Multidimensional modelling for the carotid artery blood flow

A detailed three-dimensional (3D) model of the coronary artery tree with cardiac motion has great potential for applications in a wide variety of medical imaging research areas. In this work, we first developed a computer-generated 3D model of the coronary arterial tree for the heart in the extended cardiac-torso (XCAT) phantom, thereby creating a realistic computer model of the human anatomy. The coronary arterial tree model was based on two datasets: (1) a gated cardiac dual-source computed tomography (CT) angiographic dataset obtained from a normal human subject and (2) statistical morphometric data of porcine hearts. The initial proximal segments of the vasculature and the anatomical details of the boundaries of the ventricles were defined by segmenting the CT data. An iterative rule-based generation method was developed and applied to extend the coronary arterial tree beyond the initial proximal segments. The algorithm was governed by three factors: (1) statistical morphometric measurements of the connectivity, lengths and diameters of the arterial segments; (2) avoidance forces from other vessel segments and the boundaries of the myocardium, and (3) optimality principles which minimize the drag force at the bifurcations of the generated tree. Using this algorithm, the 3D computational model of the largest six orders of the coronary arterial tree was generated, which spread across the myocardium of the left and right ventricles. The 3D coronary arterial tree model was then extended to 4D to simulate different cardiac phases by deforming the original 3D model according to the motion vector map of the 4D cardiac model of the XCAT phantom at the corresponding phases. As a result, a detailed and realistic 4D model of the coronary arterial tree was developed for the XCAT phantom by imposing constraints of anatomical and physiological characteristics of the coronary vasculature. This new 4D coronary artery tree model provides a unique simulation tool that can be used in the development and evaluation of instrumentation and methods for imaging normal and pathological hearts with myocardial perfusion defects.

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the "generic 1-D model" and the "average subject" of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

Knowledge of the hemodynamics in normal arterial trees of the brain is important to better understand the mechanisms responsible for the initiation and progression of cerebrovascular diseases. Information about the baseline values of hemodynamic variables such as velocity magnitudes, swirling flows, wall shear stress, pressure drops, vascular resistances, etc. is important for characterization of the normal hemodynamics and comparison with pathological states such as aneurysms and stenoses. This paper presents image-based computational hemodynamics models of cerebral arterial trees constructed from magnetic resonance angiography (MRA) images. The construction of large models of cerebral arterial trees is challenging because of the following main reasons: a) it is necessary to acquire high resolution angiographic images covering the entire brain, b) it is necessary to construct topologically correct and geometrically accurate watertight models of the vasculature, and c) the models typically result in large computational grids which make the calculations computationally demanding. This paper presents a methodology to model the hemodynamics in the brain arterial network that combines high resolution MRA at 3T, a vector representation of the vascular structures based on semi-manual segmentation, and a novel algorithm to solve the incompressible flow equations efficiently in tubular geometries. These techniques make the study of the hemodynamics in the cerebral arterial network practical.

Velocity distribution along an elastic model of human arterial tree

Optimal treatment planning for radioembolization of hepatic cancers produces sufficient dose to tumors for control and dose to normal liver parenchyma that is below the threshold for toxicity. The non-uniform distribution of particles in liver microanatomy complicates the planning process as different functional regions receive different doses. Having realistic and patient-specific models of the arterial tree and microsphere trapping would be useful for developing more optimal treatment plans. We propose a macrocell-based growth method to generate models of the hepatic arterial tree from the proper hepatic artery to the terminal arterioles supplying the capillaries in the parenchyma. We show how these trees can be adapted to match patient values of pressure, flow, and vessel diameters while still conforming to laws controlling vessel bifurcation, changes in pressure, and blood flow. We also introduce a method to model particle transport within the tree that accounts for vessel and particle diameter distributions and show the non-uniform microsphere deposition pattern that results. Potential applications include investigating dose heterogeneity and microsphere deposition patterns.

By our method of constrained constructive optimization we generate, on the computer, highly realistic models of coronary arterial trees comprising on the order of 10* individual segments. To characterize these complex structures not only by statistical means, application-specific algorithms and computer programs have been developed to visually display their particular branching pattern. The entire tree is rendered in a realistic, threedimensional manner, similar to the appearance of corrosion casts of real arterial trees. Additionally, various physical and physiological properties can be visualized by appropriate color-coding.

We present a three-dimensional model of plaque formation and progression that was tested in a set of patients who underwent coronary Computed Tomography angiography (CTA) for anginal symptoms. The 3D blood flow is described by the Navier-Stokes equations, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection-diffusion equation. The Low Density Lipoprotein (LDL) transports in lumen of the vessel and through the vessel tissue (which has a mass consumption term) are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. A full three-dimensional model was created. Furthermore, features potentially affecting plaque growth, such as patient risk score, circulating biomarkers, localization and composition of the initial plaque, and coronary vasodilating capability were also investigated. The proof of concept of the model effectiveness was assessed 6 months after the baseline evaluation.

Simultaneous brachial artery pressure and blood flow measurements were made in 45 men. Blood flow was evaluated by means of a pulsed Doppler device with a double transducer probe. From analysis of the pressure-flow curves during diastole, forearm arterial compliance (FAC) was determined by using the model of the forearm arterial tree as a system of tubes, each with a storage capacitance, in series with the arteriolar resistances vessels. The value of FAC for seven normal subjects, aged 44 +/- 3 (mean +/- SEM) years, was between 0.78 and 1.73 X 10(-10) m5 . N-1. By comparison, a 30% reduction in FAC was observed in 38 men of the same age with essential hypertension, which was similar whether the intra-arterial diastolic pressure was above or below 90 mmHg. In the more severe group (Intra arterial diastolic pressure greater than 90 mmHg), the reduced FAC was associated with a significant increase in brachial artery diameter; after administration of dihydralazine, blood pressure and arterial diameter returned to normal but FAC remained diminished. The study is the first to evaluate FAC in intact men. The reduced FAC in hypertension is independent of blood pressure "per se" but may reflect adaptive change in the walls of the large arteries. In the more severe hypertension, arterial calibre was increased; this could be a mechanism which could prevent FAC from decreasing further with chronic elevation of blood pressure.

To analyze the characteristics of anatomy and blood distribution of uterine arterial vascular network in vivo for healthy women aged 20-26 years by reconstructing the digital three-dimensional models based on computerized tomographic angiography (CTA) scanning technology. From August to December 2012, a total of 25 female volunteers aged 20-26 years were recruited. All of them accepted CTA scanning. Their datasets were collected for reconstructing the digital three-dimension models of normal uterine arterial vascular network by using Mimics Version 10.01 software. After recognizing the supply arteries of each part of uterus, the three dimension models were divided into corpus and cervix arterial vascular network, left and right corpus arterial vascular network, left and right cervical artery vasc ular network and then calculated the proportion of vascular volume. Digital three-dimension models of normal uterine arterial vascular network of 25 cases were successfully reconstructed, which clearly showed the structure of the uterine artery and its branches at all levels. Under normal physiological conditions, vascular network of corpus developed in 21 cases (84%, 21/25). In these cases, bilateral vascular network were developed and supplied by the ipsilateral uterine artery respectively, where the distribution of vascular were bilateral balanced in 18 cases and unilateral predominant in 3 cases.However, 4 cases (16%, 4/25) of vascular network of corpus were not developed. There were not statistically significant of vascular network volume between both sides of uterine corpus of 25 cases digital three dimension models of normal uterine arterial vascular network (t = 1.817, P = 0.077). The cervical arterial vascular networks didn't develop in 23 cases (92%, 23/25), whereas it developed in 2 cases (8%, 2/25). This study successfully reconstructed the three dimensional models of uterine arterial vascular network for healthy females aged 20-26 years, confirming that the overall normal uterine vascular network distribution has the characteristics of bilateral, ipsilateral blood tendentious and balanced. But the cervical vascular network is rarely developing.

Atherosclerosis is becoming the number one cause of death worldwide. In this study, three-dimensional computer model of plaque formation and development for human carotid artery is developed. The three-dimensional blood flow is described by the Navier-Stokes equation, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection-diffusion equation. The low-density lipoproteins transports in lumen of the vessel and through the vessel tissue are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. Fluid-structure interaction is used to estimate effective wall stress analysis. Plaque growth functions for volume progression are correlated with shear stress and effective wall stress distribution. We choose two specific patients from MRI study with significant plaque progression. Plaque volume progression using three time points for baseline, 3- and 12-month follow up is fitted. Our results for plaque localization correspond to low shear stress zone and we fitted parameters from our model using nonlinear least-square method. Determination of plaque location and composition, and computer simulation of progression in time for a specific patient shows a potential benefit for the prediction of disease progression. The proof of validity of three-dimensional computer modeling in the evaluation of atherosclerotic plaque burden may shift the clinical information of MRI from morphological assessment toward a functional tool. Understanding and prediction of the evolution of atherosclerotic plaques either into vulnerable or stable plaques are major tasks for the medical community.

Background and Objectives: Teak (Tectona grandis) is one of Thailand's most valuable economic tree species, prized for its exceptional qualities such as durability, aesthetic appeal, and resistance to pests and diseases. Its popularity spans both domestic and international markets, making accurate estimation of merchantable teak volume essential for forest management and the timber industry. Precise volume estimation facilitates accurate economic valuation and minimizes resource losses associated with traditional destructive tree-felling methods. Recent advancements in technology, light detection and ranging or LiDAR, have provided opportunities to enhance the accuracy and efficiency of forest resource data collection. Among these tools, the Terrestrial Laser Scanner (TLS) stands out for its ability to generate high-resolution three-dimensional (3D) models of individual trees and forest stands in a non-destructive method. Unlike traditional methods, TLS enables data collection without damaging trees, offering a sustainable and efficient alternative for forestry applications. This study aimed to develop a methodology for utilizing TLS to construct 3D models of teak trees to estimate merchantable wood volume. The results were compared with the traditional felling method, which is considered the most accurate but destructive. In addition, the study attempts to establish predictive equations and volume tables for estimating merchantable teak volume. These outputs aimed to support sustainable forest management practices, reduce resource wastes, and facilitate the economic valuations of teak for the timber industry. Methods: The study was conducted in the Mae Chang forest plantation, located in Mae Mo district, Lampang province, Thailand. The stratified random sampling was employed to establish 12 sample plots, each sizing 40 m × 40 m. The plots were divided into two age groups based on plantation year: 18 years old (planted in 2006) and 39 years old (planted in 1985), with six plots in each group. Data collection involved using a Faro Focus S150 TLS to scan individual trees in each plot. The TLS data were processed to create detailed 3D tree models for further analysis. Merchantable timber volume was calculated using two methods: the stem curve method and quantitative structure models (QSM), both implemented through the 3D forest software. The TLS-derived volume estimates were validated by felling selected sample trees. The diameters and merchantable lengths of these felled trees were measured, and their volumes were calculated using Huber’s formula. Statistical analysis was performed to compare TLS-derived volumes with traditional felling-based volumes using paired t-tests. The accuracy of TLS-derived estimates was evaluated using root mean square error (RMSE). Additionally, predictive equations for merchantable volume estimation were developed using regression analysis. Two types of equations were created: one using diameter at breast height (DBH) as the sole variable and the other incorporating both DBH and merchantable height (HM). A volume table was constructed based on these equations, enabling non-destructive volume estimation for teak trees of varying DBH and HM ranges. Results: The 3D models generated using TLS provided merchantable volume estimates that closely aligned with volumes derived from felled trees. Statistical analysis revealed no significant differences between TLS-derived volumes and traditional felling-based volumes (p > 0.05). The RMSE values for TLS-derived estimates were 0.02 and 0.03 cubic meters when using the stem curve and QSM methods, respectively, indicating high accuracy. Two predictive equations for merchantable volume estimation were developed. The first equation utilized DBH as a single predictor variable and demonstrated a coefficient of determination (R²) of 0.966. The second equation incorporated both DBH and HM, achieving a higher R² value of 0.988. Validation of these equations using data from felled trees showed mean absolute percentage errors (MAPE) of 17.81% and 11.01%, respectively, confirming their suitability for practical applications. The most accurate equation was subsequently used to construct a merchantable volume table, which estimating based on DBH and HM ranges without requiring tree felling. This table provides a practical tool for forest managers and timber industry stakeholders to assess teak volume efficiently and sustainably. Conclusion: The results of this study demonstrate that TLS is a reliable and effective tool for non-destructive estimation of merchantable teak volume. The 3D models generated using TLS data enable precise volume estimation through methods such as stem curve and QSM, producing results that are statistically comparable to traditional destructive felling methods. The acceptable error margins and high accuracy of TLS-derived estimates highlight its potential as a sustainable alternative to conventional volume estimation techniques. By minimizing the need for destructive sampling, TLS-based methods contribute to sustainable forest management practices, preserving valuable tree resources while maintaining economic productivity. Furthermore, the development of predictive equations and merchantable volume tables offers practical solutions for forest managers and timber industry professionals, streamlining the assessment of merchantable volume and economic valuation. Overall, this study underscores the importance of integrating advanced technologies such as TLS into forestry practices. By improving the accuracy and sustainability of resource assessments, these innovations can support long-term forest conservation and enhance the economic potential of Thailand's teak plantations.

Heterogeneous Perfusion is a Consequence of Uniform Shear Stress in Optimized Arterial Tree Models

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

The great arteries of embryos are small channels of a complex three-dimensional arrangement. Measurements of their diameters, as required for understanding cardiovascular morphogenesis and the genesis of malformations, cannot be performed in two-dimensional histological sections. We present and evaluate a quick and simple method for performing highly significant and objective measurements of the diameters of blood vessels in vertebrate embryos and used this method for providing statistics of the diameter of the semi-lunar valves and the lumina of the great arteries of early chick and mouse foetus. We employed the high-resolution episcopic microscopy technique for generating volume data and three-dimensional computer models of the arterial trees of 30 chick embryos (Hamburger Hamilton stage 34), 30 mouse embryos of the OF1 strain harvested on 14.5 dpc, 30 embryos of the OF1 strain harvested on 15.5 dpc and 28 mouse embryos of the PARKES strain harvested on 14.5 dpc. The three-dimensional models (voxel size 2 mum x 2 mum x 2 mum and 3 mum x 3 mum x 3 mum) were used for defining virtual resection planes perpendicular to the longitudinal axis of the blood vessels at comparable positions. In these planes, we measured the lumen areas and the lumen perimeters. We also calculated the lumen diameter and the true lumen area from the perimeter and present statistical analysis. Finally, we evaluate and discuss the reliability and reproducibility of our method and present all measurements in a form that minimizes the influence of specimen size variation, specimen processing and data generation methods.

On a new 3D model for incompressible euler and navier-stokes equations