Multiscale Dynamics of Blood Flow and Associated Cycling Hypoxia in Vascular Tumours
Lead Research Organisation:
UNIVERSITY OF OXFORD
Department Name: Mathematical Institute
Abstract
It has long been hypothesised that the abnormal and heterogeneous architecture of tumour vascular networks promotes irregular spatio-temporal variations in blood flow rates, haematocrit distribution, and consequent oxygen delivery. These irregularities can cause the formation of cyclic hypoxic areas - regions experiencing transient periods of oxygen deprivation and reoxygenation. Exposure to such fluctuating oxygen levels is assumed to select and promote metastatic spread and resistance to radio- and chemo-therapy. Consequently, understanding the microstructural and fluid-dynamic mechanisms that promote macroscopic oxygenation oscillations and how they may be clinically altered is of great importance.
The goal of this project is to develop a multiscale mathematical framework to model blood flow and oxygen transport within vascular tumours, in order to shed light on the links between microscopic haemodynamic mechanisms and the emergence of cycling hypoxia at the macroscale. The methodology will be based on multiple-scale homogenisation - a formal mathematical approach used to derive systems of continuum equations, by upscaling descriptions of transport phenomena from the single capillary scale to the macroscopic scale of the tumour. Using this method, I will establish how microstructural vascular heterogeneities, together with flow-nonlinearities induced by haematocrit-dependent blood viscosity and biased haematocrit partitioning at vessel branch-points, can lead to macroscopic flow-oscillations and consequent unsteady tissue oxygenation. The mathematical framework thus developed could be used, in the longer term, to identify tumour structures that will benefit from transient vascular normalisation treatments, to predict the consequent effect of such protocols on diminishing hypoxia, and thereby improve and personalise tumour responses to existing treatments.
The goal of this project is to develop a multiscale mathematical framework to model blood flow and oxygen transport within vascular tumours, in order to shed light on the links between microscopic haemodynamic mechanisms and the emergence of cycling hypoxia at the macroscale. The methodology will be based on multiple-scale homogenisation - a formal mathematical approach used to derive systems of continuum equations, by upscaling descriptions of transport phenomena from the single capillary scale to the macroscopic scale of the tumour. Using this method, I will establish how microstructural vascular heterogeneities, together with flow-nonlinearities induced by haematocrit-dependent blood viscosity and biased haematocrit partitioning at vessel branch-points, can lead to macroscopic flow-oscillations and consequent unsteady tissue oxygenation. The mathematical framework thus developed could be used, in the longer term, to identify tumour structures that will benefit from transient vascular normalisation treatments, to predict the consequent effect of such protocols on diminishing hypoxia, and thereby improve and personalise tumour responses to existing treatments.
Publications

Ben-Ami Y
(2024)
Using a probabilistic approach to derive a two-phase model of flow-induced cell migration.
in Biophysical journal

Ben-Ami Y
(2022)
Structural Features of Microvascular Networks Trigger Blood Flow Oscillations.
in Bulletin of mathematical biology

Ben-Ami Y.
(2024)
Homogenisation of nonlinear blood flow in periodic networks: the limit of small haematocrit heterogeneity
in (preprint)

Ben-Ami Y.
(2024)
Using a probabilistic approach to derive a two-phase model of flow-induced cell migration
in (accepted to Biophysical Journal)
Description | • We have identified specific structural properties of microvascular networks that promote self-sustained blood flow oscillations, shedding new light on the microscale mechanisms that may contribute to the emergence in tumours of cycling hypoxia (short transient periods during which oxygen levels fluctuate from high to low levels). • We have developed a novel model for interstitial-flow-induced cell migration that allows us to interpret experimental results and to generate new predictions regarding the cell migration near to blood vessels. This was identified as a potential mechanism leading to irregular blood flow in tumours. • We have developed an analytical methodology to homogenise blood flow in periodic microvascular network. This model can be used to simulate blood flow at the macroscale and, thus, to facilitate analysis of phenomena occurring at the scale of the tissue. |
Exploitation Route | • The specific micro-structural features that promote blood flow oscillations, which have been discovered during this award, could be validated using in-vitro microfluidic experiments. Additionally, these structures could be identified in images of tumour vasculature and used to cross-register the presence of these network motifs with instances of cycling hypoxia. • The homogenised blood flow model could be used to investigate blood/ haematocrit-related phenomena at the tissue scale. For example, it could be used to understand how the microscale geometry of the tumour vasculature affects the distribution of haematocrit at the tumour scale and the associated hypoxic landscape. • The flow-induced cell migration model could be used to generate predictions regarding the movement of tumour cells in the vicinity of blood vessels and to generate hypotheses regarding mechanisms of intravasation and vessel collapse in tumours. Such predictions could be examined in dedicated microfluidic experiments. |
Sectors | Healthcare Pharmaceuticals and Medical Biotechnology |
Title | Blood Flow Homogenisation |
Description | Developed an analytical methodology to homogenise (coarse-grain) blood flow in microvascular networks. |
Type Of Material | Computer model/algorithm |
Year Produced | 2024 |
Provided To Others? | Yes |
Impact | n/a |
URL | https://doi.org/10.48550/arXiv.2401.10932 |
Title | Multiphase cell migration model |
Description | Developed a novel model for interstitial-flow-induced cell migration, based on a hybrid approach in which the cells are modelled using a probabilistic formulation and the interstitial flow is modelled as a continuum. |
Type Of Material | Computer model/algorithm |
Year Produced | 2023 |
Provided To Others? | Yes |
Impact | n/a |
URL | https://github.com/yaronbenami/cell_migration |
Description | Brian Wood |
Organisation | Oregon State University |
Country | United States |
Sector | Academic/University |
PI Contribution | Contributed our expertise in modelling of blood flow and homogenisation of flow in networks. |
Collaborator Contribution | Contributed their expertise in different homogenisation methodologies and the use of machine learning to nonlinear closure problems. |
Impact | - Publication - https://doi.org/10.48550/arXiv.2401.10932 - Grant proposal submitted (joint EPSRC/NSF) |
Start Year | 2023 |
Description | Complexity Cluster |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Postgraduate students |
Results and Impact | Organised workshops at Keble College in Oxford (once a term during the 2023/24 academic year), in which early career researchers in mathematics shared their work with a general audience of post- and under-graduate students. The goal was to showcase how mathematics can be used to describe different phenomena and to spark interest among students. |
Year(s) Of Engagement Activity | 2023,2024 |
Description | Invited seminars |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Postgraduate students |
Results and Impact | Presented our work in a series of invited seminars in Universities across the UK in order to expose our research to the broader scientific community and increase interest in the field. |
Year(s) Of Engagement Activity | 2022,2023,2024 |