The identification of salvageable brain tissue is a major challenge at stroke presentation. Standard techniques used in this context, such as the perfusion–diffusion mismatch, remain controversial. There is thus a need for new methods to help guide treatment. The potential role of pH imaging in this context is currently being investigated. Intracellular pH varies as a function of local perfusion, intracellular energy stores and time. Low pH triggers the production of free radicals and affects the calcium balance of the cells, which may lead to apoptosis and cell death. Thus, the characterization of pH dynamics may have predictive value for cell death after stroke, particularly when combined with novel imaging techniques. Therefore, we have extended an existing model of brain cellular metabolism to simulate the pH response of cells to ischaemia. Simulation results for conditions of reduced cerebral blood flow show good agreement for the evolution of intracellular pH with previously reported measurements and encourage the development of quantitative pH imaging to validate the predictive value of pH.

A model of a globular protein is used to describe the contraction of tissue exposed to elevated temperatures. This will be useful in predicting the contraction of tissue that is observed during thermal ablation of tumours, which is a problem when trying to determine the ablation zone in post-operative images. The transitions between the states of the protein can be related to a change in the length of the molecule, which can be directly observed as a change in the length of the tissue. A three state model of a globular protein is used to describe the contraction of tissue exposed to elevated temperatures. A nonlinear fitting algorithm is considered here to fit available experimental data and thus to obtain the values of the model parameters. A sensitivity analysis of the proposed mathematical model is performed to determine the most important parameters in the model. The model parameters were obtained from experimental data of isothermal free shrinkage experiments. The predictions of the complete model show similar agreement with the data, well within the experimental error of 10%. The overall activation energy and frequency factor were found to be 201 kJ mol(-1) and [Formula: see text] s(-1) respectively. The results show that the experimental data were well described by the three state model considered here. Furthermore, it was possible to determine the most sensitive parameters in the model. The model presented here will allow predictions of thermal ablation to be corrected for tissue shrinkage, thus improving mathematical simulations for treatment planning, although clinical translation will require adapting the model from experimentally obtained tendon data to soft tissue data.

View this journal online at wileyonlinelibrary.com/journal/cnm Aims and ScopeInternational Journal for Numerical Methods in Biomedical Engineering is an international journal which publishes both full length and short refereed papers describing significant developments in numerical methods and their application to biomedical engineering problems.Contributions are encouraged in all areas of biomedical engineering, such as patient-specific modelling, biofluid and biosolid mechanics, tissue engineering, cardiovascular and respiratory mechanics, tumour modelling, medical imaging and image processing, visualisation, meshing, numerical modelling of organs, drug delivery, surgical simulation, micro-and nano-mechanics, multiscale problems, human body electromagnetics, molecular biology, medical device design, health care models and numerical methods specially designed for biomedical problems.Authors are reminded that application of a standard numerical procedure to a standard problem is not within the scope of this journal. Manuscripts that present solutions to realistic and new biomedical problems using standard numerical procedures should provide evidence of mesh convergence. For submission instructions, subscription, and all the latest information, visit wileyonlinelibrary.com/journal/cnm The cover image is based on the Original Article Quantification of blood flow patterns in the cerebral arterial circulation of individual (human) subjects by Andreas Linninger, Grant Hartung, Xinjian Du et al., https://doi.

The microvasculature plays a vital part in the cardiovascular system. Any impairment to its function can lead to significant pathophysiological effects, particularly in organs such as the brain where there is a very tight coupling between structure and function. However, it is extremely difficult to quantify the health of the microvasculature in vivo, other than by assessing perfusion, using techniques such as arterial spin labelling. Recent work has suggested that the flow distribution within a voxel could also be a valuable measure. This can also be measured clinically, but as yet has not been related to the properties of the microvasculature due to the difficulties in modelling and characterizing these strongly inter-connected networks. In this paper, we present a new technique for characterizing an existing physiologically accurate model of the cerebral microvasculature in terms of its residue function. A new analytical mathematical framework for calculation of the residue function, based on the mass transport equation, of any arbitrary network is presented together with results from simulations. We then present a method for characterizing this function, which can be directly related to clinical data, and show how the resulting parameters are affected under conditions of both reduced perfusion and reduced network density. It is found that the residue function parameters are affected in different ways by these two effects, opening up the possibility of using such parameters, when acquired from clinical data, to infer information about both the network properties and the perfusion distribution. These results open up the possibility of obtaining valuable clinical information about the health of the microvasculature in vivo, providing additional tools to clinicians working in cerebrovascular diseases, such as stroke and dementia.

International audienceThe process known as vasomotion, rhythmic oscillations in vessel diameter, has been proposed to act as a protective mechanism for tissue under conditions of reduced perfusion, since it is frequently only observed experimentally when perfusion levels are reduced. This could be due to a resultant increase in oxygen transport from the vasculature to the surrounding tissue, either directly or indirectly. It is thus potentially of significant clinical interest as a warning signal for ischemia. However, there has been little analysis performed to quantify the effects of vessel wall movement on time-averaged mass transport. We thus present a detailed analysis of such mass transport for an axisymmetric vessel with a periodically oscillating wall, by solving the non-linear mass transport equation, and quantify the differences between the time-averaged mass transport under conditions of no oscillation (i.e. the steady-state) and varying wall oscillation amplitude. The results show that if the vessel wall alone is oscillated, with an invariant wall concentration, the time-averaged mass transport is reduced relative to the steady-state, but if the vessel wall concentration is also oscillated, then mass transport is increased, although this is generally only true when these oscillate in phase with each other. The influence of Péclet number and the non-dimensional rate of consumption of oxygen in tissue, as well as the amplitude of oscillations, are fully characterised. We conclude by considering the likely implications of these results in the context of oxygen transport to tissue