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The liver lobules are a roughly hexagonal arrangement of hepatocyte plates which are separated by intervening sinusoids (small blood vessels similar to capillaries but with a fenestrated endothelium) which radiate outward from a central vein. The portal triads are located at the vertices of each hexagon. The different functions of the terminal branches of the hepatic artery, portal vein, and biliary tree occur within each lobule. A central vein drains each lobule, which is carried to the hepatic vein away from the liver.

The liver lobules are a roughly hexagonal arrangement of hepatocyte plates which are separated by intervening sinusoids (small blood vessels similar to capillaries but with a fenestrated endothelium) which radiate outward from a central vein. The portal triads are located at the vertices of each hexagon. The different functions of the terminal branches of the hepatic artery, portal vein, and biliary tree occur within each lobule. A central vein drains each lobule, which is carried to the hepatic vein away from the liver.

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Utilizing micro-computed tomography images, the hierarchical structure, interbranch segment lengths and diameters of a hepatic artery, a portal vein, and two biliary trees from intact rat liver lobes were characterized. The data were investigated by analyzing the geometric properties of the vascular structures, such as how interbranch segment diame...

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... Murray's law describes the blood vessel geometry at a bifurcation according to the relation ( is the diameters of the mother vessel [27]. ML has been described for the effect on branching geometry in large vessels [28,29] and capillaries [30]. The diameter mismatch is defined as the deviation from Murray's law. ...
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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.
... However, the quantitative computer-aided three-dimensional imaging techniques for studying the biliary tree are labor-intensive and time-consuming; they are not yet suitable for routine evaluations (Kline, Zamir, & Ritman, 2011;Ludwig et al., 1998;Masyuk, Ritman, & LaRusso, 2001). ...
Article
The study of the fractal architecture of various organs and structures expanded the possibilities for determining the ranges of their functioning and structural arrangement, which, as a result, was reflected in the development of new approaches to diagnostics and therapeutic impacts. The architecture of the excretory duct systems, similar to the hemo‐ and lymph‐ circulatory beds and the bronchial tree, is considered fractal. At the same time, information about hitherto unknown structures of the biliary tree continues to appear in the literature. We aimed to study the features of the spatial geometry of the biliary tree and assess the significance of both its fractal and Euclidean characteristics for the development of approaches that facilitate comprehensive description of intrahepatic biliary tract architecture. We investigated the architecture of the biliary trees of six men, seven male canines, and seven male Wistar rats using the corrosion casting method. Corrosion casts were prepared by injecting solidifying latexes into the bile ducts. The preparations were studied using a light stereomicroscope and a scanning electron microscope. Biliary tree branching is of various types. In addition, the correlation between variations in the caliber and length of the bile ducts and their order is not significant. Therefore, the biliary tree should not be considered as a classical fractal and it consists of the main modules, represented by the network of the bile canaliculi (first nonfractal module) and a biliary tree with a fractal branching (second module) that drains the bile canaliculi mesh and the additional modules represented by the mucosal biliary glands (in mammals with the gallbladder) or the periportal biliary plexus (in mammals without a gallbladder) and the aberrant biliary ducts. Such a configuration of the biliary bed should optimally ensure the smooth implementation of the physiological function of the liver, as well as its adaptation to different pathologies accompanied by biliary hypertension. It also might be considered in the diagnosis and assessment of ductular reaction, biliary regeneration, and/or carcinogenesis. The paper is provided by the graphical illustration depicting the spatial architecture of a biliary tree in both mammals with ‐ and without a gallbladder. The figure shows all basic (fractal and non‐fractal) and additional modules of the biliary pathway.
... Nano-computed tomography (nano-CT) has been widely utilized in the analysis of vascularity and bony microarchitecture of animals and human anatomical structures. 17,26,29,46 Additionally, nano-CT is capable of acquiring 3D images of complex anatomical soft tissue structures like the plantar plate, although its utility is comparatively limited in this regard. 28 In this study, we sought to compare the intact plantar plate microvasculature network to the microvasculature network of plantar plates in the presence of toe deformity using similar perfusion and nano-CT imaging methods. ...
Article
Background: Recent surgical techniques have focused on anatomic repair of lesser toe metatarsophalangeal (MTP) plantar plate tears, yet it remains unknown whether the plantar plate has the biological capacity to heal these repairs. Therefore, a better understanding of the plantar plate vasculature in response to injury may provide further insight into the potential for healing after anatomic plantar plate repair. Recently, a study demonstrated that the microvasculature of the normal plantar plate is densest at the proximal and distal attachments. The purpose of this study was to compare the intact plantar plate microvasculature network to the microvasculature network of plantar plates in the presence of toe deformity using similar perfusion and nano-computed tomographic (CT) imaging methods. Methods: Seven fresh-frozen human cadaveric lower extremities with lesser toe deformities including hammertoe or crossover toe were perfused using a barium solution. The soft tissues of each foot were counterstained with phosphomolybdic acid (PMA). Then using nano-CT imaging, the second through fourth toe metatarsophalangeal joints of 7 feet were imaged. These images were then reconstructed, plantar plate tears were identified, and 11 toes remained. The plantar plate microvasculature for these 11 toes was analyzed, and calculation of vascular density along the plantar plate was performed. Using analysis of variance (ANOVA), this experimental group was compared to a control group of 35 toes from cadaveric feet without deformity and the vascular density compared between quartiles of plantar plate length proximal to distal. A power analysis was performed, determining that 11 experimental toes and 35 control toes would be adequate to provide 80% power with an alpha of 0.05. Results: Significantly greater vascular density (vascular volume/tissue volume) was found along the entire length of the plantar plate for the torn plantar plates compared to intact plantar plates (ANOVA, P < .001). For the first quartile of length (proximal to distal), the vascular density for the torn plantar plates was 0.365 (SD 0.058) compared to 0.281 (SD 0.036) for intact plantar plates; in the second quartile it was 0.300 (SD 0.044) vs 0.175 (SD 0.025); third quartile it was 0.326 (SD 0.051) vs 0.117 (SD 0.015); and fourth (most distal) quartile was 0.600 (SD 0.183) vs 0.319 (SD 0.082). Conclusion: Torn plantar plates showed increased vascular density throughout the length of the plantar plate with an increase in density most notable in the region at or just proximal to the attachment to the proximal phalanx. Our analysis revealed that torn plantar plates exhibit neovascularization around the site of a plantar plate tear that does not exist in normal plantar plates. Clinical relevance: The clinical significance of the increased vascularity of torn plantar plates is unknown at this time. However, the increase in vasculature may suggest that the plantar plate is a structure that is attempting to heal.
... In this study, we focused on establishing a simple, robust, antibody-free and inexpensive method for whole organ visualization of lumenized structures. We built on previous work to image a single network using resin (Masyuk et al., 2003;Kline et al., 2011;Walter et al., 2012) and imaging with mCT. First, in order to visualize multiple structures, we tested different radiopaque substances to enhance the resin contrast, resulting in mixing of two MICROFIL resins with distinctive radiopacity. ...
... In contrast, immunostaining and clearing allows 3D analysis, but success is variable and highly dependent on tissue fixation, antibody quality, penetrance and tissue autofluorescence. Here, we further advanced organ resin casting, which was previously used to analyze one system at a time (Masyuk et al., 2003;Kline et al., 2011;Walter et al., 2012). We developed a simple, robust and inexpensive method (DUCT) for simultaneous visualization and digitalization of two lumenized systems in mouse to analyze organ architecture. ...
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Organ function depends on tissues adopting the correct architecture. However, insights into organ architecture are currently hampered by an absence of standardized quantitative 3D analysis. We aimed to develop a robust technology to visualize, digitalize, and segment the architecture of two tubular systems in 3D: double resin casting micro computed tomography (DUCT). As proof of principle, we applied DUCT to a mouse model for Alagille syndrome (Jag1Ndr/Ndr mice), characterized by intrahepatic bile duct paucity, that can spontaneously generate a biliary system in adulthood. DUCT identified increased central biliary branching and peripheral bile duct tortuosity as two compensatory processes occurring in distinct regions of Jag1Ndr/Ndr liver, leading to full reconstitution of wild-type biliary volume and phenotypic recovery. DUCT is thus a powerful new technology for 3D analysis, which can reveal novel phenotypes and provide a standardized method of defining liver architecture in mouse models.
... doi: 10.21037/qims- View this article at: https://dx.doi.org/10.21037/qims- measuring the diameter of the vessels (22,28,29). However, various abnormal features, such as vascular tortuosity, distortion, and deformation, exist in the hepatic vessels in liver fibrosis (30,31), making it difficult to measure the diameter of the vessels accurately. ...
... Moreover, the volume-averaged method was utilized to evaluate the intrahepatic circulation during the fibrosis and regression stages. For the bifurcation system of normal livers, the measured values showed reasonable agreement with the calculated optimal values, indicating that the normal hepatic vessels complied well with Murray's law, confirming previous studies of the normal liver (29). However, with fibrotic livers, Murray's deviation increased with the development of fibrosis and reached its maximum at the severe fibrotic phase, and subsequently decreased rapidly during regression, which showed a significant correlation with the vascular morphological alterations. ...
... Furthermore, Murray's deviation did, in fact decrease but failed to completely return to normalcy, corroborating with previous histopathological findings that fibrosis is not fully reversible, especially with regards to the changes in liver microvasculature (40,41). As shown in the present study and others (22,28,29), the value of Murray's deviation in normal livers is very close to the theoretical value of unity given by Murray's law (Murray's deviation =1), and the trend of Murray's deviation during fibrogenesis in this study were in good agreement with our previous reports on liver fibrosis (9) and cirrhosis (23). Notably, the assessment methods used in this study were significantly superior compared to those used in previous studies. ...
Article
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.
... A moving average filter was then used to smooth them. It is legitimate to assume that the arteries in the hepatic arterial tree have a circular cross-section [18,19]. Thus, a circular surface centered at the centerline with a radius of smoothed rins was created at each point along the centerline trajectory to build the CFD model ( Figure 1a). ...
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Transarterial embolization is a minimally invasive treatment for advanced liver cancer using microspheres loaded with a chemotherapeutic drug or radioactive yttrium-90 (90Y) that are injected into the hepatic arterial tree through a catheter. For personalized treatment, the microsphere distribution in the liver should be optimized through the injection volume and location. Computational fluid dynamics (CFD) simulations of the blood flow in the hepatic artery can help estimate this distribution if carefully parameterized. An important aspect is the choice of the boundary conditions imposed at the inlet and outlets of the computational domain. In this study, the effect of boundary conditions on the hepatic arterial tree hemodynamics was investigated. The outlet boundary conditions were modeled with three-element Windkessel circuits, representative of the downstream vasculature resistance. Results demonstrated that the downstream vasculature resistance affected the hepatic artery hemodynamics such as the velocity field, the pressure field and the blood flow streamline trajectories. Moreover, the number of microspheres received by the tumor significantly changed (more than 10% of the total injected microspheres) with downstream resistance variations. These findings suggest that patient-specific boundary conditions should be used in order to achieve a more accurate drug distribution estimation with CFD in transarterial embolization treatment planning.
... D, UF regions of blood vessels are known to have intact GCX resulting in the inability of CTC to attach to the endothelium. E, Branched areas will produce DF; we hypothesize that this DF will result in degradation of the endothelial GCX enhancing attachment of CTC to the endothelium distant organs where metastasis is more likely to occur, due to the high frequency of branched or curved blood vessels in these organs, 10,11 which includes the lungs, liver, and several other organs. 12 The branches and curves, as suggested by Guo et al, exhibit localized vorticity and shear rates which are different from the straight sections of the vessel. ...
Article
Cancer metastasis and secondary tumor initiation largely depend on circulating tumor cell (CTC) and vascular endothelial cell (EC) interactions by incompletely understood mechanisms. Endothelial glycocalyx (GCX) dysfunction may play a significant role in this process. GCX structure depends on vascular flow patterns, which are irregular in tumor environments. This work presents evidence that disturbed flow (DF) induces GCX degradation, leading to CTC homing to the endothelium, a first step in secondary tumor formation. A 2-fold greater attachment of CTCs to human ECs was found to occur under DF conditions, compared to uniform flow (UF) conditions. These results corresponded to an approximately 50% decrease in wheat germ agglutinin (WGA)-labeled components of the GCX under DF conditions, vs UF conditions, with undifferentiated levels of CTC-recruiting E-selectin under DF vs UF conditions. Confirming the role of the GCX, neuraminidase induced the degradation of WGA-labeled GCX under UF cell culture conditions or in Balb/C mice and led to an over 2-fold increase in CTC attachment to ECs or Balb/C mouse lungs, respectively, compared to untreated conditions. These experiments confirm that flow-induced GCX degradation can enable metastatic CTC arrest. This work, therefore, provides new insight into pathways of secondary tumor formation.
... Additionally, the branching geometry of the vasculature is investigated in normal liver based on Murray's law, and the study demonstrates that the hepatic artery and portal vein strongly adheres to Murray's cube law. In other words, the vascular system may diverge from the law in a diseased liver, which may result in Murray's deviation (MD) and an abnormal branch angle (6). In this study, we hypothesized that vascular morphologic features might be used to distinguish portal hypertension. ...
... Murray's law indicates the optimal vascular bifurcation such that the cube of the diameter of a mother vessel equals the sum of the cubes of the diameters of the daughters (22), and this has been widely used to analyze the branching geometry of vessels (23,24). In general, normal vessels obey Murray's law, but there may be an increase of MD due to the loss of an optimal circulatory system with the development of liver disease (6). MD can be described by the following formula: where d 0 represents the radius of the mother vessel, and d 2 and d 2 are the radii of daughters. ...
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Background: Portal hypertension is one of the major complications of cirrhosis. The changes in hepatic microvasculature are considered as critical pathophysiological characteristics of portal hypertension. X-ray phase-contrast computed tomography (PCCT) is a new imaging technique that can detect liver vessels at a micrometric level without contrast agents. Methods: In this study, male Sprague-Dawley rats with liver cirrhosis induced by carbon tetrachloride (CCl4) or bile duct ligation (BDL) were investigated with PCCT. The portal pressures of rats were recorded before euthanasia. The branch angle and Murray's deviation (MD) were measured based on the branching geometry of the three-dimensional (3D) microvasculature of liver cirrhosis in rats. Statistical analyses were performed to determine the correlation between branching geometry and portal pressure in liver fibrosis. Results: The results demonstrated that the branch angle and MD significantly increased in the CCl4 model and BDL model compared with their corresponding normal group or sham group. The portal pressure was significantly correlated with the branching morphologic features (all R≥0.761 and P<0.01). Conclusions: The branch angle and MD could accurately distinguish portal pressure in cirrhotic rats, suggesting that branching geometric characteristics of the microvasculature may be a promising marker in the prognosis of portal hypertension in liver cirrhosis.
... In order to fully analyze liver vasculopathy or biliary dysmorphology in mouse models, we developed a robust pipeline to visualize and quantify the 3D architecture of the intrahepatic biliary and portal vein systems. Building on extensive meticulous previous work to image intrahepatic architecture using resin [20][21][22] , or ink 23 , we devised double resin-casting micro () computed tomography (DUCT) to image and analyze two networks in 3D, in tandem. To our knowledge, this is the first tool that digitally reconstructs both structures in 3D simultaneously, allowing an in-depth understanding of their relationship. ...
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BACKGROUND AND AIMS: Alagille syndrome, like several other liver diseases, is characterized by malformation of lumenized structures, such as the circulatory or biliary systems. Liver architecture has typically been studied through 2D sections and, more recently, using thick tissue sections combined with immunofluorescence. We aimed to develop a robust method to image, digitalize and quantify 3D architecture of the biliary and vascular systems in tandem. METHODS: The biliary and portal vein trees of the mouse liver were injected with Microfil resin, followed by microCT scanning. Tomographic data was segmented and analyzed using a MATLAB script we wrote to investigate length, volume, tortuosity, branching, and the relation between the vascular and biliary systems. Double resin casting micro computed tomography (DUCT) was applied to a mouse model for Alagille syndrome (Jag1Ndr/Ndr mice), in which the biliary system is absent at postnatal stages, but regenerates by adulthood. Phenotypes discovered using DUCT were validated with cumbersome consecutive liver sections from mouse and human liver including patients with Alagille syndrome. RESULTS: DUCT revealed tortuous bile ducts either placed further from portal veins, or ectopically traversing the parenchyma and connecting two portal areas, in Jag1Ndr/Ndr mice. Furthermore, bile ducts either ended abruptly, or branched independently of portal vein branching, with bifurcations placed hilar or peripheral to portal vein branches. The branching defects, parenchymal bile ducts, and blunt endings were confirmed in patient samples. CONCLUSION: DUCT is a powerful technique, which provides computerized 3D reconstruction of casted networks. It exposes and quantifies previously unknown vascular and biliary phenotypes in mouse models, revealing new phenotypes in patients.
... This was based on the assumption that variation in the value of x over the relatively small number of generations in each of these microvascular trees was small, and that the calculated value provided a good approximation of the average. Figure 3 shows an example of the segmented microvasculature within one myocardial specimen that was generated as described in Experimental Methods and segmented using methods described in Ref. 10. ...
Article
A combination of experimental, theoretical, and imaging methodologies is used to examine the hierarchical structure and function of intramyocardial arteriolar trees in porcine hearts to provide a window onto a region of myocardial microvasculature which has been difficult to fully explore so far. A total of 66 microvascular trees from 6 isolated myocardial specimens were analyzed, with a cumulative number of 2438 arteriolar branches greater than or equal to 40 μm lumen diameter. The distribution of flow rates within each tree was derived from an assumed power law relationship for that tree between the diameter of vessel segments and flow rates that are consistent with that power law and subject to conservation of mass along hierarchical structure of the tree. The results indicate that the power law index increases at levels of arteriolar vasculature closer to the capillary level, consistent with a concomitant decrease in shear stress acting on endothelial tissue. These results resolve a long standing predicament which could not be resolved previously because of lack of data about the 3D, interconnected, arterioles. In the context of myocardial perfusion, the results indicate that the coefficient of variation of flow rate in pre-capillary distal arterioles is high, suggesting that heterogeneity of flow rate in these arterioles is not entirely random but may be due at least in part to active control.