David O'Neill

Image-based multi-scale modelling and validation of radio-frequency ablation in liver tumours

The treatment of cancerous tumours in the liver remains clinically challenging, despite the wide range of treatment possibilities, including radio-frequency ablation (RFA), high-intensity focused ultrasound and resection, which are currently available. Each has its own advantages and disadvantages. For non- or minimally invasive modalities, such as RFA, considered here, it is difficult to monitor the treatment in vivo. This is particularly problematic in the liver, where large blood vessels act as heat sinks, dissipating delivered heat and shrinking the size of the lesion (the volume damaged by the heat treatment) locally; considerable experience is needed on the part of the clinician to optimize the heat treatment to prevent recurrence. In this paper, we outline our work towards developing a simulation tool kit that could be used both to optimize treatment protocols in advance and to train the less-experienced clinicians for RFA treatment of liver tumours. This tool is based on a comprehensive mathematical model of bio-heat transfer and cell death. We show how simulations of ablations in two pigs, based on individualized imaging data, compare directly with experimentally measured lesion sizes and discuss the likely sources of error and routes towards clinical implementation. This is the first time that such a ‘loop’ of mathematical modelling and experimental validation in vivo has been performed in this context, and such validation enables us to make quantitative estimates of error.

Modelling of the physiological response of the brain to ischaemic stroke

Identification of salvageable brain tissue is a major challenge when planning the treatment of ischaemic stroke. As the standard technique used in this context, the perfusion–diffusion mismatch, has not shown total accuracy, there is an ongoing search for new imaging protocols that could better identify the region of the brain at risk and for new physiological models that could, on the one hand, incorporate the imaged parameters and predict the evolution of the condition for the individual, and, on the other hand, identify future biomarkers and thus suggest new directions for the design of imaging protocols. Recently, models of cellular metabolism after stroke and blood–brain barrier transport at tissue level have been introduced. We now extend these results by developing a model of the propagation of key metabolites in the brains extracellular space owing to stroke-related oedema and chemical concentration gradients between the ischaemic and normal brain. We also couple the resulting chemical changes in the extracellular space with cellular metabolism. Our work enables the first patient-specific simulations of stroke progression with finite volume models to be made.

A mechanistic physicochemical model of carbon dioxide transport in blood

A number of mathematical models have been produced that, given the Pco2 and Po2 of blood, will calculate the total concentrations for CO2 and O2 in blood. However, all these models contain at least some empirical features, and thus do not represent all of the underlying physicochemical processes in an entirely mechanistic manner. The aim of this study was to develop a physicochemical model of CO2 carriage by the blood to determine whether our understanding of the physical chemistry of the major chemical components of blood together with their interactions is sufficiently strong to predict the physiological properties of CO2 carriage by whole blood. Standard values are used for the ionic composition of the blood, the plasma albumin concentration, and the hemoglobin concentration. All Km values required for the model are taken from the literature. The distribution of bicarbonate, chloride, and H+ ions across the red blood cell membrane follows that of a Gibbs-Donnan equilibrium. The system of equations that results is solved numerically using constraints for mass balance and electroneutrality. The model reproduces the phenomena associated with CO2 carriage, including the magnitude of the Haldane effect, very well. The structural nature of the model allows various hypothetical scenarios to be explored. Here we examine the effects of 1) removing the ability of hemoglobin to form carbamino compounds; 2) allowing a degree of Cl- binding to deoxygenated hemoglobin; and 3) removing the chloride (Hamburger) shift. The insights gained could not have been obtained from empirical models. NEW & NOTEWORTHY This study is the first to incorporate a mechanistic model of chloride-bicarbonate exchange between the erythrocyte and plasma into a full physicochemical model of the carriage of carbon dioxide in blood. The mechanistic nature of the model allowed a theoretical study of the quantitative significance for carbon dioxide transport of carbamino compound formation; the putative binding of chloride to deoxygenated hemoglobin, and the chloride (Hamburger) shift.

A two-equation coupled system model for determination of liver tissue temperature during radio frequency ablation

A model is presented that is an alternative approach to the bio-heat equation for use in radio frequency heating of the liver. The model comprises both a tissue subvolume and a blood subvolume. Separate bio-heat equations are determined for each subvolume, but with an additional term exchanging heat between them, thus creating a coupled system. The derivation for the two coupled differential equations is outlined and sample simulations are presented to demonstrate the importance of considering the two subvolumes separately, even when the blood subvolume is a small fraction of the tissue subvolume. 1

Potential for noninvasive assessment of lung inhomogeneity using highly precise, highly time-resolved measurements of gas exchange

Inhomogeneity in the lung impairs gas exchange and can be an early marker of lung disease. We hypothesized that highly precise measurements of gas exchange contain sufficient information to quantify many aspects of the inhomogeneity noninvasively. Our aim was to explore whether one parameterization of lung inhomogeneity could both fit such data and provide reliable parameter estimates. A mathematical model of gas exchange in an inhomogeneous lung was developed, containing inhomogeneity parameters for compliance, vascular conductance, and dead space, all relative to lung volume. Inputs were respiratory flow, cardiac output, and the inspiratory and pulmonary arterial gas compositions. Outputs were expiratory and pulmonary venous gas compositions. All values were specified every 10 ms. Some parameters were set to physiologically plausible values. To estimate the remaining unknown parameters and inputs, the model was embedded within a nonlinear estimation routine to minimize the deviations between model and data for CO2, O2, and N2 flows during expiration. Three groups, each of six individuals, were studied: young (20-30 yr); old (70-80 yr); and patients with mild to moderate chronic obstructive pulmonary disease (COPD). Each participant undertook a 15-min measurement protocol six times. For all parameters reflecting inhomogeneity, highly significant differences were found between the three participant groups ( P < 0.001, ANOVA). Intraclass correlation coefficients were 0.96, 0.99, and 0.94 for the parameters reflecting inhomogeneity in deadspace, compliance, and vascular conductance, respectively. We conclude that, for the particular participants selected, highly repeatable estimates for parameters reflecting inhomogeneity could be obtained from noninvasive measurements of respiratory gas exchange. NEW & NOTEWORTHY This study describes a new method, based on highly precise measures of gas exchange, that quantifies three distributions that are intrinsic to the lung. These distributions represent three fundamentally different types of inhomogeneity that together give rise to ventilation-perfusion mismatch and result in impaired gas exchange. The measurement technique has potentially broad clinical applicability because it is simple for both patient and operator, it does not involve ionizing radiation, and it is completely noninvasive.

High-resolution contrast enhanced multi-phase hepatic Computed Tomography data fromaporcine Radio-Frequency Ablation study

Data below 1 mm voxel size is getting more and more common in the clinical practice but it is still hard to obtain a consistent collection of such datasets for medical image processing research. With this paper we provide a large collection of Contrast Enhanced (CE) Computed Tomography (CT) data from porcine animal experiments and describe their acquisition procedure and peculiarities. We have acquired three CE-CT phases at the highest available scanner resolution of 57 porcine livers during induced respiratory arrest. These phases capture contrast enhanced hepatic arteries, portal venous veins and hepatic veins. Therefore, we provide scan data that allows for a highly accurate reconstruction of hepatic vessel trees. Several datasets have been acquired during Radio-Frequency Ablation (RFA) experiments. Hence, many datasets show also artificially induced hepatic lesions, which can be used for the evaluation of structure detection methods.

Mathematical study of the effects of different intrahepatic cooling on thermal ablation zones

Thermal ablation of a tumour in the liver with Radio Frequency energy can be accomplished by using a probe inserted into the tissue under the guidance of medical imaging. The extent of ablation can be significantly affected by heat loss due to the high blood perfusion in the liver, especially when the tumour is located close to large vessels. A mathematical model is thus presented here to investigate the heat sinking effects of large vessels, combining a 3D two-equation coupled bio-heat model and a 1D model of convective heat transport across the blood vessel surface. The model simulation is able to recover the experimentally observed different intrahepatic cooling on thermal ablation zones: hepatic veins showed a focal indentation whereas portal veins showed broad flattening of the ablation zones. Moreover, this study also illustrates that this shape derivation can largely be attributed to the temperature variations between the microvascular branches of portal vein as compared with hepatic vein. In contrast, different amount of surface heat convection on the vessel wall between these two types of veins, however, has a minor effect.

The response of hepatocyte cell volume to hyperthermia and its role in oedema

A novel mathematical model for hepatocytes and surrounding volume is presented here; in addition to tracking ion transport and diffusion the new model allows for changing cell volume. Using temporally and spatially varying temperature as an input, this paper shows how differences between diffusion coefficients directly influence increases in cell volume. The multiscale nature of the model presents a possible link from established cellular equations to the observed clinical result of oedema present in thermal treatments of cancer.

1-D steady state analysis of a two-equation coupled system for determination of tissue temperature in liver during radio frequency ablation

An analytical solution is provided for a two-equation coupled model for determination of liver tissue temperature during radio frequency ablation in the steady state with one-dimension in space1. Both analytical analysis and model simulation were conducted to investigate the effects of two crucial system parameters: blood perfusion rate and convective heat transfer coefficient on the tissue temperature field. The quantitative criteria were also derived, under which the two-equation coupled system can be approximated to a conventional single bio-heat equation system such as the Pennes model2.