A new fundamental bioheat equation for muscle tissue--part II: Temperature of SAV vessels

In this study, a new theoretical framework was developed to investigate temperature variations along countercurrent SAV blood vessels from 300 to 1000 microm diameter in skeletal muscle. Vessels of this size lie outside the range of validity of the Weinbaum-Jiji bioheat equation and, heretofore, have been treated using discrete numerical methods. A new tissue cylinder surrounding these vessel pairs is defined based on vascular anatomy, Murray's law, and the assumption of uniform perfusion. The thermal interaction between the blood vessel pair and surrounding tissue is investigated for two vascular branching patterns, pure branching and pure perfusion. It is shown that temperature variations along these large vessel pairs strongly depend on the branching pattern and the local blood perfusion rate. The arterial supply temperature in different vessel generations was evaluated to estimate the arterial inlet temperature in the modified perfusion source term for the s vessels in Part I of this study. In addition, results from the current research enable one to explore the relative contribution of the SAV vessels and the s vessels to the overall thermal equilibration between blood and tissue.     

The bleed off perfusion term in the Weinbaum-Jiji bioheat equation.

The microvascular organization and thermal equilibration of the primary and secondary arteries and veins that comprise the bleed off circulation to the muscle fibers from the parent countercurrent supply artery and veins are analyzed. The blood perfusion heat source term in the tissue energy equation is shown to be related to this vascular organization and to undergo a fundamental change in behavior as one proceeds from the more peripheral tissue, where the perfusion term is proportional to the Ta--Tv difference in the parent supply vessels, to the deeper tissue layers where the bleed off vessels themselves form a branching countercurrent system for each muscle tissue cylinder and the venous return temperature can vary between the local tissue temperature and Ta. The consequences of this change in behavior are examined for the Weinbaum-Jiji bioheat equation and a modified expression for the effective conductivity of perfused tissue is derived for countercurrent bleed off exchange.     

Numerical evaluation reveals the effect of branching morphology on vessel transport properties during angiogenesis

Blood flow governs transport of oxygen and nutrients into tissues. Hypoxic tissues secrete VEGFs to promote angiogenesis during development and in tissue homeostasis. In contrast, tumors enhance pathologic angiogenesis during growth and metastasis, suggesting suppression of tumor angiogenesis could limit tumor growth. In line with these observations, various factors have been identified to control vessel formation in the last decades. However, their impacts on the vascular transport properties of oxygen remain elusive. Here, we take a computational approach to examine the effects of vascular branching on blood flow in the growing vasculature. First of all, we reconstruct a 3D vascular model from the 2D confocal images of the growing vasculature at postnatal day 5 (P5) mouse retina, then simulate blood flow in the vasculatures, which are obtained from the gene targeting mouse models causing hypo- or hyper-branching vascular formation. Interestingly, hyper-branching morphology attenuates effective blood flow at the angiogenic front, likely promoting tissue hypoxia. In contrast, vascular hypo-branching enhances blood supply at the angiogenic front of the growing vasculature. Oxygen supply by newly formed blood vessels improves local hypoxia and decreases VEGF expression at the angiogenic front during angiogenesis. Consistent with the simulation results indicating improved blood flow in the hypo-branching vasculature, VEGF expression around the angiogenic front is reduced in those mouse retinas. Conversely, VEGF expression is enhanced in the angiogenic front of hyper-branching vasculature. Our results indicate the importance of detailed flow analysis in evaluating the vascular transport properties of branching morphology of the blood vessels.     

Hydrodynamics of arterial branching--the effect of arterial branching on distal blood supply

A study was conducted to investigate the hydrodynamics of branching flow in relation to the blood supply to the basal part of the brain. A series of measurements of the branching loss-coefficients under laminar steady flow were conducted using model branches with various geometries, and the effect of branching on blood supply to distal areas was described using a lumped-parameter model of the vascular structure. It was revealed that in the blood circulation, branching loss is important where a small artery divides off with a large branching angle from a large trunk. It was also indicated that the effect of such branching on the distal blood supply might become more significant when the peripheral resistance is reduced, thereby increasing the blood velocity in the trunk.     

Renal microvasculature in the adult pipid frog,Xenopus laevis: A scanning electron microscope study of vascular corrosion casts

We studied the opisthonephric (mesonephric) kidneys of adult male and female Xenopus laevis using scanning electron microscopy (SEM) of vascular corrosion casts and light microscopy of paraplast embedded tissue sections. Both techniques displayed glomeruli from ventral to mid-dorsal regions of the kidneys with single glomeruli located dorsally close beneath the renal capsule. Glomeruli in general were fed by a single afferent arteriole and drained via a single thinner efferent arteriole into peritubular vessels. Light microscopy and SEM of vascular corrosion casts revealed sphincters at the origins of afferent arterioles, which arose closely, spaced from their parent renal arteries. The second source of renal blood supply via renal portal veins varied interindividually in branching patterns with vessels showing up to five branching orders before they became peritubular vessels. Main trunks and their first- and second-order branches revealed clear longish endothelial cell nuclei imprint patterns oriented parallel to the vessels longitudinal axis, a pattern characteristic for arteries. Peritubular vessels had irregular contours and were never seen as clear cylindrical structures. They ran rather parallel, anastomosed with neighbors and changed into renal venules and veins, which finally emptied into the ventrally located posterior caval vein. A third source of blood supply of the peritubular vessels by straight terminal portions of renal arteries (vasa recta) was not found.     

Predicting effects of blood flow rate and size of vessels in a vasculature on hyperthermia treatments using computer simulation

Background

Pennes Bio Heat Transfer Equation (PBHTE) has been widely used to approximate the overall temperature distribution in tissue using a perfusion parameter term in the equation during hyperthermia treatment. In the similar modeling, effective thermal conductivity (K_eff) model uses thermal conductivity as a parameter to predict temperatures. However the equations do not describe the thermal contribution of blood vessels. A countercurrent vascular network model which represents a more fundamental approach to modeling temperatures in tissue than do the generally used approximate equations such as the Pennes BHTE or effective thermal conductivity equations was presented in 1996. This type of model is capable of calculating the blood temperature in vessels and describing a vasculature in the tissue regions.

Methods

In this paper, a countercurrent blood vessel network (CBVN) model for calculating tissue temperatures has been developed for studying hyperthermia cancer treatment. We use a systematic approach to reveal the impact of a vasculature of blood vessels against a single vessel which most studies have presented. A vasculature illustrates branching vessels at the periphery of the tumor volume. The general trends present in this vascular model are similar to those shown for physiological systems in Green and Whitmore. The 3-D temperature distributions are obtained by solving the conduction equation in the tissue and the convective energy equation with specified Nusselt number in the vessels.

Results

This paper investigates effects of size of blood vessels in the CBVN model on total absorbed power in the treated region and blood flow rates (or perfusion rate) in the CBVN on temperature distributions during hyperthermia cancer treatment. Also, the same optimized power distribution during hyperthermia treatment is used to illustrate the differences between PBHTE and CBVN models. K_eff (effective thermal conductivity model) delivers the same difference as compared to the CBVN model. The optimization used here is adjusting power based on the local temperature in the treated region in an attempt to reach the ideal therapeutic temperature of 43°C. The scheme can be used (or adapted) in a non-invasive power supply application such as high-intensity focused ultrasound (HIFU). Results show that, for low perfusion rates in CBVN model vessels, impacts on tissue temperature becomes insignificant. Uniform temperature in the treated region is obtained.

Conclusion

Therefore, any method that could decrease or prevent blood flow rates into the tumorous region is recommended as a pre-process to hyperthermia cancer treatment. Second, the size of vessels in vasculatures does not significantly affect on total power consumption during hyperthermia therapy when the total blood flow rate is constant. It is about 0.8% decreasing in total optimized absorbed power in the heated region as γ (the ratio of diameters of successive vessel generations) increases from 0.6 to 0.7, or from 0.7 to 0.8, or from 0.8 to 0.9. Last, in hyperthermia treatments, when the heated region consists of thermally significant vessels, much of absorbed power is required to heat the region and (provided that finer spatial power deposition exists) to heat vessels which could lead to higher blood temperatures than tissue temperatures when modeled them using PBHTE.     

Angioarchitectonics of the auricular and atrial walls of the human heart

Preparations of 103 human hearts at various ages have been investigated. The coronary veins are injected with contrast lead mass and a successive roentgenoangiography of the preparations is performed. The sources of blood supply of the atrial and auricular walls are determined taking into account branching variants of the atrial vessels. Vascularization peculiarities of the atrii and auriculae are described at the sinistrocoronary, dextrocoronary and even variants of the atrial branches. With age the diameter, length of the main atrial and auxillary auricular branches increase, as does their convolutivness. In the atrial and auricular walls there are areas comparatively poor in blood vessels. The branching variants do not always coinside with the types of the cardiac blood supply.     

Blood flow regulation in the cerebral microvasculature with an arcadal network: a numerical simulation

Blood flow regulation in the cerebral microvasculature with an arcadal network was investigated using a numerical simulation. A mathematical model for blood flow in the arcadal network, based on in vivo data of cat cerebral microvasculature and flow velocity was developed. The network model consists of 45 vessel segments and 25 branching points. To simulate microvascular response to blood flow, non-reactive (solid), cerebral arteriole-like, or skeletal muscle arteriole-like responses to wall shear stress were taken into account. Numerical calculation was carried out in the flow condition where the inlet (arterial) pressure was changed from 60 to 120 mmHg. Flow-rate in each efferent vessel and the mean flow-rate over all efferent vessels were evaluated for assessment of blood supply to the local area of cerebral tissue. The simulation demonstrated the wall shear stress-induced vasodilation in the arcadal network worked to maintain the blood flow at a constant level with pressure variable in a wide range. It is suggested that an individual microvessel (segment) should join in the regulatory process of flow, interacting with other microvessels (cooperative regulation).     

Sources of the vascularization of the human interatrial septum of the heart with different variants of the atrial blood supply

Angiograms of 110 preparations of the human hearts at various ages have been studied. In order to reveal vessels of the coronary bed, roentgen contrast lead mass has been used. Peculiarities of vascularization have been described in all parts of the interatrial septum and in the fossa ovalis area at various variants of branching of the atrial vessels: right coronary, left coronary and even. With age, in the fossa ovalis area certain decrease in the number of the blood vessels is observed and the network they form becomes less dense. In the interatrial septum its middle part and the fossa ovalis area are the regions which contain the least amount of vessels. In the antero-inferior part of this septum a comparatively dense vascular network is revealed.     

Electron microscopic study of the interrelations of the bush-like receptor terminals with the tissue

A study was made of the ultrastructure of elements linking the bush-like receptors with tissues of the frog bladder. It is demonstrated that the connection is realized mainly by collagen fibres, whose dense and irregular net is branching the nervous terminals. Besides, a dense contact has been found between the terminals and epithelial cells without any layer of collagen fibres. No desmosomal connection between terminals and tissue elements was found. It is suggested that the above peculiarities of the connections may influence considerably the functional-adaptational characteristics of the receptors.     

Formation of the circulatory bed of the neuromuscular spindles in forearm and hand muscles]

The data are presented on the formation and main constitutional principles in the blood supply of the neuromuscular spindles in the human forearm and hand during embryogenesis and early postnatal life. It has been stated that the neuromuscular spindles posses their own microcirculatory bed which is formed by the vessels of the surrounding muscular tissue, tends to separate in the course of development and subdivides into two parts: extracapsular and intracapsular. The vessels of the extracapsular part form dense capillary nets on the external surface of the capsule and follow extracapsular parts of the intrafusal muscular fibres. The intracapsular vessels either cover the internal surface of the capsule, or adjoin the intrafusal muscular fibres, or else run in the free subcapsular space.     

In vitro culture and maintenance of trophoblastic vesicles: Observations on the development of contractile structures with concurrent vessel development

The use of trophoblastic vesicles as a model for the study of maternal recognition of pregnancy, embryo development and cell to cell interaction has increased in recent years. In this report, we describe the long-term culture of trophoblastic vesicles derived from enzymatically dispersed porcine blastocysts. Day 12 to 14 porcine embryos were enzymatically dispersed to form single cell suspensions, then allowed to plate in 25 cm(3) tissue-culture flasks. Vesicles formed 3 to 14 d following plating and ranged in size from 0.1 to 4.0mm in diameter. Vesicles larger than 1.5 mm at formation were able to float free in the medium for up to 65 days, at which time vesicles were histologically sectioned. Contractile elements formed in association with dense cell areas, and were found with tubular vascular vessels. Movement of cells that resembled eosinophilic cells was observed in the vessels and pulsed in synchrony with contractions of the primitive heart. Histological examination gave evidence of primitive blood cells and cardiac tissue, and no evidence of neural tissue was found, indicating the probability that the contractions were induced by permeable membrane depolarization. It is hypothesized from the observations reported in this paper that the cell differentiation required to form the contractile region and the vessel are under the control of the dense cell area. This indicates that trophoblastic vesicles fromed by the enzymatic dispersal of porcine blastocysts is a possible model for the study of induced cell differentiation and formation of the cardiac organ system in vitro.     

Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels.

Studies of the origin of pulmonary blood flow heterogeneity have highlighted the significant role of vessel branching structure on flow distribution. To enable more detailed investigation of structure-function relationships in the pulmonary circulation, an anatomically based finite element model of the arterial and venous networks has been developed to more accurately reflect the geometry found in vivo. Geometric models of the arterial and venous tree structures are created using a combination of multidetector row X-ray computed tomography imaging to define around 2,500 vessels from each tree, a volume-filling branching algorithm to generate the remaining accompanying conducting vessels, and an empirically based algorithm to generate the supernumerary vessel geometry. The explicit generation of supernumerary vessels is a unique feature of the computational model. Analysis of branching properties and geometric parameters demonstrates close correlation between the model geometry and anatomical measures of human pulmonary blood vessels. A total of 12 Strahler orders for the arterial system and 10 Strahler orders for the venous system are generated, down to the equivalent level of the terminal bronchioles in the bronchial tree. A simple Poiseuille flow solution, assuming rigid vessels, is obtained within the arterial geometry of the left lung, demonstrating a large amount of heterogeneity in the flow distribution, especially with inclusion of supernumerary vessels. This model has been constructed to accurately represent available morphometric data derived from the complex asymmetric branching structure of the human pulmonary vasculature in a form that will be suitable for application in functional simulations.     

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.     

Electron microscopic study on the innervation of the pancreas of the domestic fowl

Summary The innervation of the pancreas of the domestic fowl was studied electron microscopically. The extrapancreatic nerve is composed mostly of unmyelinated nerve fibers with a smaller component of myelinated nerve fibers. The latter are not found in the parenchyma. The pancreas contains ganglion cells in the interlobular connective tissue. The unmyelinated nerve fibers branch off along blood vessels. Their synaptic terminals contact with the exocrine and endocrine tissues. The synaptic terminals can be divided into four types based on a combination of three kinds of synaptic vesicles. Type I synaptic terminals contain only small clear vesicles about 600 Å in diameter. Type II terminals are characterized by small clear and large dense core vesicles 1,000 Å in diameter. Type III terminals contain small clear vesicles and small dense core vesicles 500 Å in diameter. Type IV terminals are characterized by small and large dense core vesicles. The exocrine tissue receives a richer nervous supply than the endocrine tissue. Type II and IV terminals are distributed in the acinus, and they contact A and D cells of the islets. B cells and pancreatic ducts are supplied mainly by Type II terminals, the blood vessels by Type IV terminals.This work was supported by a scientific research grant (No. 144017) and (No. 136031) from the Ministry of Education of Japan to Prof. M. Yasuda     

Localization of the haemopoietic tissue of polychaete annelids. II. Site of chlorocruorin synthesis (author's transl)

The perivasal tissue of some blood vessels (antero-lateral vessels of Pomatoceros triqueter, ventral and lateral vessels of Sabella pavonina) shows a remarkable quantity of iron and pseudo-peroxidase activity. At the EM level, this tissue is characterized by numerous dense DAB positive inclusions and well developed granular endoplasmic reticulum and Golgi. Its function in chlorocruorin synthesis is discussed.     

Identification of vascular territory resistances in one-dimensional hemodynamics simulations

The present work deals with the parameter identification problem in outflow models used in one-dimensional simulations of arterial blood flow. Specifically, the resistive elements that define the models used to account for the blood supply to the vascular territories in arterial networks are computed by solving a system of non-linear equations using a Broyden method. This strategy is employed to compute the terminal parameters in the vascular territories of an anatomically detailed model of the arm comprising 67 arterial segments and 16 vascular territories. A comparison with a simple analytical approach, in terms of vascular territory resistances, average blood flows and time-dependent hemodynamic quantities, is performed. Also, a sensitivity analysis is presented to assess the performance of this new approach in normal and abnormal cardiovascular scenarios. This identification procedure allows to correctly set up hemodynamics simulations in highly detailed arterial networks making possible to gain insight in the aspects related to the blood circulation in arterial vessels.     

Parametric studies on the three-layer microcirculatory model for surface tissue energy exchange

The new three-layer microvascular mathematical model for surface tissue heat transfer developed in, which is based on detailed vascular casts and tissue temperature measurements in the rabbit thigh, is used to investigate the thermal characteristics of surface tissue under a wide variety of physiological conditions. Studies are carried out to examine the effects of vascular configuration, arterial blood supply rate, distribution of capillary perfusion, cutaneous blood circulation and metabolic heat production on the average tissue temperature profile, the local arterial-venous blood temperature difference in the thermally significant countercurrent vessels, and surface heat flux.