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Stress-strain behavior of the passive basilar artery in normotension and hypertension.

Vascular cells are very responsive to even subtle changes in their local mechanical environment, thus there is a pressing need to quantify normal states of stress and strain as well as any perturbations from these normal states. Toward this end, we must quantify constitutive behaviors for both normal and adapted (maladapted) arteries. In this note, we report the first quantification of changes in the biaxial mechanical behavior of the passive basilar artery due to hypertension.

Basilar Artery↗

Lessons learned about slow discontinuous conduction from models of impulse propagation.

Propagation of excitation in the heart involves action potential generation by cardiac cells and its propagation in the multicellular tissue. Action potential conduction is the outcome of complex interactions between cellular processes (membrane ion channels and transporters), electrical communication between cells, and the macroscopic architecture of cardiac tissue. This high level of complexity and non linearity requires computer modeling in order to elucidate mechanisms and explain experimentally observed behaviors. This article reviews studies that we have conducted in 1-dimensional models that contain both, cellular ionic processes and intercellular communication through gap junctions. We have defined and computed a quantitative measure of the robustness of conduction, the safety factor, as a function of gap junction coupling and showed that reduced coupling can support very slow and very safe conduction. Such conduction is highly discontinuous and is supported by the L-type calcium current. We also show that gap junction coupling and the associated load has a strong effect on spatial repolarization gradients in cardiac tissue.

Action Potentials↗

Two analytical solutions for a model of pulsed arterial spin labeling with randomized blood arrival times.

A fairly general theoretical model for pulsed arterial spin labeling perfusion methods has been available for some time but analytical solutions were derived for only a small number of arterial blood input functions. These mostly assumed a sudden and simultaneous arrival of the tagged blood into the imaged region. More general cases had to be handled numerically. We present analytical solutions for two more realistic arterial input functions. They both allow the arrival times of the molecules of tagged arterial blood to be statistically distributed. We consider cases of (1) a uniform distribution on a finite time interval and (2) a normal distribution characterized by its mean and standard deviation. These models are physiologically meaningful because the statistical nature of the arrival times reflects the distribution of velocities and path lengths that the blood water molecules undertake from the tagging region to the imaged region. The model parameters can be estimated from the measured dependency of the perfusion signal on the tag inversion time.

Algorithms↗

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities. Effects of impermeable susceptibility inclusions.

A detailed theoretical description of the signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is presented in the framework of the Gaussian phase distribution approximation for two geometrical models of the field inhomogeneity sources--impermeable spheres and infinitely long cylinders. Analytical expressions for free induction decay (FID) and spin echo (SE) signal attenuation functions Gamma(t) approximately -1nS(t) are obtained and comparison with the case of unrestricted diffusion (susceptibility inclusions with freely permeable surfaces) is provided. For short times, the leading term in the FID signal attenuation function is proportional to t2 similar to the case of unrestricted diffusion; the next term behaves as t3 as compared to t 5/2 for the "permeable" case. For the SE signal, the leading term is proportional to t3 as compared to t 5/2 for unrestricted diffusion. It is shown that the t3 approximation can be used for an adequate description of the SE signal only for extremely short times compared to a characteristic diffusion time. In the long-time limit, the attenuation function in the impermeable and permeable sphere model contains not only terms linear in time, but also important terms proportional to t 1/2. In the cylindrical geometry, the leading term in the long-time expansion of the attenuation function is proportional to t 1n t for both the permeable and impermeable models. Application to description of MR in biological tissues signal in the presence of blood vessel networks and contrast agents is discussed. The validity criterion of the Gaussian approximation is also proposed.

Algorithms↗

A modified Zeeman model for producing HRV signals and its application to ECG signal generation.

Developing a mathematical model for the artificial generation of electrocardiogram (ECG) signals is a subject that has been widely investigated. One of the challenges is to generate ECG signals with a wide range of waveforms, power spectra and variations in heart rate variability (HRV)--all of which are important indexes of human heart functions. In this paper we present a comprehensive model for generating such artificial ECG signals. We incorporate into our model the effects of respiratory sinus arrhythmia, Mayer waves and the important very low-frequency component in the power spectrum of HRV. We use a new modified Zeeman model for generating the time series for HRV, and a single cycle of ECG is produced by using a simple neural network. The importance of the work is the model's ability to produce artificial ECG signals that resemble experimental recordings under various physiological conditions. As such the model provides a useful tool to simulate and analyse the main characteristics of ECG, such as its power spectrum and HRV under different conditions. Potential applications of this model include using the generated ECG as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

Arrhythmia, Sinus↗

Blood flow and structure interactions in a stented abdominal aortic aneurysm model.

Since the introduction of endovascular techniques in the early 1990s for the treatment of abdominal aortic aneurysms (AAAs), the insertion of an endovascular graft (EVG) into the affected artery segment has been greatly successful for a certain group of AAA patients and is continuously evolving. However, although minimally invasive endovascular aneurysm repair (EVAR) is very attractive, post-operative complications may occur. Typically, they are the result of excessive fluid-structure interaction dynamics, possibly leading to EVG migration. Considering a 3D stented AAA, a coupled fluid flow and solid mechanics solver was employed to simulate and analyze the interactive dynamics, i.e., pulsatile blood flow in the EVG lumen, pressure levels in the stagnant blood filling the AAA cavity, as well as stresses and displacements in the EVG and AAA walls. The validated numerical results show that a securely placed EVG shields the diseased AAA wall from the pulsatile blood pressure and hence keeps the maximum wall stress 20 times below the wall stress value in the non-stented AAA. The sac pressure is reduced significantly but remains non-zero and transient, caused by the complex fluid-structure interactions between luminal blood flow, EVG wall, stagnant sac blood, and aneurysm wall. The time-varying drag force on the EVG exerted by physiological blood flow is unavoidable, where for patients with severe hypertension the risk of EVG migration is very high.

Algorithms↗

On the use of PRD and CR parameters for ECG compression.

The quality measurement of the reconstructed signal in an electrocardiogram (ECG) compression scheme must be obtained by objective means being the percentage root-mean-square difference (PRD) the most widely used. However, this parameter is dependent on the dc level so that confusion can be stated in the evaluation of ECG compressors. In this communication, it will be shown that if the performance of an ECG coder is evaluated only in terms of quality, considering exclusively the PRD parameter, incorrect conclusions can be inferred. The objective of this work is to propose the joint use of several parameters, as simulations will show, effectiveness and performance of the ECG coder are evaluated with more precision, and the way of inferring conclusions from the obtained results is more reliable.

Algorithms↗

Numerical modelling of Newtonian and non-Newtonian representation of blood in a distal end-to-side vascular bypass graft anastomosis.

The proliferation of disease at the bed of the distal junction of an end-to-side anastomosis is attributed to abnormal wall shear stress (WSS) distribution. WSS is proportional to the viscosity and shear rate of the flowing fluid. Blood is characterised by a shear rate dependent viscosity. Various constitutive equations have been developed to represent the shear rate dependence of blood viscosity: Newtonian, Carreau, Power law, Carreau-Yasuda, Bi-exponential, Cross, Modified Cross, Herschel-Bulkley, etc. In the femoral artery, the instantaneous shear rate varies from 1-1200 s(-1) over a cardiac cycle. An idealised, 45 degrees rigid, 6mm diameter, end-to-side femoral anastomosis was modelled on a Computational Fluid Dynamic software package Fluent 6.0. A steady flow of 0.15 and 0.01 m/s was applied to the inlet to model high and low wall shear rate environments respectively. Blood was modelled using the various constitutive equations. The resulting WSS distribution on the bed of the artery was then obtained. At high shear rates there was no significant difference between WSS distribution. At low shear rates there were qualitative differences of up to 300%. In conclusion, the choice of blood constitutive equation has to be based on the particular situation under study e.g. flow rate, steady/unsteady flow, and geometry.

Anastomosis, Surgical↗

A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms.

It is generally believed that knowledge of the wall stress distribution could help to find better rupture risk predictors of abdominal aortic aneurysms (AAAs). Although AAA wall stress results from combined action between blood, wall and intraluminal thrombus, previously published models for patient-specific assessment of the wall stress predominantly did not include fluid-dynamic effects. In order to facilitate the incorporation of fluid-structure interaction in the assessment of AAA wall stress, in this paper, a method for generating patient-specific hexahedral finite element meshes of the AAA lumen and wall is presented. The applicability of the meshes is illustrated by simulations of the wall stress, blood velocity distribution and wall shear stress in a characteristic AAA. The presented method yields a flexible, semi-automated approach for generating patient-specific hexahedral meshes of the AAA lumen and wall with predefined element distributions. The combined fluid/solid mesh allows for simulations of AAA blood dynamics and AAA wall mechanics and the interaction between the two. The mechanical quantities computed in these simulations need to be validated in a clinical setting, after which they could be included in clinical trials in search of risk factors for AAA rupture.

Aortic Aneurysm, Abdominal↗

First-order system least-squares (FOSLS) for modeling blood flow.

The modeling of blood flow through a compliant vessel requires solving a system of coupled nonlinear partial differential equations (PDEs). Traditional methods for solving the system of PDEs do not scale optimally, i.e., doubling the discrete problem size results in a computational time increase of more than a factor of 2. However, the development of multigrid algorithms and, more recently, the first-order system least-squares (FOSLS) finite-element formulation has enabled optimal computational scalability for an ever increasing set of problems. Previous work has demonstrated, and in some cases proved, optimal computational scalability in solving Stokes, Navier-Stokes, elasticity, and elliptic grid generation problems separately. Additionally, coupled fluid-elastic systems have been solved in an optimal manner in 2D for some geometries. This paper presents a FOSLS approach for solving a 3D model of blood flow in a compliant vessel. Blood is modeled as a Newtonian fluid, and the vessel wall is modeled as a linear elastic material of finite thickness. The approach is demonstrated on three different geometries, and optimal scalability is shown to occur over a range of problem sizes. The FOSLS formulation has other benefits, including that the functional is a sharp, a posteriori error measure.

Algorithms↗

Simulation and experimental observation of contact conditions between stents and artery models.

Treatment of coronary artery stenosis with percutaneous coronary angioplasty and stenting is sometimes complicated by neointimal hyperplasia, possibly due to interaction of the stent with the arterial wall within a specific contact area. Therefore, we characterized the stress distribution at the contacts between the stent and the artery using mathematical and experimental modeling (an arterial cylinder model with a tube-like structure and an arterial stenosis model, consisting of a tube and plaque portion) and two kinds of link stents with different numbers of cells and links. First, the contact condition was investigated using a finite element method (FEM). Second, experimental visualization of the contact area between the stent and the artery models was performed. Comparison of the experimental results with the FEM analysis revealed that the contact area between the stent (with a high number of cells and links) and the artery model was distributed over the total surface of the stent. Further, values obtained from the experimental distribution and the calculated distribution were similar. These data indicate that experimental modeling and FEM analysis are useful methods for analyzing the relationship between stent structure and stent/wall stress distributions and may help guide the design of new stents.

Angioplasty, Balloon, Coronary↗

Epicardial potential distribution reconstruction from recordings of intravenous and transthoracic mapping catheters: a feasibility study.

Catheter-based epicardial mapping is possible with two access methods: transthoracic pericardial access and transvenous access. Transthoracic pericardial access is based on the introduction of the catheters into the pericardial space using a percutaneous subxiphoid puncture and may at times require lengthy sequential mapping procedures. From the transthoracic pericardial approach major regions of the epicardium may also be inaccessible. Transvenous access uses the multielectrode (4-20 electrodes) catheters placed in the coronary veins thus increases the speed of the mapping procedure, however, leaves most of the epicardium inaccessible to direct measurement. The aim of this present study is to demonstrate that the reconstruction of the high-resolution maps using sparse measurements from different sites on the epicardium and on the multielectrode catheters is possible with a reasonably high accuracy in terms of locating the origin of the ventricular arrhythmia. In this study we investigated strategies for the reconstruction of epicardial potential distribution from recordings of intravenous and transthoracic epicardial mapping catheters, alone and in combination. For this purpose, we first examined the problem of best number of epicardial measurement sites (or best sampling resolution) using transthoracic mapping catheters and secondly studied the feasibility of the combined usage of both mapping approaches. In the prediction of the surrogate measurements at inaccessible sites from the measurements localized to the cardiac veins and sparse epicardial sites we evaluated two prediction methods: the Laplacian interpolation and statistical estimation, to overcome the sparsity of the measurements. We performed 14 dog experiments with various interventions to create a high-resolution epicardial potential map database. This database included a total of 592 beats which were recorded using a sock array placed on the ventricles of dog hearts. We found that 2 cm sampling resolution is quite feasible, which means that the time for the mapping procedure may be reduced considerably. Predictions from the combination of 21 intravenous catheter leads and 30 transthoracic catheter leads were better than when only 21 or 30 leads were used. The results of this study encourage further investigation and provide adequate evidence that an epicardial mapping approach based on the combined usage of transvenous and transthoracic pericardial access methods for the mapping of the outer surface of the heart is feasible and can provide adequate accuracy for clinical applications.

Algorithms↗

Assessment of endoleak significance after endovascular repair of abdominal aortic aneurysms: a lumped parameter model.

The outcome of endovascular repair of abdominal aortic aneurysms (AAAs) is greatly compromised by the possible occurrence of endoleak. Previously, the causes and effects of endoleak on a patient-specific basis have mainly been investigated in experimental studies. In order to both reconcile and physically substantiate the various experimental findings, a lumped parameter model of an incompletely excluded AAA was developed. After experimental validation, the model was applied to study the effects on the intrasac pressure of the degree of endoleak, the degree of stent-graft compliance, and the resistance of a possible outflow tract formed by a branching vessel. It is concluded that the presence of endoleak leads to elevated intrasac pressure, the mean of which is mainly governed by the outflow tract resistance, while the pulse pressure is governed by both the endoleak resistance and the stent-graft compliance. Based on the agreement of the current results with previous findings, it is further concluded that the lumped parameter modelling method provides a useful numerical tool for validating experimental endoleak studies.

Algorithms↗

Statistical shape model of atria, ventricles and epicardium from short- and long-axis MR images.

We describe a new 3-D statistical shape model of the heart consisting of atria, ventricles and epicardium. The model was constructed by combining information on standard short- and long-axis cardiac MR images. In the model, the variability of the shape was modeled with PCA- and ICA-based shape models as well as with non-parametric landmark probability distributions and a probabilistic atlas. The statistical atlas was built from 25 healthy subjects. The shape model was evaluated by applying it to image segmentation. The probabilistic atlas was found to be superior to the other shape models (P < 0.001) in this study.

Adult↗

Can local ventricular fibrillation interval predict ventricular refractory period in human hearts?

Assessment of the spatial dispersion of ventricular refractory periods has become an important part of electrophysiological study in both experimental and clinical settings, because inhomogeneity of ventricular refractoriness is associated with an increased risk of life-threatening ventricular arrhythmias. Previous animal studies in dog and sheep have demonstrated that local ventricular fibrillation (VF) intervals measured from the heart surface correlate well with the ventricular effective refractory periods measured from the same ventricular sites. We hypothesise that local VF intervals may also predict the ventricular refractory periods in human hearts, hence, can be used to assess the spatial dispersion of refractoriness and to predict the risk of ventricular arrhythmias.

Animals↗

The arterial circle of Willis of the mouse helps to decipher secrets of cerebral vascular accidents in the human.

The human brain represents an elaborate product of hominizing evolution. Likewise, its supporting vasculature may also embody evolutionary consequences. Thus, it is conceivable that the human tendency to develop cerebral vascular accidents (CVAs) might represent a disease of hominization. In a search for hominizing changes on the arterial circle of Willis (hWAC), we attempted an anatomical comparison of the hWAC with that of the mouse (mWAC) by injecting aliquots of resin into the vasculature of the mouse and then creating vascular endocasts of the mWAC. The internal carotid artery of the mouse (mICA) unites with the mWAC midway between the middle cerebral artery (mMCA) and posterior cerebral artery (mPCA). The mWAC does not complete a circle: the mWAC nourishes the anterior portion of the circle which branches out to the olfactory artery (OlfA) and mPCA, along with the mMCA, and the basilar artery (mBA) does not connect to the mPCA. The OlfA is thicker than the mMCA. The relative brain weight of the mouse was 74 g on average for a 60 kg male and 86 g for a 60 kg female, respectively, as compared with 1424 g for a 60 kg man. These findings are consistent with the mouse being a nocturnal carnivore that lives on olfactory information in contrast to the human that lives diurnally and depends on visual and auditory information. In man, the human ICA (hICA) unites with the hWAC at a point where the human middle cerebral artery (hMCA) branches out, and thus, blood from the hICA does not flow through the hWAC but drains into the hMCA directly. The hMCA is thicker than the anterior cerebral artery. The hPCA receives blood from the hBA rather than from the hICA, and thus, the entire hWAC forms a closed circuit. Since the hICA drains directly into the hMCA without flowing a distance through the hWAC, the capacitor and equalizer functions of the WAC will be mitigated so much that the resultant hemodynamic changes would render the hMCA more likely to contribute to CVAs. Thus, anatomical findings and possibly functions of the arterial circle of Willi may vary from one species to another, depending on one's specific cerebral evolution.

Animals↗

The role of altered impedance in the pathophysiology of normal pressure hydrocephalus, Alzheimer's disease and syringomyelia.

Normal pressure hydrocephalus, Alzheimer's disease and syringomyelia appear to be completely unrelated diseases, however, they share a reduction in subarachnoid space compliance as part of their pathophysiology. This paper discusses the physiology of pulsatile fluid flow and its relationship to compliance/impedance. Unlike continuous or non-pulsatile flow where the vessel resistance and pressure gradient are the major determinants of the volume of fluid flowing, when the fluid flow in a vessel pulsates then the vessel compliance/impedance becomes important. A reduction in compliance in the craniospinal cavity in each of the three diseases discussed, leads to a limitation of the outflow vessel compliance. Therefore, there is an increase in outflow vessel impedance. The venous blood, CSF and interstitial brain/spinal cord fluid all have significantly pulsatile flow and an increase in the impedance of the fluid outflow in each disease would limit the volume of these fluids as they attempt to cross the subarachnoid space. It is hypothesised that a reduction in the efficiency of the outflow of venous blood, CSF and interstitial brain/spinal cord fluid would lead to the accumulation of CSF in NPH, cord fluid in syringomyelia and delay the excretion of beta amyloid via the interstitial drainage pathways in AD.

Alzheimer Disease↗

Hypothesis about the physiopathology of acute deterioration and sudden death caused by colloid cysts of the third ventricle.

In this paper, the authors review the mechanisms of acute deterioration and sudden death caused by colloid cysts (CCs). These dreaded events are widely recognized complications of CC, however the mechanism(s) in cause has been subject to controversy. Increased intracranial pressure (ICP) is a common event associated with many cerebral disorders, including colloid cysts, though compensatory mechanisms may allow ICP to remain at normal levels. However, a compensated system might decompensate for many factors such as intracranial haemorrhage, acute hydrocephalus, brain oedema, or an increase in sagittal sinus pressure (SSP). The sagittal sinus in adults with brain tumours appears to respond unpredictably when ICP increases and in some patients, when ICP increased the SSP increased too due to the fact that their sinuses collapse. We therefore speculate that the mechanism of acute deterioration and sudden death is a multifactorial and dynamic process, in which the increase in sagittal sinus pressure would appear to be an important element. It seems possible that acute deterioration is initiated by an increase in sagittal sinus pressure, which provokes acute brain swelling, with a series of often-irreversible events, leading to sudden death. Since the majority of cases of acute deterioration and death are due to CCs of the third ventricle, the authors suggest that surgical resection should be carried out on diagnosed CCs measuring over 1 cm, because sudden death has not been reported as having been caused by colloid cysts measuring less than this dimension.

Acute Disease↗