A computational model of intussusceptive microvascular growth and remodeling

Non-sprouting angiogenesis, also known as intussusceptive angiogenesis (IA), is an important modality of blood vessel morphogenesis in growing tissues. We present a novel computational framework for simulation of IA to answer some of the questions concerning the underlying mechanisms of the remodeling process. The model relies on mechanical interactions between blood and tissue, includes the structural maturation of the vessel wall, and is controlled by stimulating or inhibiting chemical agents. The model provides a simple explanation for the formation of microvessels and bifurcations from capillaries via IA, allowing for both maintenance and avoidance of shunt vessels. Detailed hemodynamic and transport properties for oxygen, metabolites or growth factors can be predicted. The model is an in silico framework for testing certain conceptual ideas about the mechanisms of intussusceptive growth and remodeling, in particular those related to mechanical and transport phenomena.     

Prevention of microvascular thrombosis with low-dose tissue plasminogen activator.

In a blind, randomized study, two groups, each of seven rabbits, were treated with either a very low dose of human melanoma cell line-derived tissue-type plasminogen activator (t-PA) or isotonic saline. t-PA (0.067 mg/kg of body weight) was administered intraaortically, 20 percent being given as a 30-second "bolus" infusion just prior to the reperfusion of intimectomized central ear arteries and the rest as a continuous infusion during the next 2 hours. Arteriotomic bleeding times, accumulations of 32P-labeled platelets, patency, and sizes of thrombus deposits 2 hours after reperfusion were recorded. To confirm the presence of tissue plasminogen activator in plasma, fibrin-plate lysis assays of arterial plasma were performed immediately before and 1/2 hour and 2 hours after starting drug infusion. Arteriotomic bleeding times were similar in both groups. Transient "oozing" from wound edges occurred in 40 percent of rabbits treated with tissue plasminogen activator. Patency was significantly increased and thrombus deposits were smaller in the tissue plasminogen activator group. Plasma from animals treated with tissue plasminogen activator caused massive lysis of fibrin plates, whereas plasma from control animals caused little or no lysis. Platelet accumulations were very similar in both groups, indicating that occlusive thrombi mainly consisted of other elements than platelets (e.g., fibrin and red cells). Scanning electron microscopy showed normally adhering and aggregating platelets in both groups. This study shows that mild fibrinolytic stimulation with tissue plasminogen activator significantly improves patency in severely traumatized small-caliber arteries and indicates that such treatment may be one approach to prevent thrombosis at microvascular anastomotic sites.     

A new modified canine model of portal vein thrombosis

Portal vein thrombosis (PVT) is a common complication of liver cirrhosis. Gao et al. [1] reported that the prevalence of PVT in patients with cirrhosis is 8.82%. With the rapid developments in image-based diagnostic technology, the diagnosis rate of PVT is gradually increasing [2]. A follow-up study of 1243 patients with cirrhosis revealed that the cumulative incidences of PVT at 1, 3, and 5 years are 4.6%, 8.2%, and 10.7%, respectively [3]. PVT is a life-threatening factor for patients with cirrhosis, leading to portal hypertension and aggravating gastrointestinal hemorrhage [4]. The prevention of PVT has become a focus of clinical concern nowadays. It is well known that the establishment of animal models is the basis of scientific research. However, it is currently difficult to establish PVT models in large animals. Thereby, the establishment of a stable PVT animal model to study PVT is urgent and significant. We successfully established a new canine model of PVT involving the injection of an autologous thrombus through an indwelling catheter in the portal vein. This model is reliable for further studies of surgical treatment and drug therapy for PVT.     

A functional model of the rat kidney

Summary A mathematical model of the nephron was developed by writing a set of material balance equations for the flow of urea, salt and water along the length of the nephron. The geometric proportions have been elaborated in a foregoing study and are taken here as a basis, in particular the model configuration of the collecting duct system. The medullary interstitial solute concentration profiles are taken to increase linearly in outer and inner zone. The several transepithelial fluxes are driven by diffusion, osmosis, solvent drag and active transport. The development of osmotic gradient in the inner medulla is taken here to be caused by active secretion of salt into the descending limb of Henle's loop. The parameters in the flux equations for all parts of the nephron and the concentration values at the end of each tubular section are determined by collecting and averaging the values given in literature and by extrapolating the measurement data.The simulation of the model equations with these averaged parameters resulted in concentration profiles which at the ends of the several tubular sections were consistent with the values observed in experimental investigations.This work was supported by the Deutsche Forschungsgemeinschaft.     

A combined macro and microvascular model for whole limb heat transfer

A new prototype model for whole limb heat transfer is proposed wherein the countercurrent heat exchange from the large central arteries and veins in the core of the limb is coupled to microvascular models for the surrounding muscle and the cutaneous tissue layers. The local microvascular temperature field in the muscle tissue is described by the bioheat equation of Weinbaum and Jiji. The new model allows for an arbitrary axial variation of cross-sectional area and blood distribution between the muscle and cutaneous tissue, accounts for the blood flow to and heat loss from the hand and treats the venous return temperature and surface temperature distribution as unknowns that are determined as part of the solution to the overall boundary value problem. Representative solutions are presented for a wide range of environmental conditions for a limb in both the resting state and during exercise.     

A quantitative model of venous stasis thrombosis in rats.

A quantitative model of stasis-type of venous thrombosis in rats is described. The ligated bowel loop was used after provocation by an injection of kaolin. The mesenteric vessels of the loop were cut in a dish filled with distilled water and the extinction of escaped haemoglobin was measured photometrically. Heparin was highly effective in this model. Vessel wall lesion may be used or inducing thrombosis instead of kaolin.     

Structural and functional units in the pial microvascular system

A study was made of the pial arterial microcircles formed upon successive branching and anastomosing of the terminal pial vessels on the brain cortex surface at different levels of the phylogenetic development of the vertebrata. It was discovered that the pial arterial microcircles progressively become more complicated in the following order: chicken, rabbit, cat, dog, monkey. The morphological signs of the microcircles undergo progressive development: 1) they are formed primarily from small pial arterial branches possessing high vasomotor activity; 2) the area of each circle becomes less and less and their amount per unit of the brain surface increases respectively; 3) the quantity of the feeding arterial branches rises despite the reduction of the circle size; 4) the number of outgoing precortical and radial arteries entering the brain cortex increases; 5) the areas of the brain cortex supplied by individual radial arteries become less and less. This ensures increasingly delicate regulation of adequate blood supply of the smallest areas of the brain cortex.     

A factor analysis model for functional genomics

Background  

Expression array data are used to predict biological functions of uncharacterized genes by comparing their expression profiles to those of characterized genes. While biologically plausible, this is both statistically and computationally challenging. Typical approaches are computationally expensive and ignore correlations among expression profiles and functional categories.     

Conodont assemblages: A new functional model

A functional model for the conodont apparatus is proposed based on Carboniferous bedding plane assemblages. It is proposed that the conodont assemblage functioned as a filter feeding and respiratory organ in organisms of unknown affinities, and that the organisation of elements in the assemblage genus Scottognathus can be used as a basic plan for interpreting the arrangement of conodont elements in other assemblages. In our model the Platform Blades opened and closed the anterior end of the system, the sieve consisted of Arched Blades, Pick-shaped Blades (assemblage genera Lewistownella and Lochriea) and the main cusps of the Elongate Blades; the denticulated bars of Elongate Blades and Pick-shaped Blades (form genera Scottognathus and Westphalicus) acted as a support for ciliated tissue. A radial and bilateral arrangement for the Elongate Blades is presented and discussed. Using this model as a guide we have reconstructed the assemblage genus Duboisella.The success of conodont organisms is attributed to the genetic plasticity of elements of the filter respiratory system, which enabled the system to adapt to evolutionary changes in the marine plankton. Ideas for further research are presented. In this account we have chosen to refer to the morphological form of conodont elements (Rhodes, 1954) rather than to the form generic and specific names assigned to them in the literature, e.g., we use the term Elongate Blades, instead of Hindeodella.     

Structural adaptation of microvascular networks: functional roles of adaptive responses

Terminal vascular beds continually adapt to changing demands. A theoretical model is used to simulate structural diameter changes in response to hemodynamic and metabolic stimuli in microvascular networks. Increased wall shear stress and decreased intravascular pressure are assumed to stimulate diameter increase. Intravascular partial pressure of oxygen (PO(2)) is estimated for each segment. Decreasing PO(2) is assumed to generate a metabolic stimulus for diameter increase, which acts locally, upstream via conduction along vessel walls, and downstream via metabolite convection. By adjusting the sensitivities to these stimuli, good agreement is achieved between predicted network characteristics and experimental data from microvascular networks in rat mesentery. Reduced pressure sensitivity leads to increased capillary pressure with reduced viscous energy dissipation and little change in tissue oxygenation. Dissipation decreases strongly with decreased metabolic response. Below a threshold level of metabolic response flow shifts to shorter pathways through the network, and oxygen supply efficiency decreases sharply. In summary, the distribution of vessel diameters generated by the simulated adaptive process allows the network to meet the functional demands of tissue while avoiding excessive viscous energy dissipation.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behaviour of a system, differential equations have proved to be powerful for modelling and unravelling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge–Kutta fourth-order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

A general model of functional constraints on phenotypic evolution

A general model of the functional constraints on the rate and direction of phenotypic evolution is developed using a decomposition of the Lande-Arnold model of multivariate phenotypic evolution. The important feature of the model is the F matrix of performance coefficients reflecting the causal relationship between morphophysiological (m-p) and functional performance traits. The structure of F, which reflects the functional architecture of the organism, constrains the shape of the adaptive landscape and thus the rate and direction of m-p trait evolution. The rate of m-p trait evolution is a function of the pattern of coefficients in a row of F. The sums and variances of these rows are related to current concepts of evolvability. The direction of m-p trait evolution through m-p trait space is a function of the functional covariances among m-p traits. The functional covariance between a pair of m-p traits is a measure of how much the traits function together and is computed as the covariance between rows of F. Finally, it is shown that genetic covariances between m-p traits and performance traits are a function of the F matrix, but a G matrix that includes these covariances cannot be used to model functional constraints effectively.     

A non-stationary model for functional mapping of complex traits

SUMMARY: Understanding the genetic control of growth is fundamental to agricultural, evolutionary and biomedical genetic research. In this article, we present a statistical model for mapping quantitative trait loci (QTL) that are responsible for genetic differences in growth trajectories during ontogenetic development. This model is derived within the maximum likelihood context, implemented with the expectation-maximization algorithm. We incorporate mathematical aspects of growth processes to model the mean vector and structured antedependence models to approximate time-dependent covariance matrices for longitudinal traits. Our model has been employed to map QTL that affect body mass growth trajectories in both male and female mice of an F2 population derived from the Large and Small mouse strains. The results from this model are compared with those from the autoregressive-based functional mapping approach. Based on results from computer simulation studies, we suggest that these two models are alternative to one another and should be used simultaneously for the same dataset.     

Therapeutic value of intravenous heparin in microvascular surgery: an experimental vascular thrombosis study

In an attempt to decrease a 10 to 15 percent vascular thrombosis rate leading to graft occlusion, low-dose human-grade heparin was studied to determine if carefully monitored intravenous therapy would increase 7-day patency in a known potent thrombosis model. In New Zealand white rabbits, the type of infusate administered intravenously, either saline (30 animals) or heparin (35 animals), was selected at random after completing a 2-mm arterial inversion graft in the femoral artery. A 72-hour infusion was used in all animals; the control group received sterile saline and the experimental group received a heparin infusion at 45 microliters per hour after a 500-unit bolus. All grafts in both groups were patent at the time of groin closure. Patency in the heparin-perfused group was 67 percent (24 of 35) as compared to 19 percent (6 of 30) in the control group (p less than 0.05) 1 week postoperatively. Scanning electron microscopy showed significantly less dense fibrin deposition and a decrease in the number of aggregated platelets in the heparin-perfused grafts. Partial tissue thromboplastin time values in the experimental group ranged between 55 and 75 seconds (control 20 to 25 seconds). We have shown that heparin, an inexpensive and readily available agent, maintains 1-week microarterial patency and results in few complications in a reliable, reproducible, and versatile thrombosis model. The clinical ramifications of using an antiplatelet agent that diminishes fibrin deposition in microsurgery are apparent.