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R Karch

Publications and source records attributed to R Karch.

6 recordsLinked to original sources
PubMed2000

Staged growth of optimized arterial model trees.

There is a marked difference in the structure of the arterial tree between epi- and endocardial layers of the human heart. To model these structural variations, we developed an extension to the computational method of constrained constructive optimization (CCO). Within the framework of CCO, a model tree is represented as a dichotomously branching network of straight cylindrical tubes, with flow conditions governed by Poiseuille's law. The tree is grown by successively adding new terminal segments from randomly selected points within the perfusion volume while optimizing the geometric location and topological site of each new connection with respect to minimum intravascular volume. The proposed method of "staged growth" guides the generation of new terminal sites by means of an additional time-dependent boundary condition, thereby inducing a sequence of domains of vascular growth within the given perfusion volume. Model trees generated in this way are very similar to reality in their visual appearance and predict diameter ratios of parent and daughter segments, the distribution of symmetry, the transmural distribution of flow, the volume of large arteries, as well as the ratio of small arterial volume in subendocardial and subepicardial layers in good agreement with experimental data. From this study we conclude that the method of CCO combined with staged growth reproduces many characteristics of the different arterial branching patterns in the subendocardium and the subepicardium, which could not be obtained by applying the principle of minimum volume alone.

Algorithms↗
PubMed1999

Shear stress distribution in arterial tree models, generated by constrained constructive optimization.

Models of arterial trees are generated by the algorithm of Constrained Constructive Optimization (CCO). Straight cylindrical, binary branching tubes are arranged in an optimized fashion so as to convey blood to the terminal sites of the tree, which are distributed over a predefined area, representing the tissue to be perfused. All terminal segments supply equal flows at a unique terminal pressure, and the radii of parent and daughter segments are related via a bifurcation law. The connective structure and geometry of the model are optimized according to a target function such as total intravascular volume. The shear rate between blood and the vessel walls is computed in each segment and a new method is presented for rescaling a given CCO tree to a desired value of shear rate in the root segment. The effect of viscosity varying with shear rate is evaluated and a new method is presented for rescaling a CCO-tree segment by segment to consistent values of radii and variable viscosity. Shear stress is evaluated for its deviation from being proportional to shear rate and then subjected to various types of analyses. Usually both, shear stress and its variability, are found to be larger in the smaller than in the larger segments of the CCO-model trees. However, it is shown how the shear-stress distribution can be reshuffled between small and large segments when rescaling a CCO tree to obey a different bifurcation law, while its whole geometry remains unchanged and all boundary conditions remain fulfilled. The selection of optimization target is found to drastically affect shear-stress variability within bifurcations, which reaches a distinct minimum if the model is optimized according to intravascular volume. Finally, a rank-analysis of shear stress within each bifurcation shows that only two out of six possible rank patterns actually occur: the parent segment always experiences medium shear stress while minimum shear stress resides mostly in the larger, less frequently in the smaller daughter.

Arteries↗
PubMed1999

A three-dimensional model for arterial tree representation, generated by constrained constructive optimization.

The computational method of constrained constructive optimization (CCO) has been generalized in two important respects: (1) arterial model trees are now grown within a convex, three-dimensional piece of tissue and (2) terminal flow variability has been incorporated into the model to account for the heterogeneity of blood flow observed in real vascular beds. Although no direct information from topographic anatomy enters the model, computer-generated CCO trees closely resemble corrosion casts of real arterial trees, both on a visual basis and with regard to morphometric parameters. Terminal flow variability was found to induce transitions in the connective structure early in the trees' development. The present generalization of CCO offers--for the first time--the possibility to generate optimized arterial model trees in three dimensions, representing a realistic geometrical substrate for hemodynamic simulation studies. With the implementation of terminal flow variability the model is ready to simulate processes such as the adaptation of arterial diameters to changes in blood flow rate or the formation of different patterns of angiogenesis induced by changing needs of blood supply.

Algorithms↗
PubMed1997

Limited bifurcation asymmetry in coronary arterial tree models generated by constrained constructive optimization.

Models of coronary arterial trees are generated by the algorithm of constrained constructive optimization (CCO). In a given perfusion area a binary branching network of straight cylindrical tubes is generated by successively adding terminal segments to the growing structure. In each step the site of connection is chosen according to an optimization target function (total intravascular volume), and in any stage of development the tree fulfills physiologic boundary conditions (constraints involving pressures, flows and bifurcation rules). CCO generates structures which in many aspects resemble real coronary arterial trees, except for very asymmetric bifurcations, occurring when a large branch gives off a tiny terminal segment. In the present work we evaluate an additional constraint within CCO, namely imposing a limit on the asymmetry of bifurcations during the construction process. Model trees are grown with different limits imposed, and the effects on structure are studied both phenomenologically and via statistical descriptors. As the limit to asymmetry is tightened, blood is conveyed to the perfusion sites via detours rather than directly and the comparison with measured data shows that the structure to change from a conveying to a delivering type of function. Simultaneously total intravascular volume, surface and sum of segments' lengths increase. It is shown why and how local bifurcation asymmetry is able to determine the global structure of the optimized arterial tree model. Surprisingly, the pressure profile from inlet to terminals, being a functional characteristic, remains unaffected.

Algorithms↗
PubMedDate not supplied

Functional characteristics of optimized arterial tree models perfusing volumes of different thickness and shape.

The relationship between the 'shape of an organ' and the 'cost of blood transport' to perfuse its tissue was evaluated on the basis of optimized arterial model trees simulated to perfuse square-based 100-cm(3) volumes of different shape ('flat' versus 'thick' as defined by the ratio of thickness to side-length h/s < or =1). Specifically, the effects of 'shape' on tree structure, blood transport, and on hemodynamic characteristics were investigated. Branching models of arterial trees were generated by constrained constructive optimization (CCO), based on an identical set of model parameters. All model trees were geometrically and topologically optimized for intravascular volume. Tree structures achieved tremendous savings of blood (transport medium) in comparison to a system of separate tubes. Thickening the perfusion volume (increasing h/s) resulted in a significant decrease of mean transport length, deposition time, and intravascular total volume in the tree. 'Thick' perfusion volumes induced CCO trees to branch more symmetrically into a number of equivalent subtrees repetitiously splitting into smaller ones; 'flat' structures were dominated throughout by a few asymmetrically branching major vessels. In summary, we conclude from systematic variation of shape that thicker perfusion volumes (h/s >0.1) facilitate efficient delivery of blood in comparison to large amounts of 'dead volume' to be carried over long distances in very thin pieces of tissue.

Arteries↗