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A simulated dye method for flow visualization with a computational model for blood flow.

A numerical dye method for the visualization of unsteady three-dimensional flow calculations is introduced by coupling the unsteady convection-diffusion equation to the Navier-Stokes equation for mass and momentum. This system of equations is descretized using a finite volume projection-like algorithm with generalized coordinates and overset grids. A powerful pressure prediction method is used to accelerate the convergence of the Pressure Poisson equation. To demonstrate the visualization technique, blood flow through the aortic arch region and the three main arterial branches is computed using various Womersley numbers. In this technique, parcels of fluid are followed in time as a function of the cardiac cycle without having to track individual particles, which in turn aids us to better understand some important aspects of the three-dimensionality of the developing unsteady flow. Using this numerical dye method we analyze the strength of the cross flow during the cardiac cycle, the relationship between the penetration of blood into the aortic branches from its relative position in the ascending aortic region and the effects of the Womersley parameter. This technique can be very useful in the design and development of stents where the topology of the device would require understanding where the blood emanating from the heart ends up at the end of the cardiac cycle. Moreover, this method could be useful in investigating the influence of flow and geometry on the local introduction of medication.

Aorta, Thoracic↗

Transition from acute to chronic hypercapnia in patients with periodic breathing: predictions from a computer model.

Acute hypercapnia may develop during periodic breathing from an imbalance between abnormal ventilatory patterns during apnea and/or hypopnea and compensatory ventilatory response in the interevent periods. However, transition of this acute hypercapnia into chronic sustained hypercapnia during wakefulness remains unexplained. We hypothesized that respiratory-renal interactions would play a critical role in this transition. Because this transition cannot be readily addressed clinically, we modified a previously published model of whole-body CO2 kinetics by adding respiratory control and renal bicarbonate kinetics. We enforced a pattern of 8 h of periodic breathing (sleep) and 16 h of regular ventilation (wakefulness) repeated for 20 days. Interventions included varying the initial awake respiratory CO2 response and varying the rate of renal bicarbonate excretion within the physiological range. The results showed that acute hypercapnia during periodic breathing could transition into chronic sustained hypercapnia during wakefulness. Although acute hypercapnia could be attributed to periodic breathing alone, transition from acute to chronic hypercapnia required either slowing of renal bicarbonate kinetics, reduction of ventilatory CO2 responsiveness, or both. Thus the model showed that the interaction between the time constant for bicarbonate excretion and respiratory control results in both failure of bicarbonate concentration to fully normalize before the next period of sleep and persistence of hypercapnia through blunting of ventilatory drive. These respiratory-renal interactions create a cumulative effect over subsequent periods of sleep that eventually results in a self-perpetuating state of chronic hypercapnia.

Acute Disease↗

A critical interpretation of experiments on binding of peptide hormone to specific receptors by computer modelling.

Many investigations dealing with the interaction of peptide hormones and specific cell membrane receptors imply the existence of two classes of independent binding sites. On class is characterized by high affinity and low capacity, the other one by low affinity and high capacity. This conclusion has been derived from the fact that the Scatchard plots of binding data show a significant upward curvature. Using a more precise and critical method of evaluation these findings probably must be revised in some cases. Other conclusions taken from linear plots concerning the regulation of hormone receptors should be discussed more carefully. Some sources of errors caused by an uncritical interpretation of Scatchard plots are demonstrated.

Animals↗

The effect of perfusion on soft tissue mechanical properties: a computational model.

Some simple finite element models were constructed to investigate the magnitude and character of changes in mechanical properties of very soft tissues due to the loss of perfusion. Changes in the apparent stress-strain curve were used to characterise the effect of simulated blood perfusion pressure on the engineering stress-strain curve. The results indicated that the blood to tissue volume ratio and the perfusion pressure have the strongest effect on the effective stress-strain response of a representative tissue cell. Tissue viscoelasticity increased the sensitivity of the system to perfusion pressure changes.

Brain↗

The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage.

Articular cartilage plays a vital role in the function of diarthrodial joints. Due to osteoarthritis degeneration of articular cartilage occurs. The initial event that triggers the pathological process of cartilage degeneration is still unknown. Cartilage damage due to osteoarthritis is believed to be mechanically induced. Hence, to investigate the initiation of osteoarthritis the stresses and strains in the cartilage must be determined. So far the most common method to accomplish that is finite element analysis. This paper provides an overview of computational descriptions developed for this purpose, and what they can be used for. Articular cartilage composition and structure are discussed in relation with degenerative changes, and how these affect mechanical properties.

Animals↗

Computer modelling studies of ribonuclease A-pyrimidine nucleotide complexes.

Different modes of binding of pyrimidine monophosphates 2'-UMP, 3'-UMP, 2'-CMP and 3'-CMP to ribonuclease (RNase) A are studied by energy minimization in torsion angle and subsequently in Cartesian coordinate space. The results are analysed in the light of primary binding sites. The hydrogen bonding pattern brings out roles for amino acids such as Asn44 and Ser123 apart from the well known active site residues viz., His12,Lys41,Thr45 and His119. Amino acid segments 43-45 and 119-121 seem to be guiding the ligand binding by forming a pocket. Many of the active site charged residues display considerable movement upon nucleotide binding.

Animals↗

Genetic selection strategies: computer modeling.

There are four primary factors to consider in genetic selection strategies: 1) accuracy of selection, 2) selection intensity, 3) effective population size, and 4) mating system. Current theory indicates that optimum response to selection is achieved by maximizing the first three factors and using a mating systems that allows optimization of reproductive characteristics in dam lines and production characteristics in sire lines. However, with limited resources, compromises among the first three factors are needed. Simulations are useful for examining those compromises. Unrealistic simplifying assumptions are necessary for analytic theoretical results and thus do not address real world breeding problems. Using simulations, the relationship between selection accuracy, which is increased by use of family selection indices or Best Linear Unbiased Prediction (BLUP), and response to selection was examined. Results show that those procedures place a great restriction on effective population size, which offsets most of their advantage, i.e., there is too little emphasis on effective population size. A revision of the methodology and a reappraisal of the results of selection theory for optimization of genetic response is required. Another relationship that is of fundamental importance in breeding programs is that between selection intensity and effective population size. Analytical results for the additive case have been developed but have never been extended to heterotic traits. A gene level simulation program was developed to examine that relationship. Results show that the optimal selection strategy depends on the trait being selected. For additive traits and in the short term (20 generations), one should maximize selection intensity. For heterotic traits, an intermediate proportion (25% of each sex) gives optimal response. In all breeding strategies, primary attention must be given to the rate of inbreeding, which is increased by increasing either accuracy of selection or selection intensity. Inbreeding reduces response to selection in two ways. First, for both additive and nonadditive traits, inbreeding is a measure of the amount of random genetic drift that has occurred. Genetic drift causes loss of favorable alleles. Once lost, those alleles can never be recovered and thus genetic drift lowers the selection limit. Second, for heterotic traits, inbreeding results in a depression of the mean caused by directional dominance.

Animals↗

Intracarotid pressure measurements in the evaluation of a computer model of the cerebral circulation.

BACKGROUND: It is difficult to predict which patients will tolerate occlusion of the internal carotid artery. This difficulty arises primarily because of uncertainties in the prediction of the adequacy of collateral circulation. Because of these uncertainties, balloon test occlusion and other methods have been developed to determine a priori the safety of carotid occlusion. However, all the methods are associated with significant false-positive and false-negative rates, as well as other neurologic complications. Because of these problems, more accurate and less invasive methods for predicting tolerance of carotid occlusion are needed. METHODS: In this report, we present the initial clinical evaluation of a new method for assessing the collateral circulation aided by a mathematical model of the cerebral vasculature. Data from the angiograms of 14 patients who underwent carotid endarterectomy were used to create individualized simulations of their cerebral circulations. As a test of the accuracy of the simulations, we compared values of the intracarotid stump pressures predicted by the model to those measured at surgery during the period of carotid occlusion. RESULTS: The pressure predictions of the model correlated well with those measured at surgery. Linear regression analysis of measured versus predicted values yielded a line with slope 1.05. The line with slope 1.00, which denotes perfect agreement between predictions and measurements, is within the 95% confidence interval of the slope determined from the regression analysis. CONCLUSIONS: Mathematical models of the cerebrovascular circulation can provide good predictions of intravascular pressure in the collateral circulation, and may provide accurate predictions of the flow as well. The present study reveals several areas that need further development, such as the models of the microvasculature, measurement of the arterial dimensions from angiograms, and consideration of other collateral sources such as the leptomeningeal and retrograde ophthalmic sources of flow. Incorporation of these improvements may lead to a clinically useful, noninvasive assessment of the state of the cerebrovascular collateral circulation in the individual patient.

Angiography↗

Influence of anisotropy on local and global measures of potential gradient in computer models of defibrillation.

A heart-torso model including fiber orientation is used to calculate electric field strength in an active-can transvenous defibrillation system and estimate errors due to inadequate description of the anisotropy of the myocardium. Using a minimum potential gradient (5 V/cm) in a critical mass (95%) of the tissue, the estimated defibrillation voltage threshold for a right ventricular transvenous lead placement differs by only 4.5% when using isotropic myocardial conductivity compared to a model with realistic fiber architecture. In addition, pointwise comparisons of the two solutions reveal differences of 10.8% rms in potential gradient strength and 31.6% rms in current density magnitude in the myocardium, resulting in a change in the location of the low gradient regions. These results suggest that if a minimum potential gradient throughout the heart is necessary to avoid reinitiation of fibrillatory wave fronts, then isotropic models are adequate for modeling the electric field in the heart. Alternatively, the model demonstrates the use of physiologically based descriptions of anisotropy and fiber orientation, which will soon allow simulations of shock induced membrane polarization during defibrillation.

Adult↗

A new computer model of mitral valve hemodynamics during ventricular filling.

OBJECTIVE: Quantitative description of left ventricular diastolic filling and mitral valve function remains difficult despite advances in echocardiography. The purpose of the present study was to develop a lumped parameter model of left ventricular filling and validate it in porcine trials under physiological conditions and after valve replacement. METHODS: Six animals were instrumented with aortic flow meter, left atrial pressure catheter and combined left ventricular pressure-conductance catheter. The model simulates ventricular and arterial pressures and flows during diastolic filling. Input parameters include maximum mitral valve area, blood viscosity and density, atrial compliance, left ventricular active relaxation characteristics and initial pressure and flow values. The outputs of the model are atrial and ventricular pressure as well as transmitral flow as a function of time. The model primarily consists of a system of four first-order, non-linear ordinary differential equations which were solved with MATLAB software. RESULTS: Left atrial and ventricular pressure data and model flow curves were nearly identical under baseline conditions, during rapid preload reduction by vena caval occlusion and after prosthetic valve replacement. Measured and model based calculation of early diastolic filling volume (E-wave), showed an excellent correlation under all three conditions (r = 0.998, P < 0.0001; r = 0.997, P < 0.0001; r = 0.974, P < 0.0001, respectively) with a mean difference less then two percent. CONCLUSION: The new lumped parameter model of left ventricular filling allows for the first time a detailed simulation of pressure and flow curves in the left heart including transmitral hemodynamics.

Animals↗

Computer modeling of the rhamnogalacturonase-"hairy" pectin complex.

The structure of a pectin-bound complex of rhamnogalacturonase was modeled to identify the amino acid residues involved in catalysis and substrate binding. The "hairy" region of pectin, represented by six repeating stretches of (1-->4)-D-galacturonate-(1-->2)-L-rhamnose dimer, was flexibly docked into the putative binding site of rhamnogalacturonase from Aspergillus aculeatus whose X-ray structure is known. A search of the complex configurational space was performed using AutoDock for the dimeric and tetrameric sugar units in which the -1 galacturonate residue has various ring conformations. Then the plausible AutoDock solutions were manually extended to the dodecameric pectin models. Subsequently, the resulting complex models were subjected to solvated molecular dynamics using AMBER. In the best model, the substrate has an extended pseudo-threefold helix with the -1 ring in a 4H3 half-chair that approaches the transition state conformation. The catalytic machinery is clearly defined: Asp197 is a general acid and the activated water bound between Asp177 and Glu198 is a nucleophile. The active site is similar, with a small yet significant difference, to that of polygalacturonase that degrades the pectic "smooth" region of linear homopolymer of D-(1-->4)-linked galacturonic acid. Rhamnogalacturonase has ten binding subsites ranging from -3 to +7, while polygalacturonase has eight subsites from -5 to +3. The model suggests that the eight amino acids including three arginine and three lysine residues, all of which are invariantly conserved in the rhamnogalacturonase family of proteins, are important in substrate binding. The present study may aid in designing mutational studies to characterize rhamnogalacturonase.

Amino Acid Sequence↗

Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers.

Mitochondria in excitable cells are recurrently exposed to pulsatile calcium gradients that activate cell function. Rapid calcium uptake by the mitochondria has previously been shown to cause uncoupling of oxidative phosphorylation. To test (i) if periodic nerve firing may cause oscillation of the cytosolic thermodynamic potential of ATP hydrolysis and (ii) if cytosolic adenylate (AK) and creatine kinase (CK) ATP buffering reactions dampen such oscillations, a lumped kinetic model of an excitable cell capturing major aspects of the physiology has been developed. Activation of ATP metabolism by low-frequency calcium pulses caused large oscillation of the cytosolic, but not mitochondrial ATP/ADP, ratio. This outcome was independent of net ATP synthesis or hydrolysis during mitochondrial calcium uptake. The AK/CK ATP buffering reactions dampened the amplitude and rate of cytosolic ATP/ADP changes on a timescale of seconds, but not milliseconds. These model predictions suggest that alternative sources of capacitance in neurons and striated muscles should be considered to protect ATP-free energy-driven cell functions.

Action Potentials↗

Probing the activation of protein C by the thrombin-thrombomodulin complex using structural analysis, site-directed mutagenesis, and computer modeling.

Protein C (PC) is activated to an essential anticoagulant enzyme (activated PC or APC) by thrombin (T) bound to thrombomodulin (TM), a membrane receptor present on the surface of endothelial cells. The understanding of this complex biological system is in part limited due to the lack of integration of experimental and structural data. In the work presented here, we analyze the PC-T-TM pathway in the context of both types of information. First, structural analysis of the serine protease domain of PC suggests that a positively charged cluster of amino acids could be involved in the activation process. To investigate the importance of these basic amino acids, two recombinant PC mutants were constructed using computer-guided site-directed mutagenesis. The double mutant had the K62[217]N/K63[218]D substitution and in the single mutant, K86[241] was changed to S. Both mutants were activated by free thrombin at rates equivalent to that of wild-type PC (wt-PC) and they demonstrated similar calcium-dependent inhibition of their activation. The K86[241]S mutant and wt-PC were activated by thrombin bound to soluble TM at a similar rate. In contrast, the K62[217]N/ K63[218]D mutant was activated by the T-TM complex at a 10-fold lower catalytic efficiency due to a lowering in k(cat) and increase in Km. Molecular models for PC and thrombin bound to a segment of TM were developed. The experimental results and the modeling data both indicate that electrostatic interactions are of crucial importance to orient PC onto the T-TM complex. A key electropositive region centered around loops 37[191] and 60[214] of PC is defined. PC loop 37[191] is located 7-8 A from the TM epidermal growth factor (EGF) 4 while the loop 60[214] is about 10 A away from TM EGF4. Both loops are far from thrombin. A key function of TM could be to create an additional binding site for PC. The Gla domain of PC points toward the membrane and away from thrombin or the EGF modules of TM during the activation process.

Cell Line↗

A computational model of symbiotic composition in evolutionary transitions.

Several of the major transitions in evolutionary history, such as the symbiogenic origin of eukaryotes from prokaryotes, share the feature that existing entities became the components of composite entities at a higher-level of organization. This composition of pre-adapted extant entities into a new whole is a fundamentally different source of variation from the gradual accumulation of small random variations, and it has some interesting consequences for issues of evolvability. Intuitively, the pre-adaptation of sets of features in reproductively independent specialists suggests a form of 'divide and conquer' decomposition of the adaptive domain. Moreover, the compositions resulting from one level may become the components for compositions at the next level, thus scaling-up the variation mechanism. In this paper, we explore and develop these concepts using a simple abstract model of symbiotic composition to examine its impact on evolvability. To exemplify the adaptive capacity of the composition model, we employ a scale-invariant fitness landscape exhibiting significant ruggedness at all scales. Whilst innovation by mutation and by conventional evolutionary algorithms becomes increasingly more difficult as evolution continues in this landscape, innovation by composition is not impeded as it discovers and assembles component entities through successive hierarchical levels.

Adaptation, Physiological↗

Development of a computer model of the population dynamics of Amblyomma variegatum and simulations of eradication strategies for use in the Caribbean.

Control or eradication efforts should cover wide areas because of long-range migration potential of immature ticks attached to birds, such as cattle egrets. Careful follow-up inspections are also imperative. Simulation 1 shows how rapidly the population numbers may expand from small numbers, either introduced or missed. Simulation 4 indicates extending the treatment cycle beyond the residual effectiveness of the acaricide to save labor or funds would be false economy. The result could be to maintain the tick population indefinitely, with an accompanying increase in long-term control costs. Simulations 2 and 3 indicate that eradication is possible if response is prompt and the treatment cycle is less than the period of residual effectiveness of the acaricide used.

Animals↗

The solution structure of human coagulation factor VIIa in its complex with tissue factor is similar to free factor VIIa: a study of a heterodimeric receptor-ligand complex by X-ray and neutron scattering and computational modeling.

Factor VIIa (FVIIa) is a soluble four-domain plasma serine protease coagulation factor that forms a tight complex with the two extracellular domains of the transmembrane protein tissue factor in the initiating step of blood coagulation. To date, there is no crystal structure for free FVIIa. X-ray and neutron scattering data in solution for free FVIIa and the complex between FVIIa and soluble tissue factor (sTF) had been obtained for comparison with crystal structures of the FVIIa-sTF complex and of free factor IXa (FIXa). The solution structure of free FVIIa as derived from scattering data is consistent with the extended domain arrangement of FVIIa seen in the crystal structure of its complex with sTF, but is incompatible with the bent, less extended domain conformation seen in the FIXa crystal structure. The FVIIa scattering curve is also compatible with a subset of 317 possible extended structures derived from a constrained automated conformational search of 15 625 FVIIa domain models. Thus, the scattering data support extended domain models for FVIIa free in solution. Similar analyses showed that the solution scattering derived and crystal structures of the FVIIa-sTF complex were in good agreement. An automated constrained search for allowed structures for the complex in solution based on scattering curves showed that only a small family of compact models gave good agreement, namely those in which FVIIa and sTF interact closely over a large surface area. The general utility of this approach for structural analysis of heterodimeric complexes in solution is discussed. Analytical ultracentrifugation data and the modeling of these data were consistent with the scattering results. It is concluded that in solution FVIIa has an extended or elongated domain structure, which allows rapid interaction with sTF over a large surface area to form a high-affinity complex.

Amino Acid Sequence↗

Computer modelling of a cataract waiting list.

AIM: To compare three different strategies for determining admission dates for patients awaiting cataract extraction after scoring for visual impairment. METHODS: 357 patients attending for assessment for cataract surgery were scored for visual impairment. These scores were used as a basis for ranking patients into three impairment strata. A computer simulation was used to compare 3 years' operation of different admission strategies-a first come first served booking system, a triage booking system, and a waiting list system in which admissions were strictly ordered according to priority stratum. Differences in priority weighted delays before treatment were analysed. RESULTS: Both the triage system and the priority based waiting list system gave considerable reduction in priority weighted delay compared with a first come first served admission policy. The percentage reduction achieved (30%-60%) is strongly influenced by the number of weeks fully booked when the booking systems are introduced. The priority weighted delay of the triage system, where booking decisions were made at the time of the outpatient assessment, was consistently and substantially outperformed by the priority based waiting list system where the decision to allocate an admission date was delayed as long as possible. CONCLUSIONS: There is considerable scope for reducing delays to high priority patients if simple rules are used to determine admission dates. Using these rules, booking patients at the time of the outpatient assessment gives substantially less benefit in terms of reducing delays to high priority patients than if the decision about the admission date is deferred.

Cataract Extraction↗