Investigating Murray's law in the chick embryo

Ultrasound high-definition microvasculature imaging with novel quantitative biomarkers improves breast cancer detection accuracy

OBJECTIVES

To overcome the limitations of power Doppler in imaging angiogenesis, we sought to develop and investigate new quantitative biomarkers of a contrast-free ultrasound microvasculature imaging technique for differentiation of benign from malignant pathologies of breast lesion.

METHODS

In this prospective study, a new high-definition microvasculature imaging (HDMI) was tested on 521 patients with 527 ultrasound-identified suspicious breast masses indicated for biopsy. Four new morphological features of tumor microvessels, microvessel fractal dimension (mvFD), Murray's deviation (MD), bifurcation angle (BA), and spatial vascularity pattern (SVP) as well as initial biomarkers were extracted and analyzed, and the results correlated with pathology. Multivariable logistic regression analysis was used to study the performance of different prediction models, initial biomarkers, new biomarkers, and combined new and initial biomarkers in differentiating benign from malignant lesions.

RESULTS

The new HDMI biomarkers, mvFD, BA, MD, and SVP, were statistically significantly different in malignant and benign lesions, regardless of tumor size. Sensitivity and specificity of the new biomarkers in lesions > 20 mm were 95.6% and 100%, respectively. Combining the new and initial biomarkers together showed an AUC, sensitivity, and specificity of 97% (95% CI: 95-98%), 93.8%, and 89.2%, respectively, for all lesions regardless of mass size. The classification was further improved by adding the Breast Imaging Reporting and Data System (BI-RADS) score to the prediction model, showing an AUC, sensitivity, and specificity of 97% (95% CI: 95-98%), 93.8%, and 89.2%, respectively.

CONCLUSION

The addition of new quantitative HDMI biomarkers significantly improved the accuracy in breast lesion characterization when used as a complementary imaging tool to the conventional ultrasound.

KEY POINTS

• Novel quantitative biomarkers extracted from tumor microvessel images increase the sensitivity and specificity in discriminating malignant from benign breast masses. • New HDMI biomarkers Murray's deviation, bifurcation angles, microvessel fractal dimension, and spatial vascularity pattern outperformed the initial biomarkers. • The addition of BI-RADS scores based on US descriptors to the multivariable analysis using all biomarkers remarkably increased the sensitivity, specificity, and AUC in all size groups.

Use of the volume-averaged Murray's deviation method for the characterization of branching geometry in liver fibrosis: a preliminary study on vascular circulation

Background

Vascular changes in liver fibrosis can result in increased intrahepatic vascular resistance and impaired blood circulation. This can hinder the recovery from fibrosis and may eventually lead to portal hypertension, a major cirrhosis complication. This report proposed a volume-averaged Murray's deviation method to characterize intrahepatic circulation in the liver during fibrosis and its subsequent regression via X-ray phase-contrast computed tomography (PCCT).

Methods

Liver fibrosis was induced in 24 Sprague-Dawley rats by exposure to carbon tetrachloride (CCl₄) for up to 10 weeks, after which, spontaneous regression commenced and continued until week 30. High-resolution three-dimensional (3D) imaging of the livers was performed with PCCT. The values of Murray's deviation based on the volume-averaged and the conventional diameter-based methods were compared. After that, the intrahepatic circulation at different stages of fibrosis was evaluated using the volume-averaged method. The increase in collagen during liver fibrosis was assessed by pathological analyses.

Results

A comparison of the 2 methods showed that with an increase in the number of diameter measurements, the value of Murrary's deviation obtained using the diameter-based method gradually approaches those of the volume-averaged method, with minimal variations. The value of Murray's deviation increased with the development of fibrosis. After reversal, the value rapidly decreased and approached that of the normal state in both the main branches (1.05±0.17, 1.17±0.21, 1.34±0.18, and 1.17±0.19 in the normal, moderate, severe, and regressive groups, respectively; P<0.05 between the severe group and other groups) and the small branches (1.05±0.09, 1.42±0.48, 1.79±0.57, and 1.18±0.28 in the normal, moderate, severe, and regressive group, respectively; P<0.05 between adjacent groups). An analysis of Murray's deviation and the pathological results showed that the vascular circulation in this disease model was consistent with the progression and recovery from fibrosis.

Conclusions

This study showed the validity of the volume-averaged method for calculating Murray's deviation and demonstrated that it could accurately evaluate the blood circulation state of the liver during fibrosis and its subsequent regression. Thus, the volume-averaged method of calculating Murray's deviation may be an objective and valuable staging criterion to evaluate intrahepatic circulation during liver fibrosis.

Hybrid high-definition microvessel imaging/shear wave elastography improves breast lesion characterization

BACKGROUND

Low specificity in current breast imaging modalities leads to increased unnecessary follow-ups and biopsies. The purpose of this study is to evaluate the efficacy of combining the quantitative parameters of high-definition microvasculature imaging (HDMI) and 2D shear wave elastography (SWE) with clinical factors (lesion depth and age) for improving breast lesion differentiation.

METHODS

In this prospective study, from June 2016 through April 2021, patients with breast lesions identified on diagnostic ultrasound and recommended for core needle biopsy were recruited. HDMI and SWE were conducted prior to biopsies. Two new HDMI parameters, Murray's deviation and bifurcation angle, and a new SWE parameter, mass characteristic frequency, were included for quantitative analysis. Lesion malignancy prediction models based on HDMI only, SWE only, the combination of HDMI and SWE, and the combination of HDMI, SWE and clinical factors were trained via elastic net logistic regression with 70% (360/514) randomly selected data and validated with the remaining 30% (154/514) data. Prediction performances in the validation test set were compared across models with respect to area under the ROC curve as well as sensitivity and specificity based on optimized threshold selection.

RESULTS

A total of 508 participants (mean age, 54 years ± 15), including 507 female participants and 1 male participant, with 514 suspicious breast lesions (range, 4-72 mm, median size, 13 mm) were included. Of the lesions, 204 were malignant. The SWE-HDMI prediction model, combining quantitative parameters from SWE and HDMI, with AUC of 0.973 (95% CI 0.95-0.99), was significantly higher than the result predicted with the SWE model or HDMI model alone. With an optimal cutoff of 0.25 for the malignancy probability, the sensitivity and specificity were 95.5% and 89.7%, respectively. The specificity was further improved with the addition of clinical factors. The corresponding model defined as the SWE-HDMI-C prediction model had an AUC of 0.981 (95% CI 0.96-1.00).

CONCLUSIONS

The SWE-HDMI-C detection model, a combination of SWE estimates, HDMI quantitative biomarkers and clinical factors, greatly improved the accuracy in breast lesion characterization.

Quantitative Biomarkers for Cancer Detection Using Contrast-Free Ultrasound High-Definition Microvessel Imaging: Fractal Dimension, Murray's Deviation, Bifurcation Angle & Spatial Vascularity Pattern

A growing body of evidence indicates that there is a strong correlation between microvascular morphological features and malignant tumors. Therefore, quantification of these features might allow more accurate differentiation of benign and malignant tumors. The main objective of this research project is to improve the quantification of microvascular networks depicted in contrast-free ultrasound microvessel images. To achieve this goal, a new series of quantitative microvessel morphological parameters are introduced for differentiation of breast masses using contrast-free ultrasound-based high-definition microvessel imaging (HDMI). Using HDMI, we quantified and analyzed four new parameters: 1) microvessel fractal dimension (mvFD), a marker of tumor microvascular complexity; 2) Murray's deviation (MD), the diameter mismatch, defined as the deviation from Murray's law; 3) bifurcation angle (BA), abnormally decreased angle; and 4) spatial vascular pattern (SVP), indicating tumor vascular distribution pattern, either intratumoral or peritumoral. The new biomarkers have been tested on 60 patients with breast masses. Validation of the feature's extraction algorithm was performed using a synthetic data set. All the proposed parameters had the power to discriminate the breast lesion malignancy (p < 0.05), displaying BA as the most sensitive test, with a sensitivity of 90.6%, and mvFD as the most specific test, with a specificity of 92%. The results of all four new biomarkers showed an AUC = 0.889, sensitivity of 80% and specificity of 91.4% In conclusion, the added value of the proposed quantitative morphological parameters, as new biomarkers of angiogenesis within breast masses, paves the way for more accurate breast cancer detection with higher specificity.

The structural properties of carotid arteries in carotid artery diseases - a retrospective computed tomography angiography study

Purpose

Aim of the study was to find answers to the following questions: What haemodynamic changes may occur in patients with stenotic, aneurysmal, dissection of the carotid artery and its branches? How do these changes differ in patients with normal and carotid disease?

Material and methods

In order to achieve this aim, the cranio-cervical CT angiography images of patients who were referred to our clinic for any reason and received the diagnosis of carotid stenosis, carotid dissection, and extra or intracranial aneurysm were reviewed retrospectively.

Results

Significant differences were detected in the carotid arteries of normal patients and those with aneurysm and dissection. When normal and aneurismal patients were compared, right and left ICA diameters (p = 0.000, p = 0.002, respectively), total ICA diameters (p = 0.000), carotid left Ø diameters (p = 0.026), right and left total Ø diameters (p = 0.024), and Murray’s and our cosine values of Ø angles (p = 0.001 and p = 0.022, respectively) were found to be different. Also, in a comparison made between normal patients and patients with dissection, right CCA (p = 0.000), ICA (p = 0.001), ECA (p = 0.004) diameters, total CCA (p = 0.001), ICA (p = 0.009), and ECA (p = 0.003) diameters were also found to be different.

Conclusions

This study showed that the presence of aneurysm plays an important role in the remodelling of the carotid arteries. Also, it is understood that Murray’s laws are still valid for the detection of structural deterioration in carotid artery diseases. Hence, it is believed that these data can be used in artificial intelligence studies.

Analyzing transfer properties of zeolites using small-world networks

Hierarchical structures bring efficiency to many processes, including metabolism, plant growth, and even social networks. In society, connectivity among people results in a hierarchical network with a superior efficiency for information transfer. These networks are known as small-world networks. Although the number of people known by a single person is insignificant compared with the total number of people in a society, a small number of long-range connections can bring extremely high information transfer efficiency to the social network. This is the key property of the small-world network. By modeling zeolite structures as small-world networks and regarding vacancies and cracks as long-range connections, we managed to quantify efficiency in hierarchical zeolite structures. We showed the influence of cracks and vacancies on the transfer phenomenon in zeolite structures. By adding 6% vacancies into a perfect 3D zeolite structure, we obtained a 30% equivalent volume reduction in zeolite crystals. This approach might result in new methodology for quantifying zeolite transfer and broaden horizons for zeolite structure design.

A generalized optimization principle for asymmetric branching in fluidic networks

When applied to a branching network, Murray’s law states that the optimal branching of vascular networks is achieved when the cube of the parent channel radius is equal to the sum of the cubes of the daughter channel radii. It is considered integral to understanding biological networks and for the biomimetic design of artificial fluidic systems. However, despite its ubiquity, we demonstrate that Murray’s law is only optimal (i.e. maximizes flow conductance per unit volume) for symmetric branching, where the local optimization of each individual channel corresponds to the global optimum of the network as a whole. In this paper, we present a generalized law that is valid for asymmetric branching, for any cross-sectional shape, and for a range of fluidic models. We verify our analytical solutions with the numerical optimization of a bifurcating fluidic network for the examples of laminar, turbulent and non-Newtonian fluid flows.

The role of endothelial mechanosensitive genes in atherosclerosis and omics approaches

Atherosclerosis is the leading cause of morbidity and mortality in the U.S., and is a multifactorial disease that preferentially occurs in regions of the arterial tree exposed to disturbed blood flow. The detailed mechanisms by which d-flow induces atherosclerosis involve changes in the expression of genes, epigenetic patterns, and metabolites of multiple vascular cells, especially endothelial cells. This review presents an overview of endothelial mechanobiology and its relation to the pathogenesis of atherosclerosis with special reference to the anatomy of the artery and the underlying fluid mechanics, followed by a discussion of a variety of experimental models to study the role of fluid mechanics and atherosclerosis. Various in vitro and in vivo models to study the role of flow in endothelial biology and pathobiology are discussed in this review. Furthermore, strategies used for the global profiling of the genome, transcriptome, miR-nome, DNA methylome, and metabolome, as they are important to define the biological and pathophysiological mechanisms of atherosclerosis. These "omics" approaches, especially those which derive data based on a single animal model, provide unprecedented opportunities to not only better understand the pathophysiology of atherosclerosis development in a holistic and integrative manner, but also to identify novel molecular and diagnostic targets.

Toward an optimal design principle in symmetric and asymmetric tree flow networks

Fluid flow in tree-shaped networks plays an important role in both natural and engineered systems. This paper focuses on laminar flows of Newtonian and non-Newtonian power law fluids in symmetric and asymmetric bifurcating trees. Based on the constructal law, we predict the tree-shaped architecture that provides greater access to the flow subjected to the total network volume constraint. The relationships between the sizes of parent and daughter tubes are presented both for symmetric and asymmetric branching tubes. We also approach the wall-shear stresses and the flow resistance in terms of first tube size, degree of asymmetry between daughter branches, and rheological behavior of the fluid. The influence of tubes obstructing the fluid flow is also accounted for. The predictions obtained by our theory-driven approach find clear support in the findings of previous experimental studies.

Obstructions in Vascular Networks: Relation Between Network Morphology and Blood Supply

We relate vascular network structure to hemodynamics after vessel obstructions. We consider tree-like networks with a viscoelastic fluid with the rheological characteristics of blood. We analyze the network hemodynamic response, which is a function of the frequencies involved in the driving, and a measurement of the resistance to flow. This response function allows the study of the hemodynamics of the system, without the knowledge of a particular pressure gradient. We find analytical expressions for the network response, which explicitly show the roles played by the network structure, the degree of obstruction, and the geometrical place in which obstructions occur. Notably, we find that the sequence of resistances of the network without occlusions strongly determines the tendencies that the response function has with the anatomical place where obstructions are located. We identify anatomical sites in a network that are critical for its overall capacity to supply blood to a tissue after obstructions. We demonstrate that relatively small obstructions in such critical sites are able to cause a much larger decrease on flow than larger obstructions placed in non-critical sites. Our results indicate that, to a large extent, the response of the network is determined locally. That is, it depends on the structure that the vasculature has around the place where occlusions are found. This result is manifest in a network that follows Murray’s law, which is in reasonable agreement with several mammalian vasculatures. For this one, occlusions in early generation vessels have a radically different effect than occlusions in late generation vessels occluding the same percentage of area available to flow. This locality implies that whenever there is a tissue irrigated by a tree-like in vivo vasculature, our model is able to interpret how important obstructions are for the irrigation of such tissue.

A Modification of Murray's Law for Shear-Thinning Rheology

This study reformulates Murray's well-known principle of minimum work as applied to the cardiovascular system to include the effects of the shear-thinning rheology of blood. The viscous behavior is described using the extended modified power law (EMPL), which is a time-independent, but shear-thinning rheological constitutive equation. The resulting minimization problem is solved numerically for typical parameter ranges. The non-Newtonian analysis still predicts the classical cubic diameter dependence of the volume flow rate and the cubic branching law. The current analysis also predicts a constant wall shear stress throughout the vascular tree, albeit with a numerical value about 15–25% higher than the Newtonian analysis. Thus, experimentally observed deviations from the cubic branching law or the predicted constant wall shear stress in the vasculature cannot likely be attributed to blood's shear-thinning behavior. Further differences between the predictions of the non-Newtonian and the Newtonian analyses are highlighted, and the limitations of the Newtonian analysis are discussed. Finally, the range and limits of applicability of the current results as applied to the human arterial tree are also discussed.

Quantification of blood flow and topology in developing vascular networks

Since fluid dynamics plays a critical role in vascular remodeling, quantification of the hemodynamics is crucial to gain more insight into this complex process. Better understanding of vascular development can improve prediction of the process, and may eventually even be used to influence the vascular structure. In this study, a methodology to quantify hemodynamics and network structure of developing vascular networks is described. The hemodynamic parameters and topology are derived from detailed local blood flow velocities, obtained by in vivo micro-PIV measurements. The use of such detailed flow measurements is shown to be essential, as blood vessels with a similar diameter can have a large variation in flow rate. Measurements are performed in the yolk sacs of seven chicken embryos at two developmental stages between HH 13+ and 17+. A large range of flow velocities (1 µm/s to 1 mm/s) is measured in blood vessels with diameters in the range of 25–500 µm. The quality of the data sets is investigated by verifying the flow balances in the branching points. This shows that the quality of the data sets of the seven embryos is comparable for all stages observed, and the data is suitable for further analysis with known accuracy. When comparing two subsequently characterized networks of the same embryo, vascular remodeling is observed in all seven networks. However, the character of remodeling in the seven embryos differs and can be non-intuitive, which confirms the necessity of quantification. To illustrate the potential of the data, we present a preliminary quantitative study of key network topology parameters and we compare these with theoretical design rules.

Extension of Murray's law including nonlinear mechanics of a composite artery wall

A goal function approach is used to derive an extension of Murray’s law that includes effects of nonlinear mechanics of the artery wall. The artery is modeled as a thin-walled tube composed of different species of nonlinear elastic materials that deform together. These materials grow and remodel in a process that is governed by a target state defined by a homeostatic radius and a homeostatic material composition. Following Murray’s original idea, this target state is defined by a principle of minimum work. We take this work to include that of pumping and maintaining blood, as well as maintaining the materials of the artery wall. The minimization is performed under a constraint imposed by mechanical equilibrium. We derive a condition for the existence of a cost-optimal homeostatic state. We also conduct parametric studies using this novel theoretical frame to investigate how the cost-optimal radius and composition of the artery wall depend on flow rate, blood pressure, and elastin content

Murray's Law in elastin haploinsufficient (Eln+/-) and wild-type (WT) mice

Using either the principle of minimum energy or constant shear stress, a relation can be derived that predicts the diameters of branching vessels at a bifurcation. This relation, known as Murray's Law, has been shown to predict vessel diameters in a variety of cardiovascular systems from adult humans to developing chicks. The goal of this study is to investigate Murray's Law in vessels from mice that are haploinsufficient for the elastin protein (Eln+/-). Elastin is one of the major proteins in the blood vessel wall and is organized in concentric rings, known as lamellae, with smooth muscle cells (SMCs) around the vessel lumen. Eln+/- mice have an increased number of lamellae, as well as smaller, thinner vessels. It is possible that due to decreased amounts of elastin available for vessel wall remodeling during development and in adulthood, Eln+/- vessels would not follow Murray's Law. We examined vessel bifurcations in six different physiologic regions, including the brain, heart, epidermis, ceocum (or cecum), testes, and intestines, in Eln+/- mice and wild-type (WT) littermates. All vessels were between 40 and 300 μm in diameter. We found that the diameters of both Eln+/- and WT vessels have an average of 13% error from the diameters predicted by Murray's Law, with no significant differences between genotypes or physiologic regions. The data suggest that vessels are optimized to follow Murray's Law, despite limitations on the proteins available for growth and remodeling of the vessel wall.

Dynamic responses of endothelial cells to changes in blood flow during vascular remodeling of the mouse yolk sac

Despite extensive work showing the importance of blood flow in angiogenesis and vessel remodeling, very little is known about how changes in vessel diameter are orchestrated at the cellular level in response to mechanical forces. To define the cellular changes necessary for remodeling, we performed live confocal imaging of cultured mouse embryos during vessel remodeling. Our data revealed that vessel diameter increase occurs via two distinct processes that are dependent on normal blood flow: vessel fusions and directed endothelial cell migrations. Vessel fusions resulted in a rapid change in vessel diameter and were restricted to regions that experience the highest flow near the vitelline artery and vein. Directed cell migrations induced by blood flow resulted in the recruitment of endothelial cells to larger vessels from smaller capillaries and were observed in larger artery segments as they expanded. The dynamic and specific endothelial cell behaviors captured in this study reveal how sensitive endothelial cells are to changes in blood flow and how such responses drive vascular remodeling.

Critical transitions in early embryonic aortic arch patterning and hemodynamics

Transformation from the bilaterally symmetric embryonic aortic arches to the mature great vessels is a complex morphogenetic process, requiring both vasculogenic and angiogenic mechanisms. Early aortic arch development occurs simultaneously with rapid changes in pulsatile blood flow, ventricular function, and downstream impedance in both invertebrate and vertebrate species. These dynamic biomechanical environmental landscapes provide critical epigenetic cues for vascular growth and remodeling. In our previous work, we examined hemodynamic loading and aortic arch growth in the chick embryo at Hamburger-Hamilton stages 18 and 24. We provided the first quantitative correlation between wall shear stress (WSS) and aortic arch diameter in the developing embryo, and observed that these two stages contained different aortic arch patterns with no inter-embryo variation. In the present study, we investigate these biomechanical events in the intermediate stage 21 to determine insights into this critical transition. We performed fluorescent dye microinjections to identify aortic arch patterns and measured diameters using both injection recordings and high-resolution optical coherence tomography. Flow and WSS were quantified with 3D computational fluid dynamics (CFD). Dye injections revealed that the transition in aortic arch pattern is not a uniform process and multiple configurations were documented at stage 21. CFD analysis showed that WSS is substantially elevated compared to both the previous (stage 18) and subsequent (stage 24) developmental time-points. These results demonstrate that acute increases in WSS are followed by a period of vascular remodeling to restore normative hemodynamic loading. Fluctuations in blood flow are one possible mechanism that impacts the timing of events such as aortic arch regression and generation, leading to the variable configurations at stage 21. Aortic arch variations noted during normal rapid vascular remodeling at stage 21 identify a temporal window of increased vulnerability to aberrant aortic arch morphogenesis with the potential for profound effects on subsequent cardiovascular morphogenesis.

Mechanotransduction in embryonic vascular development

A plethora of biochemical signals provides spatial and temporal cues that carefully orchestrate the complex process of vertebrate embryonic development. The embryonic vasculature develops not only in the context of these biochemical cues, but also in the context of the biomechanical forces imparted by blood flow. In the mature vasculature, different blood flow regimes induce distinct genetic programs, and significant progress has been made toward understanding how these forces are perceived by endothelial cells and transduced into biochemical signals. However, it cannot be assumed that paradigms that govern the mature vasculature are pertinent to the developing embryonic vasculature. The embryonic vasculature can respond to the mechanical forces of blood flow, and these responses are critical in vascular remodeling, certain aspects of sprouting angiogenesis, and maintenance of arterial-venous identity. Here, we review data regarding mechanistic aspects of endothelial cell mechanotransduction, with a focus on the response to shear stress, and elaborate upon the multifarious effects of shear stress on the embryonic vasculature. In addition, we discuss emerging predictive vascular growth models and highlight the prospect of combining signaling pathway information with computational modeling. We assert that correlation of precise measurements of hemodynamic parameters with effects on endothelial cell gene expression and cell behavior is required for fully understanding how blood flow-induced loading governs normal vascular development and shapes congenital cardiovascular abnormalities.

Interaction between alk1 and blood flow in the development of arteriovenous malformations

Arteriovenous malformations (AVMs) are fragile direct connections between arteries and veins that arise during times of active angiogenesis. To understand the etiology of AVMs and the role of blood flow in their development, we analyzed AVM development in zebrafish embryos harboring a mutation in activin receptor-like kinase I (alk1), which encodes a TGFβ family type I receptor implicated in the human vascular disorder hereditary hemorrhagic telangiectasia type 2 (HHT2). Our analyses demonstrate that increases in arterial caliber, which stem in part from increased cell number and in part from decreased cell density, precede AVM development, and that AVMs represent enlargement and stabilization of normally transient arteriovenous connections. Whereas initial increases in endothelial cell number are independent of blood flow, later increases, as well as AVMs, are dependent on flow. Furthermore, we demonstrate that alk1 expression requires blood flow, and despite normal levels of shear stress, some flow-responsive genes are dysregulated in alk1 mutant arterial endothelial cells. Taken together, our results suggest that Alk1 plays a role in transducing hemodynamic forces into a biochemical signal required to limit nascent vessel caliber, and support a novel two-step model for HHT-associated AVM development in which pathological arterial enlargement and consequent altered blood flow precipitate a flow-dependent adaptive response involving retention of normally transient arteriovenous connections, thereby generating AVMs.

Automatic algorithm for skin profile detection in photoacoustic microscopy

We have developed an automatic algorithm to detect the skin profiles in the volumetric data acquired by photoacoustic microscopy for subcutaneous vasculature imaging. This algorithm analyzes the relationship between amplitudes of photoacoustic signals generated from the skin surface and underlying blood vessels to achieve a rough estimation of the skin profile. A better approximation of the skin profile is then acquired after nonparametric smoothing and Gaussian low-pass spatial filtering. An auto-fit scan mechanism is further developed based on the detected skin profile to achieve good ultrasonic focusing on the subcutaneous vessel layer when the skin contour variation is much larger than the ultrasonic focal zone. The importance of skin profile detection in calculating the maximum-amplitude-projection images and significantly improving the image quality by employing the auto-fit scan are demonstrated by in vivo experimental results.

Optimal postnodal lymphatic network structure that maximizes active propulsion of lymph

The lymphatic system acts to return lower-pressured interstitial fluid to the higher-pressured veins by a complex network of vessels spanning more than three orders of magnitude in size. Lymphatic vessels consist of lymphangions, segments of vessels between two unidirectional valves, which contain smooth muscle that cyclically pumps lymph against a pressure gradient. Whereas the principles governing the optimal structure of arterial networks have been identified by variations of Murray's law, the principles governing the optimal structure of the lymphatic system have yet to be elucidated, although lymph flow can be identified as a critical parameter. The reason for this deficiency can be identified. Until recently, there has been no algebraic formula, such as Poiseuille's law, that relates lymphangion structure to its function. We therefore employed a recently developed mathematical model, based on the time-varying elastance model conventionally used to describe ventricular function, that was validated by data collected from postnodal bovine mesenteric lymphangions. From this lymphangion model, we developed a model to determine the structure of a lymphatic network that optimizes lymph flow. The model predicted that there is a lymphangion length that optimizes lymph flow and that symmetrical networks optimize lymph flow when the lymphangions downstream of a bifurcation are 1.26 times the length of the lymphangions immediately upstream. Measured lymphangion lengths (1.14 +/- 0.5 cm, n = 74) were consistent with the range of predicted optimal lengths (0.1-2.1 cm). This modeling approach was possible, because it allowed a structural parameter, such as length, to be treated as a variable.

Minimum mass vascular networks in multifunctional materials

A biomimetic analysis is presented in which an expression for the optimum vessel diameter for the design of minimum mass branching or vascular networks in engineering applications is derived. Agreement with constructal theory is shown. A simple design case is illustrated and application to more complex cases with branching networks of several generations discussed. The analysis is also extended into the turbulent flow regime, giving an optimization tool with considerable utility in the design of fluid distribution systems. The distribution of vessel lengths in different generations was also found to be a useful design variable. Integrating a network into a structure is also discussed. Where it is necessary to adopt a non-optimum vessel diameter for structural integration, it has been shown that small deviations from the minimum mass optimum can be tolerated, but large variations could be expected to produce a punitive and rapidly increasing mass penalty.

Large variations in absolute wall shear stress levels within one species and between species

Wall shear stress (WSS), the frictional force between blood and endothelium, is an important determinant of vascular function. It is generally assumed that WSS remains constant at a reference value of 15 dyn/cm(2). In a study of small rodents, we realized that this assumption could not be valid. This review presents an overview of recent studies in large and small animals where shear stress was measured, derived from velocity measurements or otherwise, in large vessels. The data show that large variations exist within a single species (human: variation of 2-16 N/m(2)). Moreover, when we compared different species at the same location within the arterial tree, an inverse relationship between animal size and wall shear stress was noted. When we related WSS to diameter, a unique relationship was derived for all species studied. This relationship could not be described by the well-known r(3) law of Murray, but by the r(2) law introduced by Zamir et al. in 1972. In summary, by comparing data from the literature, we have shown that: (i) the assumption of a physiological WSS level of approximately 15 dyn/cm(2) for all straight vessels in the arterial tree is incorrect; (ii) WSS is not constant throughout the vascular tree; (iii) WSS varies between species; (iv) WSS is inversely related to the vessel diameter. These data support an "r(2) law" rather than Murray's r(3) law for the larger vessels in the arterial tree.

Fabrication of a multiple-diameter branched network of microvascular channels with semi-circular cross-sections using xenon difluoride etching

The majority of microfluidic devices employ networks of channels that have rectangular cross-sections. At the microvascular scale of 30 to 300 microm in diameter, however, the distribution of fluid mechanical stresses and the induced shape of cultured cells will be quite different in a rectangular channel from the near-circular cross-sections seen in vivo. While round-cross-section channels have been produced before by wet etching, fine control of feature size has not been demonstrated, and prior work has only produced channels of a single diameter on a given device. In this work, the xenon difluoride process for isotropic etching of silicon was optimized for production of channels with semicircular cross-sections. This process was then used to produce a network of microvessel-scale semicylindrical channels on a silicon chip, the diameter of which was decreased with each level of branching. Additionally, it was demonstrated that endothelial cells will adhere to both the bottom and sides of these channels, indicating that such chips may be useful in the future for culturing in vitro models of the microvasculature.

Self-healing polymer composites: mimicking nature to enhance performance

Autonomic self-healing materials, where initiation of repair is integral to the material, are being developed for engineering applications. This bio-inspired concept offers the designer an ability to incorporate secondary functional materials capable of counteracting service degradation whilst still achieving the primary, usually structural, requirement. Most materials in nature are themselves self-healing composite materials. This paper reviews the various self-healing technologies currently being developed for fibre reinforced polymeric composite materials, most of which are bioinspired, inspired by observation of nature. The most recent self-healing work has attempted to mimic natural healing through the study of mammalian blood clotting and the design of vascular networks found in biological systems. A perspective on current and future self-healing approaches using this biomimetic technique is offered. The intention is to stimulate debate outside the engineering community and reinforce the importance of a multidisciplinary approach in this exciting field.

Localized morphometric deformations of small airways and alveoli in intact mouse lungs under quasi-static inflation

Localized morphometric deformations of small airways and alveoli during respiration have several biomechanical and physiological implications. We developed fast synchrotron radiation CT system to visualize the small airways and alveoli of an intact mouse lung without fixation and dehydration, and analyzed their localized morphometric deformations between functional residual capacity (FRC) and total lung capacity (TLC). The maximum resolution of 32.6lp/mm at the 5% modulation transfer function level can be achieved with 11.8-microm voxels and 7-min scanning. Compared with the values at FRC, the diameter and length for smaller airways (diameter at FRC <200 microm) increased by 68.8% and 29.5% (averaged value), and those for larger airways (diameter at FRC >400 microm) increased by 45.2 and 22.9% (averaged value), at TLC. Moreover we defined the volume behavior as the percentage of airway volume at FRC for TLC. The volume behavior for the small airways was not similar to that of the lung volume. These results indicated that all airways did not behave homogenously.

Shear stress depends on vascular territory: comparison between common carotid and brachial artery

Shear stress (SS) is thought to be constant throughout the vascular system. Evidence for this supposition is scarce, however. To verify this hypothesis in vivo, we assessed common carotid (CCA) and brachial artery (BA) peak and mean wall shear rate (SR) noninvasively in 10 healthy volunteers (23.7 +/- 3.4 yr) with an ultrasound SR estimation system. SS was estimated from SR and calculated whole blood viscosity. SR was higher (P < 0.05) in the CCA (mean: 359 +/- 111 s(-1); peak: 1,047 +/- 345 s(-1)) than in the BA (mean: 95 +/- 24 s(-1); peak: 770 +/- 170 s(-1)). Whole blood viscosity was higher in the BA than in the CCA (5.1 +/- 0.7 vs. 3.3 +/- 0.6 mPa. s; P < 0.001). Peak SS did not differ between the CCA and the BA, whereas mean SS was significantly higher in the CCA (1.15 +/- 0.21 Pa) than in the BA (0.48 +/- 0.15 Pa; P < 0.001). These results demonstrate that BA SS strongly deviates from CCA SS in vivo.