Branching tree model with fractal vascular resistance explains fractal perfusion heterogeneity

A Biophysical Model for Cardiovascular Effects of Acupuncture-Underlying Mechanisms Based on First Principles

According to recent translations by medical professionals of the foundational texts of Chinese Medicine, the acupuncture channel system can be reconciled with the neurovasculature. From there, the underlying mechanisms of the effects of acupuncture can be drawn from established physiology and known physical laws. A large body of research has been carried out using cardiovascular markers to measure the effects of acupuncture. Three of these parameters are re-viewed and explored anew in detail. The focus is on changes in microcirculation, blood pressure, and heart rate variability. The physiological mechanisms accounting for the observed changes are proposed to be ascending vasodilatation, resetting of the baroreceptor reflex, and re-organization of heart beating patterns around intrinsically assigned attractor sets.

3D-printed biomaterials with regional auxetic properties

Tissue engineering is replete with methods for inducing and mediating cell differentiation, which are crucial for ensuring proper regrowth of desired tissues. In this study, we developed a 3D-printed, non-positive Poisson's Ratio (NPPR) scaffold intended for future use in stretch-mediated cell differentiation applications, such as in muscle and tendon regeneration. We utilized dynamic optical projection stereolithography (DOPsL) to fabricate multi-layered, cell-laden NPPR scaffolds - these scaffolds can not only support aggregate cell growth, but can also be printed with locally-tunable force-displacement properties at length scales appropriate for tissue interaction. These NPPR multilayered mesh scaffolds can be embedded into highly elastic hydrogels in order to couple a reduced NPPR behavior to a normally Positive Poisson's Ratio (PPR) solid bulk material. This hybrid structure may potentially enable induced 'auxetic' behavior at the single-cell scale while tuning the Poisson's Ratio to a more isolated value. This would be uniquely suited for providing stretch-mediated effects for various cell-types within the tendon-to-muscle tissue transition.

Algorithmically generated rodent hepatic vascular trees in arbitrary detail

Physiologically realistic geometric models of the vasculature in the liver are indispensable for modelling hepatic blood flow, the main connection between the liver and the organism. Current in vivo imaging techniques do not provide sufficiently detailed vascular trees for many simulation applications, so it is necessary to use algorithmic refinement methods. The method of Constrained Constructive Optimization (CCO) (Schreiner et al., 2006) is well suited for this purpose. Its results after calibration have been previously compared to experimentally acquired human vascular trees (Schwen and Preusser, 2012). The goal of this paper is to extend this calibration to the case of rodents (mice and rats), the most commonly used animal models in liver research. Based on in vivo and ex vivo micro-CT scans of rodent livers and their vasculature, we performed an analysis of various geometric features of the vascular trees. Starting from pruned versions of the original vascular trees, we applied the CCO procedure and compared these algorithmic results to the original vascular trees using a suitable similarity measure. The calibration of the postprocessing improved the algorithmic results compared to those obtained using standard CCO. In terms of angular features, the average similarity increased from 0.27 to 0.61, improving the total similarity from 0.28 to 0.40. Finally, we applied the calibrated algorithm to refine measured vascular trees to the (higher) level of detail desired for specific applications. Having successfully adapted the CCO algorithm to the rodent model organism, the resulting individual-specific refined hepatic vascular trees can now be used for advanced modeling involving, e.g., detailed blood flow simulations.

Design of vascular networks: a mathematical model approach

In this paper, methods for the modeling of a realistic vascular tree in 3D space and for hemodynamic calculating throughout the simulated tree structure have been developed. Vascular trees are generated based on the power law relationship. Variations in branching asymmetry and segment length of the vasculature are precisely controlled by the designed gaussian distributions. The resolution limit of current imaging techniques for vessel detectability is simulated by designed pruning technique. On the basis of the generated diameters and lengths, the space locations of the vessel segments are calculated by optimizing the out-of-plane angles of two daughter branches. The generated vascular tree not only follows the power law relationship, but also maximizes the filling volume of the tree structure in 3D space. From the hemodynamic calculation in the simulated vasculature, the processes for which structural changes affect hemodynamic distributions are studied in detail. And also, the fractal nature and resistance of the vascular trees are quantified and compared. The developed method provides some insight into the design of the vascular trees in biology and may be used as a reference for the study of vascular diseases.

Analysis and algorithmic generation of hepatic vascular systems

A proper geometric model of the vascular systems in the liver is crucial for modeling blood flow, the connection between the organ and the rest of the organism. In vivo imaging does not provide sufficient details, so an algorithmic concept for extending measured vascular tree data is needed such that geometrically realistic structures can be generated. We develop a quantification of similarity in terms of different geometric features. This involves topological Strahler ordering of the vascular trees, statistical testing, and averaging. Invariant features are identified in human clinical in vivo CT scans. Results of the existing "Constrained Constructive Optimization" algorithm are compared to real vascular tree data. To improve bifurcation angles in the algorithmic results, we implement a postprocessing step calibrated to the measured features. This framework is finally applied to generate realistic additional details in a patient-specific hepatic vascular tree data set.

Temperature change near microbubbles within a capillary network during focused ultrasound

Preformed gas bubbles can increase energy absorption from an ultrasound beam and therefore they have been proposed for an enhancer of ultrasound treatments. Although tissue temperature measurements performed in vivo using invasive thermocouple probes and MRI thermometry have demonstrated increased tissue temperature, the microscopic temperature distribution has not been investigated so far. In this study the transfer of heat between bubbles and tissue during focused ultrasound was simulated. Microbubble oscillations were simulated within a rat cortical microvascular network reconstructed from in vivo dual-photon microscopy images and the power density of these oscillations was used as an input term in the Pennes bioheat transfer equation. The temperature solution from the bioheat transfer equation was mapped onto vascular data to produce a three-dimensional temperature map. The results showed high temperatures near the bubbles and slow temperature rise in the tissue. Heating was shown to increase with increasing bubble frequency and insonation pressure, and showed a frequency-dependent peak. The goal of this research is to characterize the effect of various parameters on bubble-enhanced therapeutic ultrasound to allow better treatment planning. These results show that the induced temperature elevations have nonuniformities which may have a significant impact on the bio-effects of the exposure.

Effects of old age on vascular complexity and dispersion of the hepatic sinusoidal network

OBJECTIVES

In old age, there are marked changes in both the structure of the liver sinusoidal endothelial cell and liver perfusion. The objective of this study was to determine whether there are also aging changes in the microvascular architecture and vascular dispersion of the liver that might influence liver function.

METHODS

Vascular corrosion casts and light micrographs of young (4 months) and old (24 months) rat livers were compared. Fractal and Fourier analyses and micro-computed tomography were used. Vascular dispersion was determined from the dispersion number for sucrose and 100-nm microspheres in impulse response experiments.

RESULTS

Age did not affect sinusoidal dimensions, sinusoidal density, or dispersion number. There were changes in the geometry and complexity of the sinusoidal network as determined by fractal dimension and degree of anisotropy.

CONCLUSIONS

There are small, age-related changes in the architecture of the liver sinusoidal network, which may influence hepatic function and reflect broader aging changes in the microcirculation. However, sinusoidal dimensions and hepatic vascular dispersion are not markedly influenced by old age.

Determination of fractional flow reserve (FFR) based on scaling laws: a simulation study

Fractional flow reserve (FFR) provides an objective physiological evaluation of stenosis severity. A technique that can measure FFR using only angiographic images would be a valuable tool in the cardiac catheterization laboratory. To perform this, the diseased blood flow can be measured with a first pass distribution analysis and the theoretical normal blood flow can be estimated from the total coronary arterial volume based on scaling laws. A computer simulation of the coronary arterial network was used to gain a better understanding of how hemodynamic conditions and coronary artery disease can affect blood flow, arterial volume and FFR estimation. Changes in coronary arterial flow and volume due to coronary stenosis, aortic pressure and venous pressure were examined to evaluate the potential use of flow and volume for FFR determination. This study showed that FFR can be estimated using arterial volume and a scaling coefficient corrected for aortic pressure. However, variations in venous pressure were found to introduce some error in FFR estimation. A relative form of FFR was introduced and was found to cancel out the influence of pressure on coronary flow, arterial volume and FFR estimation. The use of coronary flow and arterial volume for FFR determination appears promising.

Branching Morphology of the Rat Hepatic Portal Vein Tree: A Micro-CT Study

In contrast to the lung and the myocardium, the liver is a relatively homogeneous organ with fewer anatomic constraints on vascular branching. Hence, we hypothesize that the hepatic vasculature could more closely follow optimization of branching geometry than is the case in other organs. The geometrical and fractal properties of the rat hepatic portal vein tree were investigated, with the aid of three-dimensional micro-computed tomography data. Frequency distributions of vessel radii were obtained at three different voxel resolutions and fitted to a theoretical model of dichotomous branching. The model predicted an average junction exponent of 3.09. Hemodynamic model calculations showed that with generation, relative shear stress decreases. Branching angles were found to oscillate between those predicted by two optimality principles of minimum power loss and volume, and of minimum shear stress and surface. The liver shows a variation in branching morphology similar to that of other organs. Therefore, we conclude that anatomic constraints do not have a major perturbing impact.

Fractal properties of perfusion heterogeneity in optimized arterial trees: a model study

Regional blood flows in the heart muscle are remarkably heterogeneous. It is very likely that the most important factor for this heterogeneity is the metabolic need of the tissue rather than flow dispersion by the branching network of the coronary vasculature. To model the contribution of tissue needs to the observed flow heterogeneities we use arterial trees generated on the computer by constrained constructive optimization. This method allows to prescribe terminal flows as independent boundary conditions, rather than obtaining these flows by the dispersive effects of the tree structure. We study two specific cases: equal terminal flows (model 1) and terminal flows set proportional to the volumes of Voronoi polyhedra used as a model for blood supply regions of terminal segments (model 2). Model 1 predicts, depending on the number Nterm of end-points, fractal dimensions D of perfusion heterogeneities in the range 1.20 to 1.40 and positively correlated nearest-neighbor regional flows, in good agreement with experimental data of the normal heart. Although model 2 yields reasonable terminal flows well approximated by a lognormal distribution, it fails to predict D and nearest-neighbor correlation coefficients r1 of regional flows under normal physiologic conditions: model 2 gives D = 1.69 +/- 0.02 and r1 = -0.18 +/- 0.03 (n = 5), independent of Nterm and consistent with experimental data observed under coronary stenosis and under the reduction of coronary perfusion pressure. In conclusion, flow heterogeneity can be modeled by terminal positions compatible with an existing tree structure without resorting to the flow-dispersive effects of a specific branching tree model to assign terminal flows.