessed using transvaginal ultrasound [ 23 ]. However, there is currently no established method for obtaining comparable data ( a f , λ f , c f , f f , N f ) for the fallopian tubes in vivo. The parametric values for the fallopian tubes listed in Table 1 have been gathered in vitro [ 29 , 25 ]. If similar non-invasive techniques can be developed to obtain fallopian tube data, as has been done for the uterus, our proposed approach could offer a less-invasive alternative to laparoscopy. Laparoscopy, a surgical procedure currently considered the gold standard for endometriosis diagnosis, is invasive in nature [ 3 , 7 ]. This study provides a mechanophysiology-based analysis aimed at diagnosing an individual’s predisposition to developing endometriosis. By computing the endometriosis number ψ introduced in this work, we can determine the presence of retrograde flow, indicating a likelihood of endometrial cell migration beyond the uterine cavity and suggesting the onset of endometriosis. Future work focused on testing the endometriosis number ψ though clinical measurements of both patients and controls is recommended. Acknowledgments This work was funded by the by the National Science Foundation (OAC grant 1931372). References [1]. ↵ Giudice , L. C. , 2010 , “ Endometriosis ,” New England Journal of Medicine , 362 ( 25 ), pp. 2389 – 2398 . OpenUrl CrossRef PubMed Web of Science [2]. ↵ Carter , J. E. , 1994 , “ Combined hysteroscopic and laparoscopic findings in patients with chronic pelvic pain ,” The Journal of the American Association of Gynecologic Laparoscopists , 2 ( 1 ), pp. 43 – 47 . OpenUrl CrossRef PubMed Web of Science [3]. ↵ Agarwal , S. K. , Chapron , C. , Giudice , L. C. , Laufer , M. R. , Leyland , N. , Missmer , S. 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OpenUrl CrossRef PubMed [35]. ↵ Kissler , S. , Hamscho , N. , Zangos , S. , Wiegratz , I. , Schlichter , S. , Menzel , C. , Doebert , N. , Gruenwald , F. , Vogl , T. , Gaetje , R. , et al. , 2006 , “ Uterotubal transport disorder in adenomyosis and endometriosis—a cause for infertility ,” BJOG: An International Journal of Obstetrics & Gynaecology , 113 ( 8 ), pp. 902 – 908 . OpenUrl Back to top Previous Next Posted May 16, 2024. Download PDF Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. 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