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

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

Local Administration of Minocycline Improves Nerve Regeneration in Two Rat Nerve Injury Models

Peripheral nerve injuries are quite common and often require a surgical intervention. However, even after surgery, patients do not often regain satisfactory sensory and motor functions. This, in turn, results in a heavy socioeconomic burden. To some extent, neurons can regenerate from the proximal nerve stump and try to reconnect to the distal stump. However, this regenerating capacity is limited, and depending on the type and size of peripheral nerve injury, this process may not lead to a positive outcome. To date, no pharmacological approach has been used to improve nerve regeneration following repair surgery. We elected to investigate the effects of local delivery of minocycline on nerve regeneration. This molecule has been studied in the central nervous system and was shown to improve the outcome in many disease models. In this study, we first tested the effects of minocycline on SCL 4.1/F7 Schwann cells in vitro and on sciatic nerve explants. We specifically focused on the Schwann cell repair phenotype, as these cells play a central role in orchestrating nerve regeneration. Finally, we delivered minocycline locally in two different rat models of nerve injury, a sciatic nerve transection and a sciatic nerve autograft, demonstrating the capacity of local minocycline treatment to improve nerve regeneration

A hybrid neural ordinary differential equation model of the cardiovascular system

Peer reviewe

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Peer reviewe

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems

A parameterised mathematical model to elucidate osteoblast cell growth in a phosphate-glass microcarrier culture

Tissue engineering has the potential to augment bone grafting. Employing microcarriers as cell-expansion vehicles is a promising bottom-up bone tissue engineering strategy. Here we propose a collaborative approach between experimental work and mathematical modelling to develop protocols for growing microcarrier-based engineered constructs of clinically relevant size. Experiments in 96-well plates characterise cell growth with the model human cell line MG-63 using four phosphate glass microcarrier materials. Three of the materials are doped with 5 mol% TiO2 and contain 0%, 2% or 5% CoO, and the fourth material is doped only with 7% TiO2 (0% CoO). A mathematical model of cell growth is parameterised by finding material-specific growth coefficients through data-fitting against these experiments. The parameterised mathematical model offers more insight into the material performance by comparing culture outcome against clinically relevant criteria: maximising final cell number starting with the lowest cell number in the shortest time frame. Based on this analysis, material 7% TiO2 is identified as the most promising

High-speed camera characterization of voluntary eye blinking kinematics

This is the final version of the article originally published in the Journal of the Royal Society Interface here: http://rsif.royalsocietypublishing.org/content/10/85/20130227.full.pdf+html?sid=65b57db1-37cf-492f-bf3c-b08f2a8c818d.Blinking is vital to maintain the integrity of the ocular surface and its characteristics such as blink duration and speed can vary significantly, depending on the health of the eyes. The blink is so rapid that special techniques are required to characterize it. In this study, a high-speed camera was used to record and characterize voluntary blinking. The blinking motion of 25 healthy volunteers was recorded at 600 frames per second. Master curves for the palpebral aperture and blinking speed were constructed using palpebral aperture versus time data taken from the high-speed camera recordings, which show that one blink can be divided into four phases; closing, closed, early opening and late opening. Analysis of data from the high-speed camera images was used to calculate the palpebral aperture, peak blinking speed, average blinking speed and duration of voluntary blinking and compare it with data generated by other methods previously used to evaluate voluntary blinking. The advantages of the high-speed camera method over the others are discussed, thereby supporting the high potential usefulness of the method in clinical research

A mathematical investigation into the uptake kinetics of nanoparticles in vitro.

Nanoparticles have the potential to increase the efficacy of anticancer drugs whilst reducing off-target side effects. However, there remain uncertainties regarding the cellular uptake kinetics of nanoparticles which could have implications for nanoparticle design and delivery. Polymersomes are nanoparticle candidates for cancer therapy which encapsulate chemotherapy drugs. Here we develop a mathematical model to simulate the uptake of polymersomes via endocytosis, a process by which polymersomes bind to the cell surface before becoming internalised by the cell where they then break down, releasing their contents which could include chemotherapy drugs. We focus on two in vitro configurations relevant to the testing and development of cancer therapies: a well-mixed culture model and a tumour spheroid setup. Our mathematical model of the well-mixed culture model comprises a set of coupled ordinary differential equations for the unbound and bound polymersomes and associated binding dynamics. Using a singular perturbation analysis we identify an optimal number of ligands on the polymersome surface which maximises internalised polymersomes and thus intracellular chemotherapy drug concentration. In our mathematical model of the spheroid, a multiphase system of partial differential equations is developed to describe the spatial and temporal distribution of bound and unbound polymersomes via advection and diffusion, alongside oxygen, tumour growth, cell proliferation and viability. Consistent with experimental observations, the model predicts the evolution of oxygen gradients leading to a necrotic core. We investigate the impact of two different internalisation functions on spheroid growth, a constant and a bond dependent function. It was found that the constant function yields faster uptake and therefore chemotherapy delivery. We also show how various parameters, such as spheroid permeability, lead to travelling wave or steady-state solutions