Diameters and cross-sectional areas of branches in the human pulmonary arterial tree

Branching Exponents of Synthetic Vascular Trees Under Different Optimality Principles

OBJECTIVE

The branching behavior of vascular trees is often characterized using Murray's law. We investigate its validity using synthetic vascular trees generated under global optimization criteria.

METHODS

Our synthetic tree model does not incorporate Murray's law explicitly. Instead, we show that its validity depends on properties of the optimization model and investigate the effects of different physical constraints and optimization goals on the branching exponent that is now allowed to vary locally. In particular, we include variable blood viscosity due to the Fåhræus-Lindqvist effect and enforce an equal pressure drop between inflow and the micro-circulation. Using our global optimization framework, we generate vascular trees with over one million terminal vessels and compare them against a detailed corrosion cast of the portal venous tree of a human liver.

RESULTS

Murray's law is fulfilled when no additional constraints are enforced, indicating its validity in this setting. Variable blood viscosity or equal pressure drop lead to different optima but with the branching exponent inside the experimentally predicted range between 2.0 and 3.0. The validation against the corrosion cast shows good agreement from the portal vein down to the venules.

CONCLUSION

Not enforcing Murray's law increases the predictive capabilities of synthetic vascular trees, and in addition reduces the computational cost.

SIGNIFICANCE

The ability to study optimal branching exponents across different scales can improve the functional assessment of organs.

A Computational Study of Blood Flow Dynamics in the Pulmonary Arteries

In this work we study the blood dynamics in the pulmonary arteries by means of a 3D-0D geometric multiscale approach, where a detailed 3D model for the pulmonary arteries is coupled with a lumped parameters (0D) model of the cardiovascular system. We propose to investigate three strategies for the numerical solution of the 3D-0D coupled problem: the Splitting-Explicit and Implicit algorithms, where information are exchanged between 3D and 0D models at each time step at the interfaces, and the One-Way algorithm, where the 0D is solved first off-line. In our numerical experiments performed in a realistic patient-specific 3D domain with a physiologically calibrated 0D model, we discuss first the issue on instabilities that may arise when not suitable connections are considered between 3D and 0D models; second we compare the performance and accuracy of the three proposed numerical strategies. Finally, we report a comparison between a healthy and a hypertensive case, providing a preliminary result highlighting how our method could be used in future for clinical purposes.

Rigorous mathematical optimization of synthetic hepatic vascular trees

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach.

The role of vascular complexity on optimal junction exponents

We examine the role of complexity on arterial tree structures, determining globally optimal vessel arrangements using the Simulated AnneaLing Vascular Optimization algorithm, a computational method which we have previously used to reproduce features of cardiac and cerebral vasculatures. In order to progress computational methods for growing arterial networks, deeper understanding of the stability of computational arterial growth algorithms to complexity, variations in physiological parameters (such as metabolic costs for maintaining and pumping blood), and underlying assumptions regarding the value of junction exponents is needed. We determine the globally optimal structure of two-dimensional arterial trees; analysing how physiological parameters affect tree morphology and optimal bifurcation exponent. We find that considering the full complexity of arterial trees is essential for determining the fundamental properties of vasculatures. We conclude that optimisation-based arterial growth algorithms are stable against uncertainties in physiological parameters, while optimal bifurcation exponents (a key parameter for many arterial growth algorithms) are affected by the complexity of vascular networks and the boundary conditions dictated by organs.

Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood

Pulmonary artery (PA) morphometry has been extensively explored in adults, with particular focus on intra-acinar arteries. However, scaling law relationships for length and diameter of extensive preacinar PAs by age have not been previously reported for in vivo human data. To understand preacinar PA growth spanning children to adults, we performed morphometric analyses of all PAs visible in the computed tomography (CT) and magnetic resonance (MR) images from a healthy subject cohort [n = 16; age: 1-51 yr; body surface area (BSA): 0.49-2.01 m²]. Subject-specific anatomic PA models were constructed from CT and MR images, and morphometric information-diameter, length, tortuosity, bifurcation angle, and connectivity-was extracted and sorted into diameter-defined Strahler orders. Validation of Murray's law, describing optimal scaling exponents of radii for branching vessels, was performed to determine how closely PAs conform to this classical relationship. Using regression analyses of vessel diameters and lengths against orders and patient metrics (BSA, age, height), we found that diameters increased exponentially with order and allometrically with patient metrics. Length increased allometrically with patient metrics, albeit weakly. The average tortuosity index of all vessels was 0.026 ± 0.024, average bifurcation angle was 28.2 ± 15.1°, and average Murray's law exponent was 2.92 ± 1.07. We report a set of scaling laws for vessel diameter and length, along with other morphometric information. These provide an initial understanding of healthy structural preacinar PA development with age, which can be used for computational modeling studies and comparison with diseased PA anatomy.NEW & NOTEWORTHY Pulmonary artery (PA) morphometry studies to date have focused primarily on large arteries and intra-acinar arteries in either adults or children, neglecting preacinar arteries in both populations. Our study is the first to quantify in vivo preacinar PA morphometry changes spanning infants to adults. For preacinar arteries > 1 mm in diameter, we identify scaling laws for vessel diameters and lengths with patient metrics of growth and establish a healthy PA morphometry baseline for most preacinar PAs.

Coagulopathy implications using a multiscale model of traumatic bleeding matching macro- and microcirculation

Quantifying the relationship between vascular injury and the dynamic bleeding rate requires a multiscale model that accounts for changing and coupled hemodynamics between the global and microvascular levels. A lumped, global hemodynamic model of the human cardiovascular system with baroreflex control was coupled to a local 24-level bifurcating vascular network that spanned diameters from the muscular artery scale (0.1-1.3 mm) to capillaries (5-10 μm) via conservation of momentum and conservation of mass boundary conditions. For defined injuries of severing all vessels at each nth-level, the changing pressures and flowrates were calculated using prescribed shear-dependent hemostatic clot growth rates (normal or coagulopathic). Key results were as follows: 1) the upstream vascular network rapidly depressurizes to reduce blood loss; 2) wall shear rates at the hemorrhaging wound exit are sufficiently high (~10,000 s^-1) to drive von Willebrand factor unfolding; 3) full coagulopathy results in >2-liter blood loss in 2 h for severing all vessels of 0.13- to 0.005-mm diameter within the bifurcating network, whereas full hemostasis limits blood loss to <100 ml within 2 min; and 4) hemodilution from transcapillary refill increases blood loss and could be implicated in trauma-induced coagulopathy. A sensitivity analysis on length-to-diameter ratio and branching exponent demonstrated that bleeding was strongly dependent on these tissue-dependent network parameters. This is the first bleeding model that prescribes the geometry of the injury to calculate the rate of pressure-driven blood loss and local wall shear rate in the presence or absence of coagulopathic blood. NEW & NOTEWORTHY We developed a multiscale model that couples a lumped, global hemodynamic model of a patient to resolved, single-vessel wounds ranging from the small artery to capillary scale. The model is able to quantify wall shear rates, seal rates, and blood loss rates in the presence and absence of baroreflex control and hemodilution.

Branching Pattern of the Cerebral Arterial Tree

Quantitative data on branching patterns of the human cerebral arterial tree are lacking in the 1.0–0.1 mm radius range. We aimed to collect quantitative data in this range, and to study if the cerebral artery tree complies with the principle of minimal work (Law of Murray).

To enable easy quantification of branching patterns a semi‐automatic method was employed to measure 1,294 bifurcations and 2,031 segments on 7 T‐MRI scans of two corrosion casts embedded in a gel. Additionally, to measure segments with a radius smaller than 0.1 mm, 9.4 T‐MRI was used on a small cast section to characterize 1,147 bifurcations and 1,150 segments. Besides MRI, traditional methods were employed. Seven hundred thirty‐three bifurcations were manually measured on a corrosion cast and 1,808 bifurcations and 1,799 segment lengths were manually measured on a fresh dissected cerebral arterial tree. Data showed a large variation in branching pattern parameters (asymmetry‐ratio, area‐ratio, length‐radius‐ratio, tapering). Part of the variation may be explained by the variation in measurement techniques, number of measurements and location of measurement in the vascular tree.

This study confirms that the cerebral arterial tree complies with the principle of minimum work. These data are essential in the future development of more accurate mathematical blood flow models. Anat Rec, 302:1434–1446, 2019. © 2018 The Authors. The Anatomical Record published by Wiley Periodicals, Inc. on behalf of American Association of Anatomists.

High resolution 7T and 9.4T-MRI of human cerebral arterial casts enables accurate estimations of the cerebrovascular morphometry

Quantitative data on the morphology of the cerebral arterial tree could aid in modelling and understanding cerebrovascular diseases, but is scarce in the range between 200 micrometres and 1 mm diameter arteries. Traditional manual measurements are difficult and time consuming. 7T-MRI and 9.4T-MRI of human cerebral arterial plastic casts could proof feasible for acquiring detailed morphological data of the cerebral arterial tree in a time efficient method. One cast of the complete human cerebral arterial circulation embedded in gadolinium-containing gelatine gel was scanned at 7T-MRI (0.1 mm isotropic resolution). A small section of another cast was scanned at 9.4T-MRI (30 µm isotropic resolution). Subsequent 3D-reconstruction was performed using a semi-automatic approach. Validation of 7T-MRI was performed by comparing the radius calculated using MRI to manual measurements on the same cast. As manual measurement of the small section was not feasible, 9.4T-MRI was validated by scanning the small section both at 7T-MRI and 9.4T MRI and comparing the diameters of arterial segments. Linear regression slopes were 0.97 (R-squared 0.94) and 1.0 (R-squared 0.90) for 7T-MRI and 9.4T-MRI. This data shows that 7T-MRI and 9.4T-MRI and subsequent 3D reconstruction of plastic casts is feasible, and allows for characterization of human cerebral arterial tree morphology.

Multiscale systems biology of trauma-induced coagulopathy

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

A Zero-Dimensional Model and Protocol for Simulating Patient-Specific Pulmonary Hemodynamics From Limited Clinical Data

In pulmonary hypertension (PH) diagnosis and management, many useful functional markers have been proposed that are unfeasible for clinical implementation. For example, assessing right ventricular (RV) contractile response to a gradual increase in pulmonary arterial (PA) impedance requires simultaneously recording RV pressure and volume, and under different afterload/preload conditions. In addition to clinical applications, many research projects are hampered by limited retrospective clinical data and could greatly benefit from simulations that extrapolate unavailable hemodynamics. The objective of this study was to develop and validate a 0D computational model, along with a numerical implementation protocol, of the RV-PA axis. Model results are qualitatively compared with published clinical data and quantitatively validated against right heart catheterization (RHC) for 115 pediatric PH patients. The RV-PA circuit is represented using a general elastance function for the RV and a three-element Windkessel initial value problem for the PA. The circuit mathematically sits between two reservoirs of constant pressure, which represent the right and left atriums. We compared Pmax, Pmin, mPAP, cardiac output (CO), and stroke volume (SV) between the model and RHC. The model predicted between 96% and 98% of the variability in pressure and 98-99% in volumetric characteristics (CO and SV). However, Bland Altman plots showed the model to have a consistent bias for most pressure and volumetric parameters, and differences between model and RHC to have considerable error. Future studies will address this issue and compare specific waveforms, but these initial results are extremely promising as preliminary proof of concept of the modeling approach.

Circulating miRNAs in Pediatric Pulmonary Hypertension Show Promise as Biomarkers of Vascular Function

BACKGROUND/OBJECTIVES

The objective of this study was to evaluate the utility of circulating miRNAs as biomarkers of vascular function in pediatric pulmonary hypertension.

METHOD

Fourteen pediatric pulmonary arterial hypertension patients underwent simultaneous right heart catheterization (RHC) and blood biochemical analysis. Univariate and stepwise multivariate linear regression was used to identify and correlate measures of reactive and resistive afterload with circulating miRNA levels. Furthermore, circulating miRNA candidates that classified patients according to a 20% decrease in resistive afterload in response to oxygen (O₂) or inhaled nitric oxide (iNO) were identified using receiver-operating curves.

RESULTS

Thirty-two circulating miRNAs correlated with the pulmonary vascular resistance index (PVRi), pulmonary arterial distensibility, and PVRi decrease in response to O₂ and/or iNO. Multivariate models, combining the predictive capability of multiple promising miRNA candidates, revealed a good correlation with resistive (r = 0.97, P_2-tailed < 0.0001) and reactive (r = 0.86, P_2-tailed < 0.005) afterloads. Bland-Altman plots showed that 95% of the differences between multivariate models and RHC would fall within 0.13 (mmHg-min/L)m² and 0.0085/mmHg for resistive and reactive afterloads, respectively. Circulating miR-663 proved to be a good classifier for vascular responsiveness to acute O₂ and iNO challenges.

CONCLUSION

This study suggests that circulating miRNAs may be biomarkers to phenotype vascular function in pediatric PAH.

Simulated annealing approach to vascular structure with application to the coronary arteries

Do the complex processes of angiogenesis during organism development ultimately lead to a near optimal coronary vasculature in the organs of adult mammals? We examine this hypothesis using a powerful and universal method, built on physical and physiological principles, for the determination of globally energetically optimal arterial trees. The method is based on simulated annealing, and can be used to examine arteries in hollow organs with arbitrary tissue geometries. We demonstrate that the approach can generate in silico vasculatures which closely match porcine anatomical data for the coronary arteries on all length scales, and that the optimized arterial trees improve systematically as computational time increases. The method presented here is general, and could in principle be used to examine the arteries of other organs. Potential applications include improvement of medical imaging analysis and the design of vascular trees for artificial organs.

Patient-specific computational modeling of blood flow in the pulmonary arterial circulation

Computational fluid dynamics (CFD) modeling of the pulmonary vasculature has the potential to reveal continuum metrics associated with the hemodynamic stress acting on the vascular endothelium. It is widely accepted that the endothelium responds to flow-induced stress by releasing vasoactive substances that can dilate and constrict blood vessels locally. The objectives of this study are to examine the extent of patient specificity required to obtain a significant association of CFD output metrics and clinical measures in models of the pulmonary arterial circulation, and to evaluate the potential correlation of wall shear stress (WSS) with established metrics indicative of right ventricular (RV) afterload in pulmonary hypertension (PH). Right Heart Catheterization (RHC) hemodynamic data and contrast-enhanced computed tomography (CT) imaging were retrospectively acquired for 10 PH patients and processed to simulate blood flow in the pulmonary arteries. While conducting CFD modeling of the reconstructed patient-specific vasculatures, we experimented with three different outflow boundary conditions to investigate the potential for using computationally derived spatially averaged wall shear stress (SAWSS) as a metric of RV afterload. SAWSS was correlated with both pulmonary vascular resistance (PVR) (R(2)=0.77, P<0.05) and arterial compliance (C) (R(2)=0.63, P<0.05), but the extent of the correlation was affected by the degree of patient specificity incorporated in the fluid flow boundary conditions. We found that decreasing the distal PVR alters the flow distribution and changes the local velocity profile in the distal vessels, thereby increasing the local WSS. Nevertheless, implementing generic outflow boundary conditions still resulted in statistically significant SAWSS correlations with respect to both metrics of RV afterload, suggesting that the CFD model could be executed without the need for complex outflow boundary conditions that require invasively obtained patient-specific data. A preliminary study investigating the relationship between outlet diameter and flow distribution in the pulmonary tree offers a potential computationally inexpensive alternative to pressure based outflow boundary conditions.

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.

A patient-specific airway branching model for mechanically ventilated patients

BACKGROUND

Respiratory mechanics models have the potential to guide mechanical ventilation. Airway branching models (ABMs) were developed from classical fluid mechanics models but do not provide accurate models of in vivo behaviour. Hence, the ABM was improved to include patient-specific parameters and better model observed behaviour (ABMps).

METHODS

The airway pressure drop of the ABMps was compared with the well-accepted dynostatic algorithm (DSA) in patients diagnosed with acute respiratory distress syndrome (ARDS). A scaling factor (α) was used to equate the area under the pressure curve (AUC) from the ABMps to the AUC of the DSA and was linked to patient state.

RESULTS

The ABMps recorded a median α value of 0.58 (IQR: 0.54-0.63; range: 0.45-0.66) for these ARDS patients. Significantly lower α values were found for individuals with chronic obstructive pulmonary disease (P < 0.001).

CONCLUSION

The ABMps model allows the estimation of airway pressure drop at each bronchial generation with patient-specific physiological measurements and can be generated from data measured at the bedside. The distribution of patient-specific α values indicates that the overall ABM can be readily improved to better match observed data and capture patient condition.

Diverse forms of pulmonary hypertension remodel the arterial tree to a high shear phenotype

Pulmonary hypertension (PH) is associated with progressive changes in arterial network complexity. An allometric model is derived that integrates diameter branching complexity between pulmonary arterioles of generation n and the main pulmonary artery (MPA) via a power-law exponent (X) in dn = dMPA2(-n/X) and the arterial area ratio β = 2(1-2/X). Our hypothesis is that diverse forms of PH demonstrate early decrements in X independent of etiology and pathogenesis, which alters the arteriolar shear stress load from a low-shear stress (X > 2, β > 1) to a high-shear stress phenotype (X < 2, β < 1). Model assessment was accomplished by comparing theoretical predictions to retrospective morphometric and hemodynamic measurements made available from a total of 221 PH-free and PH subjects diagnosed with diverse forms (World Health Organization; WHO groups I-IV) of PH: mitral stenosis, congenital heart disease, chronic obstructive pulmonary lung disease, chronic thromboembolism, idiopathic pulmonary arterial hypertension (IPAH), familial (FPAH), collagen vascular disease, and methamphetamine exposure. X was calculated from pulmonary artery pressure (PPA), cardiac output (Q) and body weight (M), utilizing an allometric power-law prediction of X relative to a PH-free state. Comparisons of X between PAH-free and PAH subjects indicates a characteristic reduction in area that elevates arteriolar shear stress, which may contribute to mechanisms of endothelial dysfunction and injury before clinically defined thresholds of pulmonary vascular resistance and PH. We conclude that the evaluation of X may be of use in identifying reversible and irreversible phases of PH in the early course of the disease process.

Radius exponent in elastic and rigid arterial models optimized by the least energy principle

It was analyzed in normal physiological arteries whether the least energy principle would suffice to account for the radius exponent x. The mammalian arterial system was modeled as two types, the elastic or the rigid, to which Bernoulli's and Hagen-Poiseuille's equations were applied, respectively. We minimized the total energy function E, which was defined as the sum of kinetic, pressure, metabolic and thermal energies, and loss of each per unit time in a single artery transporting viscous incompressible blood. Assuming a scaling exponent α between the vessel radius (r) and length (l) to be 1.0, x resulted in 2.33 in the elastic model. The rigid model provided a continuously changing x from 2.33 to 3.0, which corresponded to Uylings' and Murray's theories, respectively, through a function combining Reynolds number with a proportional coefficient of the l - r relationship. These results were expanded to an asymmetric arterial fractal tree with the blood flow preservation rule. While x in the optimal elastic model accounted for around 2.3 in proximal systemic (r >1 mm) and whole pulmonary arteries (r ≥0.004 mm), optimal x in the rigid model explained 2.7 in elastic-muscular (0.1 < r ≤1 mm) and 3.0 in peripheral resistive systemic arteries (0.004 ≤ r ≤0.1 mm), in agreement with data obtained from angiographic, cast-morphometric, and in vivo experimental studies in the literature. The least energy principle on the total energy basis provides an alternate concept of optimality relating to mammalian arterial fractal dimensions under α = 1.0.

Considerations for numerical modeling of the pulmonary circulation--a review with a focus on pulmonary hypertension

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

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.

3D Imaging of vascular networks for biophysical modeling of perfusion distribution within the heart

One of the main determinants of perfusion distribution within an organ is the structure of its vascular network. Past studies were based on angiography or corrosion casting and lacked quantitative three dimensional, 3D, representation. Based on branching rules and other properties derived from such imaging, 3D vascular tree models were generated which were rather useful for generating and testing hypotheses on perfusion distribution in organs. Progress in advanced computational models for prediction of perfusion distribution has raised the need for more realistic representations of vascular trees with higher resolution. This paper presents an overview of the different methods developed over time for imaging and modeling the structure of vascular networks and perfusion distribution, with a focus on the heart. The strengths and limitations of these different techniques are discussed. Episcopic fluorescent imaging using a cryomicrotome is presently being developed in different laboratories. This technique is discussed in more detail, since it provides high-resolution 3D structural information that is important for the development and validation of biophysical models but also for studying the adaptations of vascular networks to diseases. An added advantage of this method being is the ability to measure local tissue perfusion. Clinically, indices for patient-specific coronary stenosis evaluation derived from vascular networks have been proposed and high-resolution noninvasive methods for perfusion distribution are in development. All these techniques depend on a proper representation of the relevant vascular network structures.

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.

Model combining hydrodynamics and fractal theory for analysis of in vivo peripheral pulmonary and systemic resistance of shunt cardiac defects

The fractal state of the arterial vascular tree is considered to have a universal dimension related to the principle of minimum work rate, but can demonstrate the capacity to adapt to other dimensions in disease states such as congenital high-flow pulmonary hypertension (PH) by a process that is incompletely understood. To document and interpret fractal adaptation in patients with different degrees of PH, pulmonary and systemic vascular resistance was analyzed by a model that evaluated the fractal dimension, x, of the Poiseuille resistance contribution of the arterial vessel radius between 10 and 100μm, via the proportionality Q∝(R(peri)/BL)(-x/4), with Q, R(peri), and BL clinically observed variables representing total pulmonary or systemic blood flow, its peripheral arterial resistance, and body length, respectively. Identification of x in the pulmonary (P) and systemic (S) beds was evaluated from hemodynamic data of 213 patients, categorized into 7 groups by PH grade. In controls without PH, x(P)=2.2 while the dimension increased to 3.0, with the systemic dimension constant at x(S)=3.1. Our model predicts that severe grades of PH are associated with: a more elongated and hindered vessel in the periphery, and reductions in vessel numbers, as unit pulmonary resistive arterial trees (N(1)) and their component intra-acinar arteries (N(W)). These model network changes suggest a complex adaptive process of arterial network reorganization in the pulmonary circulation to minimize the work rate of high-flow congenital heart defects.

FSI Analysis of a Healthy and a Stenotic Human Trachea Under Impedance-Based Boundary Conditions

In this work, a fluid-solid interaction (FSI) analysis of a healthy and a stenotic human trachea was studied to evaluate flow patterns, wall stresses, and deformations under physiological and pathological conditions. The two analyzed tracheal geometries, which include the first bifurcation after the carina, were obtained from computed tomography images of healthy and diseased patients, respectively. A finite element-based commercial software code was used to perform the simulations. The tracheal wall was modeled as a fiber reinforced hyperelastic solid material in which the anisotropy due to the orientation of the fibers was introduced. Impedance-based pressure waveforms were computed using a method developed for the cardiovascular system, where the resistance of the respiratory system was calculated taking into account the entire bronchial tree, modeled as binary fractal network. Intratracheal flow patterns and tracheal wall deformation were analyzed under different scenarios. The simulations show the possibility of predicting, with FSI computations, flow and wall behavior for healthy and pathological tracheas. The computational modeling procedure presented herein can be a useful tool capable of evaluating quantities that cannot be assessed in vivo, such as wall stresses, pressure drop, and flow patterns, and to derive parameters that could help clinical decisions and improve surgical outcomes.

Species-specific pulmonary arterial asymmetry determines species differences in regional pulmonary perfusion

The functional significance of differences in pulmonary vascular branching and diameter asymmetry between the human and quadruped lung has not previously been addressed. To evaluate the contribution of branching asymmetry to observable species differences in blood flow gradients, computed distributions of blood flow were compared in structure-based models of the human and ovine pulmonary arteries. The models were derived using a combination of computed tomography and a volume-filling algorithm. Pressure, flow, and deformed vessel diameter were calculated in both species models using equations representing conservation of mass and momentum, and a pressure-diameter relationship. The major difference between the human and ovine results was the presence of a large region of "zone 4" flow and higher mean flows in the central region of the ovine lung compared to that in the human. Heterogeneity in tissue perfusion and the contribution of gravity were similar in both species models; however, the gravitationally directed gradients of perfusion in the human and ovine models were different and each consistent with human and quadruped measurements, respectively. The results suggest that measured species differences in pulmonary perfusion gradients are largely determined by differences in branching asymmetry.

Extension of Murray's law using a non-Newtonian model of blood flow

Background

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.

Modeling

In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. ΣR^c = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n.

Results

We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.

Conclusion

It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Modelling pulmonary blood flow

Computational model analysis has been used widely to understand and interpret complexity of interactions in the pulmonary system. Pulmonary blood transport is a multi-scale phenomenon that involves scale-dependent structure and function, therefore requiring different model assumptions for the microcirculation and the arterial or venous flows. The blood transport systems interact with the surrounding lung tissue, and are dependent on hydrostatic pressure gradients, control of vasoconstriction, and the topology and material composition of the vascular trees. This review focuses on computational models that have been developed to study the different mechanisms contributing to regional perfusion of the lung. Different models for the microcirculation and the pulmonary arteries are considered, including fractal approaches and anatomically-based methods. The studies that are reviewed illustrate the different complementary approaches that can be used to address the same physiological question of flow heterogeneity.

Endoscopic evaluation of bronchial morphology in rabbits

OBJECTIVE

To evaluate bronchial morphology endoscopically in rabbits and develop a valid nomenclature for the endobronchial branching pattern.

ANIMALS

10 mature New Zealand White rabbits.

PROCEDURES

Flexible bronchoscopy was performed in rabbits anesthetized with isoflurane via nasal mask. Airways were systematically evaluated from the larynx to the terminal branches accessible with a 2.5-mm-outer diameter flexible endoscope. Airway branching patterns were identified and assessed for variation among subjects.

RESULTS

Airways of all rabbits were readily examined with the 2.5-mm flexible endoscope. Laryngeal structure and function were normal in each rabbit, and airway branching patterns in all rabbits evaluated were identical. At the carina, branching into left and right principal bronchi was evident. The left principal bronchus divided immediately into the left cranial and left caudal lobar bronchi. The left cranial lobe bronchus further divided into dorsal and ventral segmental bronchi. The left caudal lobe bronchus gave rise to branches originating dorsally, ventrally, and medially before continuing caudally. The right principal bronchus divided into the right cranial, right middle, and accessory lobar bronchi and continued distally as the right caudal lobar bronchus. The right cranial lobe bronchus also divided into dorsal and ventral segmental bronchi, and the right caudal lobe bronchus had branches that originated dorsally, ventrally, and medially.

CONCLUSIONS AND CLINICAL RELEVANCE

Definition of a standard nomenclature for airway branching in rabbits will allow precise localization of disease in clinical cases and accurate collection of airway samples in clinical and scientific evaluations.

Shear stress paradigm for perinatal fractal arterial network remodeling in lambs with pulmonary hypertension and increased pulmonary blood flow

Congenital heart disease with increased blood flow commonly leads to the development of increased pulmonary vascular reactivity and pulmonary arterial hypertension by mechanisms that remain unclear. We hypothesized a shear stress paradigm of hemodynamic reactivity and network remodeling via the persistence and/or exacerbation of a fetal diameter bifurcation phenotype [parent diameter d(0) and daughters d(1) >or= d(2) with alpha < 2 in (d(1)/d(0))(alpha) + (d(2)/d(0))(alpha) and area ratio beta < 1 in beta = (d(1)(2)+ d(2)(2))/ d(0)(2)] that mechanically acts as a high resistance magnifier/shear stress amplifier to blood flow. Evidence of a hemodynamic influence on network remodeling was assessed with a lamb model of high-flow-induced secondary pulmonary hypertension in which an aortopulmonary graft was surgically placed in one twin in utero (Shunt twin) but not in the other (Control twin). Eight weeks after birth arterial casts were made of the left pulmonary arterial circulation. Bifurcation diameter measurements down to 0.010 mm in the Shunt and Control twins were then compared with those of an unoperated fetal cast. Network organization, cumulative resistance, and pressure/shear stress distributions were evaluated via a fractal model whose dimension D(0) approximately alpha delineates hemodynamic reactivity. Fetus and Control twin D(0) differed: fetus D(0)=1.72, a high-resistance/shear stress amplifying condition; control twin D(0) = 2.02, an area-preserving transport configuration. The Shunt twin (D(0)=1.72) maintained a fetal design but paradoxically remodeled diameter geometry to decrease cumulative resistance relative to the Control twin. Our results indicate that fetal/neonatal pulmonary hemodynamic reactivity remodels in response to shear stress, but the response to elevated blood flow and pulmonary hypertension involves the persistence and exacerbation of a fetal diameter bifurcation phenotype that facilitates endothelial dysfunction/injury.

Scale dependence of branching in arterial and bronchial trees

Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verification of this dependence by comparison with data is uncommon. We compare measurements of bifurcation parameters of airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models based on minimization of pumping power and network volume. We find that the size dependence is more complex than existing theories based solely on energy and volume minimization explain, and suggest additional factors that may govern the branching at different scales.

Investigation of the relative effects of vascular branching structure and gravity on pulmonary arterial blood flow heterogeneity via an image-based computational model

RATIONALE AND OBJECTIVES

A computational model of blood flow through the human pulmonary arterial tree has been developed to investigate the relative influence of branching structure and gravity on blood flow distribution in the human lung.

MATERIALS AND METHODS

Geometric models of the largest arterial vessels and lobar boundaries were first derived using multidetector row x-ray computed tomography (MDCT) scans. Further accompanying arterial vessels were generated from the MDCT vessel endpoints into the lobar volumes using a volume-filling branching algorithm. Equations governing the conservation of mass and momentum were solved within the geometric model to calculate pressure, velocity, and vessel radius. Blood flow results in the anatomically based model, with and without gravity, and in a symmetric geometric model were compared to investigate their relative contributions to blood flow heterogeneity.

RESULTS

Results showed a persistent blood flow gradient and flow heterogeneity in the absence of gravitational forces in the anatomically based model. Comparison with flow results in the symmetric model revealed that the asymmetric vascular branching structure was largely responsible for producing this heterogeneity. Analysis of average results in varying slice thicknesses illustrated a clear flow gradient because of gravity in "lower resolution" data (thicker slices), but on examination of higher resolution data, a trend was less obvious.

CONCLUSIONS

Results suggest that although gravity does influence flow distribution, the influence of the tree branching structure is also a dominant factor. These results are consistent with high-resolution experimental studies that have demonstrated gravity to be only a minor determinant of blood flow distribution.

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.

Morphometric characterization of the airway and vascular systems of the lung of the domestic pig, Sus scrofa: comparison of the airway, arterial and venous systems

The bronchial system (BS), the pulmonary artery (PA) and the pulmonary vein (PV) of the lung of the domestic pig, Sus scrofa were simultaneously cast with silicone rubber and studied. Asymmetrical dichotomous bifurcation preponderated in the tree-like arrangement of the three conducting systems. Lengths and diameters of the various generations were measured. At the extremities of the BS and the PA, alveoli and blood capillaries related very closely. In the cranial and middle lobes of the right and left lungs, topographically, the PA and the PV closely followed the BS, but in the accessory and the caudal (diaphragmatic) lobes, only the PA accompanied the BS: the PV run intersegmentally. Certain similarities and differences were observed between the diameters and lengths of the various generations of the three conducting systems. The strong correlations between some of the structural parameters indicated a high level of structural optimization. While morphometric variations suggest that the air and the blood flow dynamics may somewhat differ between the three conducting systems, they may also register structural features unique to the lung of the domestic pig, an animal that has been highly genetically exploited for fast growth and now leads an indolent lifestyle in captivity.

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D(1))(z) = (D(2))(z) + (D(3))(z); D(1) is the parent vessel diameter and D(2) and D(3) are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.

Form and function of fetal and neonatal pulmonary arterial bifurcations

Bifurcation is a basic form of vascular connection. It is composed of a parent vessel of diameter d(0), and two daughter vessels, d(1) and d(2), where d(0) > d(1) >/= d(2). Optimal values for the bifurcation area ratio, beta = (d(1)(2) + d(2)(2))/d(0)(2), and the junction exponent, x, in d(0)(x) = d(1)(x) + d(2)(x), are postulated to be universal in nature. However, we have hypothesized that the perinatal pulmonary arterial circulation is an exception. Arterial diameters were measured in pulmonary vascular casts of a fetal lamb (140 days gestation/145 days term) and a neonatal lamb (1 day old). The values for beta and x were evaluated in 10,970 fetal and 846 neonatal bifurcations sampled from the proximal and intermediate arterial regions. Mean values and confidence intervals (CI) for the fetus were beta = 0.890 (0.886-0.895 CI) and x = 1.75 (1.74-1.76 CI); and for the newborn were beta = 0.913 (0.90-0.93 CI) and x = 1. 79 (1.75-1.82 CI). These values are significantly different from Murray's law (beta > 1, x = 3) or the West-Brown-Enquist law (beta = 1, x = 2). Therefore, perinatal pulmonary bifurcation design appears to be distinctive and exceptional. The decreasing cross-sectional area with branching leads to the hemodynamic consequence of shear stress amplification. This structural organization may be important for facilitating vascular development at low flow rates; however, it may be the origin of unstable reactivity if elevated blood flow and pressure occurs.

Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease

Increases in the low attenuation areas (LAA) of chest x-ray computed tomography images in patients with chronic obstructive pulmonary disease (COPD) have been reported to reflect the development of pathological emphysema. We examined the statistical properties of LAA clusters in COPD patients and in healthy subjects. In COPD patients, the percentage of the lung field occupied by LAAs (LAA%) ranged from 2.6 to 67.6. In contrast, LAA% was always <30% in healthy subjects. The cumulative size distribution of the LAA clusters followed a power law characterized by an exponent D. We show that D is a measure of the complexity of the terminal airspace geometry. The COPD patients with normal LAA% had significantly smaller D values than the healthy subjects, and the D values did not correlate with pulmonary function tests except for the diffusing capacity of the lung. We interpret these results by using a large elastic spring network model and find that the neighboring smaller LAA clusters tend to coalesce and form larger clusters as the weak elastic fibers separating them break under tension. This process leaves LAA% unchanged whereas it decreases the number of small clusters and increases the number of large clusters, which results in a reduction in D similar to that observed in early emphysema patients. These findings suggest that D is a sensitive and powerful parameter for the detection of the terminal airspace enlargement that occurs in early emphysema.

Structure-function relationships in the pulmonary arterial tree

Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are independent of vessel diameter, and although the actual arterial tree is quite heterogeneous, the diameter of each route, through which the blood flows, tapers from the arterial inlet to essentially the same terminal arteriolar diameter. In the model the average route is represented as a tapered tube through which the blood flow decreases with distance from the inlet because of the diversion of flow at the many bifurcations along the route. The taper and flow diversion are expressed in terms of morphometric parameters obtained using various methods for summarizing morphometric data. To help put the model parameter values in perspective, we applied one such method to morphometric data obtained from perfused dog lungs. Model simulations demonstrate the sensitivity of model pressure-flow relationships to variations in the morphometric parameters. Comparisons of simulations with experimental data also raise questions as to the "hemodynamically" appropriate ways to summarize morphometric data.

Structured tree outflow condition for blood flow in larger systemic arteries

A central problem in modeling blood flow and pressure in the larger systemic arteries is determining a physiologically based boundary condition so that the arterial tree can be truncated after a few generations. We have used a structured tree attached to the terminal branches of the truncated arterial tree in which the root impedance is estimated using a semianalytical approach based on a linearization of the viscous axisymmetric Navier-Stokes equations. This provides a dynamic boundary condition that maintains the phase lag between blood flow and pressure as well as the high-frequency oscillations present in the impedance spectra. Furthermore, it accommodates the wave propagation effects for the entire systemic arterial tree. The result is a model that is physiologically adequate as well as computationally feasible. For validation, we have compared the structured tree model with a pure resistance and a windkessel model as well as with measured data.

Mechanics of blood supply to the heart: wave reflection effects in a right coronary artery

Mechanics of blood flow in the coronary circulation have in the past been based largely on models in which the detailed architecture of the coronary network is not included because of lack of data: properties of individual vessels do not appear individually in the model but are represented collectively by the elements of a single electric circuit. Recent data from the human heart make it possible, for the first time, to examine the dynamics of flow in the coronary network based on detailed, measured vascular architecture. In particular, admittance values along the full course of the right coronary artery are computed based on actual lengths and diameters of the many thousands of branches which make up the distribution system of this vessel. The results indicate that effects of wave reflections on this flow are far more significant than those generally suspected to occur in coronary blood flow and that they are actually the reverse of the well known wave reflection effects in the aorta.

Branching design of the bronchial tree based on a diameter-flow relationship

We propose a method for designing the bronchial tree where the branching process is stochastic and the diameter (d) of a branch is determined by its flow rate (Q). We use two principles: the continuum equation for flow division and a power-law relationship between d and Q, given by Q approximately dn, where n is the diameter exponent. The value of n has been suggested to be approximately 3. We assume that flow is divided iteratively with a random variable for the flow-division ratio, defined as the ratio of flow in the branch to that in its parent branch. We show that the cumulative probability distribution function of Q, P(> Q) is proportional to Q-1. We analyzed prior morphometric airway data (O. G. Raabe, H. C. Yeh, H. M. Schum, and R. F. Phalen, Report No. LF-53, 1976) and found that the cumulative probability distribution function of diameters, P(> d), is proportional to d-n, which supports the validity of Q approximately dn since P(> Q) approximately Q-1. This allowed us to assign diameters to the segments of the flow-branching pattern. We modeled the bronchial trees of four mammals and found that their statistical features were in good accordance with the morphometric data. We conclude that our design method is appropriate for robust generation of bronchial tree models.

Applications of fractal analysis to physiology

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.