Challenges and opportunities of integrating imaging and mathematical modelling to interrogate biological processes

Berg, Maxime; Holroyd, Natalie; Walsh, Claire; West, Hannah; Walker‐Samuel, Simon; Shipley, Rebecca J.

doi:10.1016/j.biocel.2022.106195

Cited by 9 publications

(12 citation statements)

References 34 publications

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“…F I G U R E 4 Schematic description, adapted from Li & Mooney, 2016, of the link between hydrogel matrix properties and drug delivery in the context of hydrogel deformation, swelling, and matrix degradation Although rare in the PNI repair field, mathematical models of slow flow dynamics in other fields could be adapted to describe, for example, the impact of minipumps, injections, and the contribution of microvasculature-induced flows. Cancer modeling is a ripe field for technology transfer, not only through the development of sophisticated mathematical models of microvascular and extravascular flows (Berg et al, 2022;Dogra et al, 2020;Shipley et al, 2019;Stamatelos et al, 2014;Sweeney et al, 2019), but also by highlighting the importance of experimental and/or imaging data to characterize these flows in situ (d 'Esposito et al, 2018). Similarly, mathematical models of fluid flows in tissue engineering and regenerative medicine is evolving to become a rich research field including, for example, describing perfusion of fluid in and around hydrogel-based constructs (O'Dea et al, 2012;Waters et al, 2021).…”

Section: Flow-dependent Drug Deliverymentioning

confidence: 99%

Perspectives on optimizing local delivery of drugs to peripheral nerves using mathematical models

Laranjeira

Roberton

Phillips

et al. 2023

WIREs Mechanisms of Disease

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Drug therapies for treating peripheral nerve injury repair have shown significant promise in preclinical studies. Despite this, drug treatments are not used routinely clinically to treat patients with peripheral nerve injuries. Drugs delivered systemically are often associated with adverse effects to other tissues and organs; it remains challenging to predict the effective concentration needed at an injured nerve and the appropriate delivery strategy. Local drug delivery approaches are being developed to mitigate this, for example via injections or biomaterialmediated release. We propose the integration of mathematical modeling into the development of local drug delivery protocols for peripheral nerve injury repair. Mathematical models have the potential to inform understanding of the different transport mechanisms at play, as well as quantitative predictions around the efficacy of individual local delivery protocols. We discuss existing approaches in the literature, including drawing from other research fields, and present a process for taking forward an integrated mathematical-experimental approach to accelerate local drug delivery approaches for peripheral nerve injury repair.

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Section: Flow-dependent Drug Deliverymentioning

confidence: 99%

Perspectives on optimizing local delivery of drugs to peripheral nerves using mathematical models

Laranjeira

Roberton

Phillips

et al. 2023

WIREs Mechanisms of Disease

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“…That is because we have direct access to oxygen concentration measurements in the gel at early time points (cf. oxygen fields in figures [7][8][9].…”

Section: Effect Of Information Gain On Parametersmentioning

confidence: 99%

“…Combining experiments with mathematical modelling provides an opportunity to address these challenges [8][9][10]. Mathematical models benchmarked against experimental data enable computational experiments to be performed to test the role of different biological and biophysical mechanisms, as well as to explore the impact of different design scenarios.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modelling with Bayesian inference to quantitatively characterize therapeutic cell behaviour in nerve tissue engineering

Berg,

Eleftheriadou,

Phillips

et al. 2023

J. R. Soc. Interface.

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Cellular engineered neural tissues have significant potential to improve peripheral nerve repair strategies. Traditional approaches depend on quantifying tissue behaviours using experiments in isolation, presenting a challenge for an overarching framework for tissue design. By comparison, mathematical cell–solute models benchmarked against experimental data enable computational experiments to be performed to test the role of biological/biophysical mechanisms, as well as to explore the impact of different design scenarios and thus accelerate the development of new treatment strategies. Such models generally consist of a set of continuous, coupled, partial differential equations relying on a number of parameters and functional forms. They necessitate dedicated in vitro experiments to be informed, which are seldom available and often involve small datasets with limited spatio-temporal resolution, generating uncertainties. We address this issue and propose a pipeline based on Bayesian inference enabling the derivation of experimentally informed cell–solute models describing therapeutic cell behaviour in nerve tissue engineering. We apply our pipeline to three relevant cell types and obtain models that can readily be used to simulate nerve repair scenarios and quantitatively compare therapeutic cells. Beyond parameter estimation, the proposed pipeline enables model selection as well as experiment utility quantification, aimed at improving both model formulation and experimental design.

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“…Advances in biomedical imaging of vascular tissues [4][5][6][7] have paved the way for computational studies which integrate complete vascular architectures with biophysical models to probe the microenvironment in silico in a manner that is currently inaccessible in a traditional experimental setting 8 . Due to the computational challenges of simulating network-scale blood rheology and dynamics using mesh-based methods, many studies apply one-dimensional (1D) Poiseuille flow models (see Figure 1A) to these vascular network datasets to provide insight into a wide range of biological applications, for example, in cerebral blood flow [9][10][11][12] , angiogenesis 13,14 and cancer 4,[15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional, discrete-continuum model of blood pressure in microvascular networks

Sweeney

Walsh

Walker‐Samuel

et al. 2022

Preprint

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We introduce a hybrid, discrete-continuum method to model blood pressure across large microvascular networks with incomplete architectural information. Our multiscale approach couples a 1D Poiseuille flow description in large, discrete arteriolar and venular networks, via point sources of flux, to a continuum-based Darcy model for transport in the capillary bed. We test our hybrid framework using a vascular network imaged from the mouse brain medulla / pons using multi-fluorescence high-resolution episcopic microscopy. The fully-resolved vascular network is used to predicted the hydraulic conductivity of the capillary network and to generate a fully-discrete pressure solution to benchmark our novel method against. We show that the discrete-continuum methodology is a computationally tractable and effective tool for predicting blood pressure in real-world microvascular tissues when capillary microvessels are not well-defined.

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Challenges and opportunities of integrating imaging and mathematical modelling to interrogate biological processes

Cited by 9 publications

References 34 publications

Perspectives on optimizing local delivery of drugs to peripheral nerves using mathematical models

Perspectives on optimizing local delivery of drugs to peripheral nerves using mathematical models

Mathematical modelling with Bayesian inference to quantitatively characterize therapeutic cell behaviour in nerve tissue engineering

A three-dimensional, discrete-continuum model of blood pressure in microvascular networks

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