A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

     

A data-driven model to study utero-ovarian blood flow physiology during pregnancy

In this paper, we describe a mathematical model of the cardiovascular system in human pregnancy. An automated, closed-loop 1D–0D modelling framework was developed, and we demonstrate its efficacy in (1) reproducing measured multi-variate cardiovascular variables (pulse pressure, total peripheral resistance and cardiac output) and (2) providing automated estimates of variables that have not been measured (uterine arterial and venous blood flow, pulse wave velocity, pulsatility index). This is the first model capable of estimating volumetric blood flow to the uterus via the utero-ovarian communicating arteries. It is also the first model capable of capturing wave propagation phenomena in the utero-ovarian circulation, which are important for the accurate estimation of arterial stiffness in contemporary obstetric practice. The model will provide a basis for future studies aiming to elucidate the physiological mechanisms underlying the dynamic properties (changing shapes) of vascular flow waveforms that are observed with advancing gestation. This in turn will facilitate the development of methods for the earlier detection of pathologies that have an influence on vascular structure and behaviour.

     

Mechanobiology of the relocation of proteins in advecting cells: in vitro experiments,multi-physics modeling,and simulations

Cell motility—a cellular behavior of paramount relevance in embryonic development, immunological response, metastasis, or angiogenesis—demands a mechanical deformation of the cell membrane and influences the surface motion of molecules and their biochemical interactions. In this work, we develop a fully coupled multi-physics model able to capture and predict the protein flow on endothelial advecting plasma membranes. The model has been validated against co-designed in vitro experiments. The complete picture of the receptor dynamics has been understood, and limiting factors have been identified together with the laws that regulate receptor polarization. This computational approach might be insightful in the prediction of endothelial cell behavior in different tumoral environments, circumventing the time-consuming and expensive empirical characterization of each tumor.

     

Mechanisms regulating the copy numbers of six LTR retrotransposons in the genome of Drosophila melanogaster

There has been debate over the mechanisms that control the copy number of transposable elements in the genome of Drosophila melanogaster. Target sites in D. melanogaster populations are occupied at low frequencies, suggesting that there is some form of selection acting against transposable elements. Three main theories have been proposed to explain how selection acts against transposable elements: insertions of a copy of a transposable element are selected against; chromosomal rearrangements caused by ectopic exchange between element copies are selected against; or the process of transposition itself is selected against. The three theories give different predictions for the pattern of transposable element insertions in the chromosomes of D. melanogaster. We analysed the abundance of six LTR (long terminal repeat) retrotransposons on the X and fourth chromosomes of multiple strains of D. melanogaster, which we compare with the predictions of each theory. The data suggest that no one theory can account for the insertion patterns of all six retrotransposons. Comparing our results with earlier work using these transposable element families, we find a significant correlation between studies in the particular model of copy number regulation supported by the proportion of elements on the X for the different transposable element families. This suggests that different retrotransposon families are regulated by different mechanisms.     

The effects of different mesh generation methods on computational fluid dynamic analysis and power loss assessment in total cavopulmonary connection

The flow field and energetic efficiency of total cavopulmonary connection (TCPC) models have been studied by both in vitro experiment and computational fluid dynamics (CFD). All the previous CFD studies have employed the structured mesh generation method to create the TCPC simulation model. In this study, a realistic TCPC model with complete anatomical features was numerically simulated using both structured and unstructured mesh generation methods. The flow fields and energy losses were compared in these two meshes. Two different energy loss calculation methods, the control volume and viscous dissipation methods, were investigated. The energy losses were also compared to the in vitro experimental results. The results demonstrated that: (1) the flow fields in the structured model were qualitatively similar to the unstructured model; (2) more vortices were present in the structured model than in the unstructured model; (3) both models had the least energy loss when flow was equally distributed to the left and right pulmonary arteries, while high losses occurred for extreme pulmonary arterial flow splits; (4) the energy loss results calculated using the same method were significantly different for different meshes; and (5) the energy loss results calculated using different methods were significantly different for the same mesh.     

Arterial Pulsation-driven Cerebrospinal Fluid Flow in the Perivascular Space: A Computational Model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Observation of Bacterial Type I Pili Extension and Contraction under Fluid Flow

Type I pili are proteinaceous tethers that mediate bacterial adhesion of uropathogenic Escherichia coli to surfaces and are thought to help bacteria resist drag forces imparted by fluid flow via uncoiling of their quaternary structure. Uncoiling and recoiling have been observed in force spectroscopy experiments, but it is not clear if and how this process occurs under fluid flow. Here we developed an assay to study the mechanical properties of pili in a parallel plate flow chamber. We show that pili extend when attached E. coli bacteria are exposed to increasing shear stresses, that pili can help bacteria move against moderate fluid flows, and characterize two dynamic regimes of this displacement. The first regime is consistent with entropic contraction as modeled by a freely jointed chain, and the second with coiling of the quaternary structure of pili. These results confirm that coiling and uncoiling happen under flow but the observed dynamics are different from those reported previously. Using these results and those from previous studies, we review the mechanical properties of pili in the context of other elastic proteins such as the byssal threads of mussels. It has been proposed that the high extensibility of pili may help recruit more pili into tension and lower the force acting on each one by damping changes in force due to fluid flow. Our analysis of the mechanical properties suggests additional functions of pili; in particular, their extensibility may reduce tension by aligning pili with the direction of flow, and the uncoiled state of pili may complement uncoiling in regulating the force of the terminal adhesin.     

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.     

Multiscale bio-chemo-mechanical model of intimal hyperplasia

We consider a computational multiscale framework of a bio-chemo-mechanical model for intimal hyperplasia. With respect to existing models, we investigate the interactions between hemodynamics, cellular dynamics and biochemistry on the development of the pathology. Within the arterial wall, we propose a mathematical model consisting of kinetic differential equations for key vascular cell types, collagen and growth factors. The luminal hemodynamics is modeled with the Navier–Stokes equations. Coupling hypothesis among time and space scales are proposed to build a tractable modeling of such a complex multifactorial and multiscale pathology. A one-dimensional numerical test-case is presented for validation by comparing the results of the framework with experiments at short and long timescales. Our model permits to capture many cellular phenomena which have a central role in the physiopathology of intimal hyperplasia. Results are quantitatively and qualitatively consistent with experimental findings at both short and long timescales.

     

A novel,FFT-based one-dimensional blood flow solution method for arterial network

In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks.

     

Partial hepatectomy hemodynamics changes: Experimental data explained by closed-loop lumped modeling

The liver function may be degraded after partial liver ablation surgery. Adverse liver hemodynamics have been shown to be associated to liver failure. The link between these hemodynamics changes and ablation size is however poorly understood. This article proposes to explain with a closed-loop lumped model the hemodynamics changes observed during twelve surgeries in pigs. The portal venous tree is modeled with a pressure-dependent variable resistor. The variables measured, before liver ablation, are used to tune the model parameters. Then, the liver partial ablation is simulated with the model and the simulated pressures and flows are compared with post-operative measurements. Fluid infusion and blood losses occur during the surgery. The closed-loop model presented accounts for these blood volume changes. Moreover, the impact of blood volume changes and the liver lobe mass estimations on the simulated variables is studied. The typical increase of portal pressure, increase of liver pressure loss, slight decrease of portal flow and major decrease in arterial flow are quantitatively captured by the model for a 75% hepatectomy. It appears that the 75% decrease in hepatic arterial flow can be explained by the resistance increase induced by the surgery, and that no hepatic arterial buffer response (HABR) mechanism is needed to account for this change. The different post-operative states, observed in experiments, are reproduced with the proposed model. Thus, an explanation for inter-subjects post-operative variability is proposed. The presented framework can easily be adapted to other species circulations and to different pathologies for clinical hepatic applications.     

Improving load balancing for data-duplication in big data cloud computing networks

Data transmission and retrieval in a cloud computing environment are usually handled by storage device providers or physical storage units leased by third parties. Improving network performance considering power connectivity and resource stability while ensuring workload balance is a hot topic in cloud computing. In this research, we have addressed the data duplication problem by providing two dynamic models with two variant architectures to investigate the strengths and shortcomings of architectures in Big Data Cloud Computing Networks. The problems of the data duplication process will be discussed accurately in each model. Attempts have been made to improve the performance of the cloud network by taking into account and correcting the flaws of the previously proposed algorithms. The accuracy of the proposed models have been investigated by simulation. Achieved results indicate an increase in the workload balance of the network and a decrease in response time to user requests in the model with a grouped architecture for all the architectures. Also, the proposed duplicate data model with peer-to-peer network architecture has been able to increase the cloud network optimality compared to the models presented with the same architecture.

     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

The Impact of Blood Rheology on Drug Transport in Stented Arteries: Steady Simulations

Background and Methods

It is important to ensure that blood flow is modelled accurately in numerical studies of arteries featuring drug-eluting stents due to the significant proportion of drug transport from the stent into the arterial wall which is flow-mediated. Modelling blood is complicated, however, by variations in blood rheological behaviour between individuals, blood’s complex near-wall behaviour, and the large number of rheological models which have been proposed. In this study, a series of steady-state computational fluid dynamics analyses were performed in which the traditional Newtonian model was compared against a range of non-Newtonian models. The impact of these rheological models was elucidated through comparisons of haemodynamic flow details and drug transport behaviour at various blood flow rates.

Results

Recirculation lengths were found to reduce by as much as 24% with the inclusion of a non-Newtonian rheological model. Another model possessing the viscosity and density of blood plasma was also implemented to account for near-wall red blood cell losses and yielded recirculation length increases of up to 59%. However, the deviation from the average drug concentration in the tissue obtained with the Newtonian model was observed to be less than 5% in all cases except one. Despite the small sensitivity to the effects of viscosity variations, the spatial distribution of drug matter in the tissue was found to be significantly affected by rheological model selection.

Conclusions/Significance

These results may be used to guide blood rheological model selection in future numerical studies. The clinical significance of these results is that they convey that the magnitude of drug uptake in stent-based drug delivery is relatively insensitive to individual variations in blood rheology. Furthermore, the finding that flow separation regions formed downstream of the stent struts diminish drug uptake may be of interest to device designers.     

Microfluidic and computational study of structural properties and resistance to flow of blood clots under arterial shear

The ability of a blood clot to modulate blood flow is determined by the clot’s resistance, which depends on its structural features. For a flow with arterial shear, we investigated the characteristic patterns relating to clot shape, size, and composition on the one hand, and its viscous resistance, intraclot axial flow velocity, and shear distributions on the other. We used microfluidic technology to measure the kinetics of platelet, thrombin, and fibrin accumulation at a thrombogenic surface coated with collagen and tissue factor (TF), the key clot-formation trigger. We subsequently utilized the obtained data to perform additional calibration and validation of a detailed computational fluid dynamics model of spatial clot growth under flow. We then ran model simulations to gain insights into the resistance of clots formed under our experimental conditions. We found that increased thrombogenic surface length and TF surface density enhanced the bulk thrombin and fibrin generation in a nonadditive, synergistic way. The height of the platelet deposition domain—and, therefore, clot occlusivity—was rather robust to thrombogenic surface length and TF density variations, but consistently increased with time. Clot viscous resistance was non-uniform and tended to be higher in the fibrin-rich, inner “core” region of the clot. Interestingly, despite intraclot structure and viscous resistance variations, intraclot flow velocity variations were minor compared to the abrupt decrease in flow velocity around the platelet deposition region. Our results shed new light on the connection between the structure of clots under arterial shear and spatiotemporal variations in their resistance to flow.

     

Roots and calibers of the human coronary arteries

The anatomical structure of the coronary-aortic junctions in humans is studied by using corrosion casts of the coronary network. A model is proposed for the specification of these junctions in terms of vessel diameters and branching angles, and the model is used to produce morphological data on these junctions which hitherto have not been available. This anatomical model correlates poorly with the accepted theoretical model of arterial bifurcations in the cardiovascular system. The results suggest that the structure of the coronary-aortic junctions is very different from the structure of typical arterial bifurcations and, by implication, that the flow conditions under which they function are very different. A good understanding of these junctions is important in coronary bypass surgery, where the coronary-aortic junctions are emulated by creating a new anastomosis for the graft at the base of the ascending aorta, and in coronary artery disease, where atherosclerotic lesions occur not far from the coronary-aortic junctions.     

Computational model of blood flow in the aorto-coronary bypass graft

Background

Coronary artery bypass grafting surgery is an effective treatment modality for patients with severe coronary artery disease. The conduits used during the surgery include both the arterial and venous conduits. Long- term graft patency rate for the internal mammary arterial graft is superior, but the same is not true for the saphenous vein grafts. At 10 years, more than 50% of the vein grafts would have occluded and many of them are diseased. Why do the saphenous vein grafts fail the test of time? Many causes have been proposed for saphenous graft failure. Some are non-modifiable and the rest are modifiable. Non-modifiable causes include different histological structure of the vein compared to artery, size disparity between coronary artery and saphenous vein. However, researches are more interested in the modifiable causes, such as graft flow dynamics and wall shear stress distribution at the anastomotic sites. Formation of intimal hyperplasia at the anastomotic junction has been implicated as the root cause of long- term graft failure.Many researchers have analyzed the complex flow patterns in the distal sapheno-coronary anastomotic region, using various simulated model in an attempt to explain the site of preferential intimal hyperplasia based on the flow disturbances and differential wall stress distribution. In this paper, the geometrical bypass models (aorto-left coronary bypass graft model and aorto-right coronary bypass graft model) are based on real-life situations. In our models, the dimensions of the aorta, saphenous vein and the coronary artery simulate the actual dimensions at surgery. Both the proximal and distal anastomoses are considered at the same time, and we also take into the consideration the cross-sectional shape change of the venous conduit from circular to elliptical. Contrary to previous works, we have carried out computational fluid dynamics (CFD) study in the entire aorta-graft-perfused artery domain. The results reported here focus on (i) the complex flow patterns both at the proximal and distal anastomotic sites, and (ii) the wall shear stress distribution, which is an important factor that contributes to graft patency.

Methods

The three-dimensional coronary bypass models of the aorto-right coronary bypass and the aorto-left coronary bypass systems are constructed using computational fluid-dynamics software (Fluent 6.0.1). To have a better understanding of the flow dynamics at specific time instants of the cardiac cycle, quasi-steady flow simulations are performed, using a finite-volume approach. The data input to the models are the physiological measurements of flow-rates at (i) the aortic entrance, (ii) the ascending aorta, (iii) the left coronary artery, and (iv) the right coronary artery.

Results

The flow field and the wall shear stress are calculated throughout the cycle, but reported in this paper at two different instants of the cardiac cycle, one at the onset of ejection and the other during mid-diastole for both the right and left aorto-coronary bypass graft models. Plots of velocity-vector and the wall shear stress distributions are displayed in the aorto-graft-coronary arterial flow-field domain. We have shown (i) how the blocked coronary artery is being perfused in systole and diastole, (ii) the flow patterns at the two anastomotic junctions, proximal and distal anastomotic sites, and (iii) the shear stress distributions and their associations with arterial disease.

Conclusion

The computed results have revealed that (i) maximum perfusion of the occluded artery occurs during mid-diastole, and (ii) the maximum wall shear-stress variation is observed around the distal anastomotic region. These results can enable the clinicians to have a better understanding of vein graft disease, and hopefully we can offer a solution to alleviate or delay the occurrence of vein graft disease.

     

Bacteriocins: perspective for the development of novel anticancer drugs

Antimicrobial peptides (AMPs) from prokaryotic source also known as bacteriocins are ribosomally synthesized by bacteria belonging to different eubacterial taxonomic branches. Most of these AMPs are low molecular weight cationic membrane active peptides that disrupt membrane by forming pores in target cell membranes resulting in cell death. While these peptides known to exhibit broad-spectrum antimicrobial activity, including antibacterial and antifungal, they displayed minimal cytotoxicity to the host cells. Their antimicrobial efficacy has been demonstrated in vivo using diverse animal infection models. Therefore, we have discussed some of the promising peptides for their ability towards potential therapeutic applications. Further, some of these bacteriocins have also been reported to exhibit significant biological activity against various types of cancer cells in different experimental studies. In fact, differential cytotoxicity towards cancer cells as compared to normal cells by certain bacteriocins directs for a much focused research to utilize these compounds as novel therapeutic agents. In this review, bacteriocins that demonstrated antitumor activity against diverse cancer cell lines have been discussed emphasizing their biochemical features, selectivity against extra targets and molecular mechanisms of action.

     

Evaluation of blood flow velocity waveform in common carotid artery using multi-branched arterial segment model of human arteries

Arteriosclerosis is considered to be a major cause of cardiovascular diseases, which account for approximately 30% of the causes of death in the world. We have recently demonstrated a strong correlation between arteriosclerosis (arterial elasticity) and two characteristics: maximum systolic velocity (S1) and systolic second peak velocity (S2) of the common carotid artery flow velocity waveform (CCFVW). The CCFVW can be measured by using a small portable measuring device. However, there is currently no theoretical evidence supporting the causes of the relation between CCFVW and arterial elasticity, or the origin of the CCFVW characteristics. In this study, the arterial blood flow was simulated using a one-dimensional systemic arterial segments model of human artery in order to conduct a qualitative evaluation of the relationship between arterial elasticity and the characteristics of CCFVW. The simulation was carried out based on the discretized segments with the physical properties of a viscoelastic tube (the cross-sectional area at the proximal and terminal ends, the length, and the compliance per unit area of the tube (C_S)). The findings obtained through this study revealed that the simulated CCFVW had shape similar characteristics to that of the measured CCFVW. Moreover, when the compliance C_S of the model was decreased, the first peak of the simulated-CCFVW decreased and the second peak increased. Further, by separating the anterograde pulse wave and the reflected pulse wave, which form the CCFVW, we found that the decrease in the first peak of the simulated CCFVW was due to the arrival of a reflected pulse wave from the head after the common carotid artery toward the arrival of a anterograde pulse wave ejected directly from the heart and that the increase in the second peak resulted from the arrival of the peak of the reflected pulse wave from the thoracic aorta. These results establish that the CCFVW characteristics contribute to the assessment of arterial elasticity.     

A mathematical model of maternal vascular growth and remodeling and changes in maternal hemodynamics in uncomplicated pregnancy

The maternal vasculature undergoes tremendous growth and remodeling (G&R) that enables a?>?15-fold increase in blood flow through the uterine vasculature from conception to term. Hemodynamic metrics (e.g., uterine artery pulsatility index, UA-PI) are useful for the prognosis of pregnancy complications; however, improved characterization of the maternal hemodynamics is necessary to improve prognosis. The goal of this paper is to develop a mathematical framework to characterize maternal vascular G&R and hemodynamics in uncomplicated human pregnancies. A validated 1D model of the human vascular tree from the literature was adapted and inlet blood flow waveforms at the ascending aorta at 4 week increments from 0 to 40 weeks of gestation were prescribed. Peripheral resistances of each terminal vessel were adjusted to achieve target flow rates and mean arterial pressure at each gestational age. Vessel growth was governed by wall shear stress (and axial lengthening in uterine vessels), and changes in vessel distensibility were related to vessel growth. Uterine artery velocity waveforms generated from this model closely resembled ultrasound results from the literature. The literature UA-PI values changed significantly across gestation, increasing in the first month of gestation, then dramatically decreasing from 4 to 20 weeks. Our results captured well the time-course of vessel geometry, material properties, and UA-PI. This 1D fluid-G&R model captured the salient hemodynamic features across a broad range of clinical reports and across gestation for uncomplicated human pregnancy. While results capture available data well, this study highlights significant gaps in available data required to better understand vascular remodeling in pregnancy.