ArticleMathematical medicine and biology : a journal of the IMA2016
A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries.
Article in Mathematical medicine and biology : a journal of the IMA, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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Who cites it
16 citing papers in PubMed.
- Boolean network and meshless simulations for the comparison of transport and reaction mechanisms arising in one-short tri-exponential and uniform infusion electrochemotherapeutic treatments.Frontiers in bioinformatics · 2026Article
- Impact of Vascular Network Structure Heterogeneity on Retinal Tissue Oxygenation.La matematica · 2025Article
- Predicting the impact of retinal vessel density on retinal vessel and tissue oxygenation using a theoretical model.Mathematical biosciences · 2024Article
- Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma.PLoS computational biology · 2024Article
- Histology-guided mathematical model of tumor oxygenation: sensitivity analysis of physical and computational parameters.bioRxiv : the preprint server for biology · 2024Article
- Variability in Retinal Neuron Populations and Associated Variations in Mass Transport Systems of the Retina in Health and Aging.Frontiers in aging neuroscience · 2022Review
- Control of low flow regions in the cortical vasculature determines optimal arterio-venous ratios.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Bridging cell-scale simulations and radiologic images to explain short-time intratumoral oxygen fluctuations.PLoS computational biology · 2021Article
- Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations.Frontiers in physiology · 2021Article
- Ocular blood flow as a clinical observation: Value, limitations and data analysis.Progress in retinal and eye research · 2020Article
- A Systems Pharmacology Model for Drug Delivery to Solid Tumors by Antibody-Drug Conjugates: Implications for Bystander Effects.The AAPS journal · 2019Article
- Modelling the transport of fluid through heterogeneous, whole tumours in silico.PLoS computational biology · 2019Article
- Insights into cerebral haemodynamics and oxygenation utilising in vivo mural cell imaging and mathematical modelling.Scientific reports · 2018Article
- Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues.Journal of the Royal Society, Interface · 2018Review
- Therapy operating characteristic curves: tools for precision chemotherapy.Journal of medical imaging (Bellingham, Wash.) · 2016Article
- Modeling of Cerebral Oxygen Transport Based on In vivo Microscopic Imaging of Microvascular Network Structure, Blood Flow, and Oxygenation.Frontiers in computational neuroscience · 2016Review
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1 author.
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Abstract
A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.