The role of lymphatic vessels in macroscopic fluid and drug transportation in malignant tissue; and Heterogeneity-Induced Oscillations in Active Nematics
Andrew S. Brown and Alex Houston (University of Glasgow)
Thursday 23rd October 14:00-15:00
Maths 311B
Abstract
Andrew S. Brown will speak on The role of lymphatic vessels in macroscopic fluid and drug transportation in malignant tissue
Abstract:
The contribution of lymphatic capillaries in the fluid and drug transportation throughout vascularised malignant tissue is qualitatively and quantitatively discussed. Our starting point is the derivation of differential equations for coupled fluid and drug transportation across three physical domains present in vascularised tissue: the interstitium, capillary vessels and lymphatic vessels. We begin from mass and momentum balance equations in each physical domain, which are geometrically characterised by the inter-capillary distance (microscale). The Kedem-Katchalsky equations are used to account for blood and drug exchange across the vessel walls. Employing asymptotic homogenisation, we can formulate a multiscale model which allows for macroscale variations of the microstructure, under the regular assumptions such as local periodicity, accounting for spatial heterogeneity of the angiogenic nature of the capillary and lymphatic networks. At the macroscale, the fluid dynamics are governed by a triple coupled porous medium problem characterised by Darcy’s law; whereas drug dynamics are characterised by a triple coupled advection-diffusion-reaction model. The microscopic properties of the malignant tissue are effectively encoded into a series of macroscopic coefficients, which enable the analysis of geometric changes at the microscale from a macroscopic perspective. We will briefly discuss analysis of the models’ isotropic case, which reveals the existence of an optimal permeability for lymphatic vessels, allowing for optimised fluid and drug transport. The purpose of this work is to create more general theoretical models, deepening our understanding of anti-cancer strategies.
Abstract:
The contribution of lymphatic capillaries in the fluid and drug transportation throughout vascularised malignant tissue is qualitatively and quantitatively discussed. Our starting point is the derivation of differential equations for coupled fluid and drug transportation across three physical domains present in vascularised tissue: the interstitium, capillary vessels and lymphatic vessels. We begin from mass and momentum balance equations in each physical domain, which are geometrically characterised by the inter-capillary distance (microscale). The Kedem-Katchalsky equations are used to account for blood and drug exchange across the vessel walls. Employing asymptotic homogenisation, we can formulate a multiscale model which allows for macroscale variations of the microstructure, under the regular assumptions such as local periodicity, accounting for spatial heterogeneity of the angiogenic nature of the capillary and lymphatic networks. At the macroscale, the fluid dynamics are governed by a triple coupled porous medium problem characterised by Darcy’s law; whereas drug dynamics are characterised by a triple coupled advection-diffusion-reaction model. The microscopic properties of the malignant tissue are effectively encoded into a series of macroscopic coefficients, which enable the analysis of geometric changes at the microscale from a macroscopic perspective. We will briefly discuss analysis of the models’ isotropic case, which reveals the existence of an optimal permeability for lymphatic vessels, allowing for optimised fluid and drug transport. The purpose of this work is to create more general theoretical models, deepening our understanding of anti-cancer strategies.
Alex Houston will speak on Heterogeneity-Induced Oscillations in Active Nematics.
Abstract:
The framework of active nematics may be used to model many living systems, including cell layers and bacteria [1]. The study of active nematics has focused on uniform activity, but real biological systems are not homogeneous, rather they have population variance or are composed of different species. As well as arising naturally, it has been recently demonstrated that the structure of activity in a material can be controlled through modulating light intensity [2]. This provides motivation to understand the effects of activity patterning, both to gain insight into the in vivo behaviour of living systems and to enable desired dynamics to be engineered in active matter.
A central feature of active nematics is that, when confined, they exhibit a transition to a flowing state, provided their activity exceeds a critical value [3]. In this context we show that activity variation allows control of the structure of the flowing state and, most strikingly, can lead to oscillatory dynamics. We show analytically that the behaviour of the confined active nematic can be mapped onto a dynamical system, the coefficients of which are determined by the activity variation, and confirm these results numerically. We find that an activity gradient can induce oscillations, and in this case determine how the properties of the system influence the frequency of the oscillations.
- A. Doostmohammadi et al. Nat. Commun., 2018, 9, 3246.
- R. Zhang et al. Nat. Mater., 2021, 20, 875-882.
- R. Voituriez et al. EPL, 2005, 70, 404
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