An efficient full space-time discretization method for subject-specific hemodynamic simulations of cerebral arterial blood flow with distensible wall mechanics.

A computationally inexpensive mathematical solution approach using orthogonal collocations for space discretization with temporal Fourier series is proposed to compute subject-specific blood flow in distensible vessels of large cerebral arterial networks. Several models of wall biomechanics were considered to assess their impact on hemodynamic predictions. Simulations were validated against in vivo blood flow measurements in six human subjects. The average root-mean-square relative differences were found to be less than 4.3% for all subjects with a linear elastic wall model. This discrepancy decreased further in a viscoelastic Kelvin-Voigt biomechanical wall. The results provide support for the use of collocation-Fourier series approach to predict clinically relevant blood flow distribution and collateral blood supply in large portions of the cerebral circulation at reasonable computational costs. It thus opens the possibility of performing computationally inexpensive subject-specific simulations that are robust and fast enough to predict clinical results in real time on the same day.

A thermoelastic deformation model of tissue contraction during thermal ablation.

PURPOSE: Thermal ablation is an energy-based ablation technique widely used during minimally invasive cancer treatment. Simulations are used to predict the dead tissue post therapy. However, one difficulty with the simulations is accurately predicting the ablation zone in post-procedural images due to the contraction of tissue as a result of exposure to elevated temperatures. MATERIALS AND METHODS: A mathematical model of the thermoelastic deformation for an elastic isotropic material was coupled with a three state thermal denaturation model to determine the contraction of tissue during thermal ablation. A finite difference method was considered to quantify the tissue contraction for a typical temperature distribution during thermal ablation. RESULTS: The simulations show that tissue displacement during thermal ablation was not bound to the tissue heated regions only. Both tissue expansion and contraction were observed at the different stages of the heating process. Tissue contraction of up to 42% was obtained with an applicator temperature of 90 °C. A recovery of around 2% was observed with heating removed as a result of unfolded state proteins returning back to its native state. Poisson's ratio and the applicator temperature have both been shown to affect the tissue displacement significantly. The maximum tissue contraction was found to increase with both increasing Poisson's ratio and temperature. CONCLUSIONS: The model presented here will allow predictions of thermal ablation to be corrected for tissue contraction, which is an important effect, during comparison with post-procedural images, thus improving the accuracy of mathematical simulations for treatment planning.

Mathematical model of the post-ablation enhancement zone as a tissue-level oedematic response.

PURPOSE: A hyperdense rim is commonly observed at the periphery of ablation zones during post-ablation imaging (e.g. ultrasound) in tumours. A mathematical model has been developed here to investigate the occurrence of this enhanced rim, caused by the ablated cells, giving an indication of the location of the final ablation region. MATERIALS AND METHODS: The enhanced rim has been assumed here to be due to a tissue-level oedematic response of viable cells, which necessitated coupling multiple modelling elements in a spatially distributed system: thermal cell death, tissue-state dependent ion concentration dynamics, ion transport in the extracellular space, and osmotic cell volume regulation. RESULTS: In response to the imposed temperature function, an ablation zone was predicted, distinguishing the tissue state between 'dead' and 'alive'. A disturbance in intracellular/extracellular ion concentrations was induced due to ion redistribution, which acted as an osmotic stress and contributed to significant cell swelling in a thin rim at the periphery of the ablation zone. It was also found that the rim size only changed slightly with varying lesion size, in response to different temperature profiles. CONCLUSIONS: The study presents a novel mathematical model to understand the enhanced rim surrounding the ablation zone by assuming tissue-level cell oedema as the primary potential cause. The model links the direct response to thermal injury to an observable secondary response, which could be of clinical value in that the location of this bright ring could potentially be used for more accurate determination of the extent of the ablation zone.

A model of tissue contraction during thermal ablation.

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.

Modelling the effects of cerebral microvasculature morphology on oxygen transport.

The cerebral microvasculature plays a vital role in adequately supplying blood to the brain. Determining the health of the cerebral microvasculature is important during pathological conditions, such as stroke and dementia. Recent studies have shown the complex relationship between cerebral metabolic rate and transit time distribution, the transit times of all the possible pathways available dependent on network topology. In this paper, we extend a recently developed technique to solve for residue function, the amount of tracer left in the vasculature at any time, and transit time distribution in an existing model of the cerebral microvasculature to calculate cerebral metabolism. We present the mathematical theory needed to solve for oxygen concentration followed by results of the simulations. It is found that oxygen extraction fraction, the fraction of oxygen removed from the blood in the capillary network by the tissue, and cerebral metabolic rate are dependent on both mean and heterogeneity of the transit time distribution. For changes in cerebral blood flow, a positive correlation can be observed between mean transit time and oxygen extraction fraction, and a negative correlation between mean transit time and metabolic rate of oxygen. A negative correlation can also be observed between transit time heterogeneity and the metabolic rate of oxygen for a constant cerebral blood flow. A sensitivity analysis on the mean and heterogeneity of the transit time distribution was able to quantify their respective contributions to oxygen extraction fraction and metabolic rate of oxygen. Mean transit time has a greater contribution than the heterogeneity for oxygen extraction fraction. This is found to be opposite for metabolic rate of oxygen. These results provide information on the role of the cerebral microvasculature and its effects on flow and metabolism. They thus open up the possibility of obtaining additional valuable clinical information for diagnosing and treating cerebrovascular diseases.

A generalized mathematical framework for estimating the residue function for arbitrary vascular networks.

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.

Multi-spatial-frequency and phase-shifting profilometry using a liquid crystal phase modulator.

Optical profilometry is widely applied for measuring the morphology of objects by projecting predetermined patterns on them. In this technique, the compact size is one of the interesting issues for practical applications. The generation of pattern by the interference of coherent light sources has a potential to reduce the dimension of the illumination part. Moreover, this method can make fine patterns without projection optics, and the illumination part is free of restriction from the numerical aperture of the projection optics. In this paper, a phase-shifting profilometry is implemented by using a single liquid crystal (LC) cell. The LC phase modulator is designed to generate the interference patterns with several different spatial frequencies by changing selection of the spacing between the micro-pinholes. We manufactured the LC phase modulator and calibrated it by measuring the phase modulation amount depending on an applied voltage. Our optical profilometry using the single LC cell can generate multi-spatial frequency patterns as well as four steps of the phase-shifted patterns. This method can be implemented compactly, and the reconstructed depth profile is obtained without a phase-unwrapping algorithm.

A vertical-field-driven polymer-stabilized blue phase liquid crystal mode to obtain a higher transmittance and lower driving voltage.

We demonstrate a vertical-field-driven polymer-stabilized blue phase liquid crystal (PS-BPLC) mode for solving low transmittance and high driving voltage problems in conventional in-plane-switching (IPS) PS-BPLC modes. By controlling the ray directions of incident beams by means of two prism sheets attached to the top and bottom substrates, continuous grayscale properties can be achieved with a vertical field, where the transmittance of the proposed structure can be increased to become twice as high as that of a IPS PS-BPLC cell, and its driving voltage can also be lowered by about 20 V. With the vertical-field-driven PS-BPLC mode, the hysteresis problem of the IPS PS-BPLC mode can also be solved due to a reduction of the electric field required to achieve sufficient field-induced retardation.

Modelling of pH dynamics in brain cells after stroke.

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.

Optical detection of volatile organic compounds using selective tensile effects of a polymer-coated fiber Bragg grating.

We demonstrated a novel selective chemical sensing approach by incorporating a poly(dimethylsiloxane) (PDMS)-coated fiber Bragg grating (FBG) structure for optically detecting various volatile organic compounds (VOC's). When the proposed structure is exposed to a nonpolar solvent, a tensile stress is induced between the coated PDMS and the optical fiber by a VOC-dependent swelling effect of the PDMS, which results in a Bragg wavelength shift dependent on the concentration and the type of VOC's. Because of no need of an etching process of a fiber cladding, the proposed PDMS-coated FBG can be used as a simple, convenient, and durable chemical sensing element with a high sensitivity, compared with conventional FBG sensors requiring an evanescent wave coupling.

Quantification of the effects of vasomotion on mass transport to tissue from axisymmetric blood vessels.

The 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.

The effects of non-linearities on shear stress in periodic flow in axi-symmetric vessels.

In this paper, a power series and a Fourier series approach is used to solve the governing equations of motion in an elastic axi-symmetric vessel, assuming that blood is an incompressible Newtonian fluid. The time averaged flow has shown to be greater than the steady state flow leading to a larger wall shear stress. Oscillations can also be observed, which is not present in the steady state solution. This is due to the nonlinear momentum terms causing interaction between the harmonics.

Variable wavelength surface plasmon resonance (SPR) in biosensing.

In this study, we fabricated a novel variable wavelength surface plasmon resonance (SPR) sensor, which detects resonance conditions such as a maximum attenuation wavelength, measuring change of microscopic refractive index. Such a change was measured to detect a salmonella antigen-antibody reaction and a penicillinase-penicillin reaction. Our experiments were performed after immobilizing a salmonella antibody on the sensor chip. We measured the shift in resonant wavelength during the antigen-antibody reaction for 30 min by injecting 5 x 10(7) cells/ml concentration of salmonella antigen solution into the sample chamber. Also, after immobilizing penicillinase on the sensor chip, we measured the shift in resonant wavelength during the reaction. Penicillin solution at 10mM was injected into the sample chamber. The shift of resonant wavelength for each experiment was measured using a white light source, multimode optical fiber, a part of sensor chip and an optical spectrum analyzer. As a result, the resonant wavelength shifted about 0.26 nm/min owing to the salmonella antibody-antigen reaction. Thus, we could detect the change in wavelength (0.8 nm/min) through the interaction of penicillin and penicillinase for 15 min using variable wavelength SPR sensor.