Computational patient-specific models based on 3-D ultrasound data to quantify uterine arterial flow during pregnancy

Hemodynamic and Structural Comparison of Human Fetal Heart Development Between Normally Growing and Hypoplastic Left Heart Syndrome-Diagnosed Hearts

Congenital heart defects (CHDs) affect a wide range of societies with an incidence rate of 1.0–1.2%. These defects initiate at the early developmental stage and result in critical health disorders. Although genetic factors play a role in the formation of CHDs, the occurrence of cases in families with no history of CHDs suggests that mechanobiological forces may also play a role in the initiation and progression of CHDs. Hypoplastic left heart syndrome (HLHS) is a critical CHD, which is responsible for 25–40% of all prenatal cardiac deaths. The comparison of healthy and HLHS hearts helps in understanding the main hemodynamic differences related to HLHS. Echocardiography is the most common imaging modality utilized for fetal cardiac assessment. In this study, we utilized echocardiographic images to compare healthy and HLHS human fetal hearts for determining the differences in terms of heart chamber dimensions, valvular flow rates, and hemodynamics. The cross-sectional areas of chamber dimensions are determined from 2D b-mode ultrasound images. Valvular flow rates are measured via Doppler echocardiography, and hemodynamic quantifications are performed with the use of computational fluid dynamics (CFD) simulations. The obtained results indicate that cross-sectional areas of the left and right sides of the heart are similar for healthy fetuses during gestational development. The left side of HLHS heart is underdeveloped, and as a result, the hemodynamic parameters such as flow velocity, pressure, and wall shear stress (WSS) are significantly altered compared to those of healthy hearts.

Numerical Investigation of the Fetal Left Heart Hemodynamics During Gestational Stages

Flow-driven hemodynamic forces on the cardiac tissues have critical importance, and have a significant role in the proper development of the heart. These mechanobiological mechanisms govern the cellular responses for the growth and remodeling of the heart, where the altered hemodynamic environment is believed to be a major factor that is leading to congenital heart defects (CHDs). In order to investigate the mechanobiological development of the normal and diseased hearts, identification of the blood flow patterns and wall shear stresses (WSS) on these tissues are required for an accurate hemodynamic assessment. In this study, we focus on the left heart hemodynamics of the human fetuses throughout the gestational stages. Computational fetal left heart models are created for the healthy fetuses using the ultrasound images at various gestational weeks. Realistic inflow boundary conditions are implemented in the models using the Doppler ultrasound measurements for resolving the specific blood flow waveforms in the mitral valve. Obtained results indicate that WSS and vorticity levels in the fetal left heart decrease with the development of the fetus. The maximum WSS around the mitral valve is determined around 36 Pa at the gestational week of 16. This maximum WSS decreases to 11 Pa at the gestational week of 27, indicating nearly three-times reduction in the peak shear stress. These findings reveal the highly dynamic nature of the left heart hemodynamics throughout the development of the human fetus and shed light into the relevance of hemodynamic environment and development of CHDs.

Blood flow and transport in the human placenta

The placenta is a multi-functional organ that exchanges blood gases and nutrients between a mother and her developing fetus. In humans, fetal blood flows through intricate networks of vessels confined within villous trees, the branches of which are bathed in pools of maternal blood. Fluid mechanics and transport processes play a central role in understanding how these elaborate structures contribute to the function of the placenta, and how their disorganization may lead to disease. Recent advances in imaging and computation have spurred significant advances in simulations of fetal and maternal flows within the placenta, across a range of lengthscales. Models describe jets of maternal blood emerging from spiral arteries into a disordered and deformable porous medium, and solute uptake by fetal blood flowing through elaborate three-dimensional capillary networks. We survey recent developments and emerging challenges in modeling flow and transport in this complex organ.

Dynamic modeling of uteroplacental blood flow in IUGR indicates vortices and elevated pressure in the intervillous space - a pilot study

Ischemic placental disease is a concept that links intrauterine growth retardation (IUGR) and preeclampsia (PE) back to insufficient remodeling of uterine spiral arteries. The rheological consequences of insufficient remodeling of uterine spiral arteries were hypothesized to mediate the considerably later manifestation of obstetric disease. However, the micro-rheology in the intervillous space (IVS) cannot be examined clinically and rheological animal models of the human IVS do not exist. Thus, an in silico approach was implemented to provide in vivo inaccessible data. The morphology of a spiral artery and the inflow region of the IVS were three-dimensionally reconstructed to provide a morphological stage for the simulations. Advanced high-end supercomputing resources were used to provide blood flow simulations at high spatial resolution. Our simulations revealed turbulent blood flow (high-velocity jets and vortices) combined with elevated blood pressure in the IVS and increased wall shear stress at the villous surface in conjunction with insufficient spiral artery remodeling only. Post-hoc histological analysis of uterine veins showed evidence of increased trophoblast shedding in an IUGR placenta. Our data support that rheological alteration in the IVS is a relevant mechanism linking ischemic placental disease to altered structural integrity and function of the placenta.

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

Doppler Assessment of Uterine Blood Flow in Pre-eclampsia: A Review

Doppler ultrasonography plays an ever-increasing role in obstetric imaging. Although commonly purported to assess blood flow, most studies in this area report purely on velocimetric parameters, rather than true volumetric flow. This review article highlights the physiological importance of this distinction, and reports on a literature review of uterine artery Doppler interrogation in the context of pre-eclampsia, which identified only four original research papers that attempted to assess blood flow. Attention is needed for true volumetric flow assessment in pre-eclampsia research, which may permit a more complete conceptualisation of the pathogenesis and haemodynamic consequences of this condition.

A practical approach to parameter estimation applied to model predicting heart rate regulation

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The "best" subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.

Uterine artery blood flow volume in pregnant women with an abnormal pulsatility index of the uterine arteries delivering normal or intrauterine growth restricted newborns

The aim of this study was to assess and compare uterine artery (UtA) blood flow volume in pregnant patients with an abnormal uterine Doppler pulsatility index (PI) who delivered fetuses with an appropriate weight for gestational age (AGA) or with intrauterine growth restricted (IUGR). We prospectively recruited singleton pregnancies with abnormal uterine arteries P.I. between 18 and 38 weeks of gestation regardless of estimated fetal weight (EFW). Vessel diameter and blood flow velocity were measured along the UtA upstream to the vessel bifurcation in both the right and left UtAs. Uterine blood flow volumes measured in these pregnancies were compared to historical Control-pregnancies. Forty-three patients delivered at term a normal weight newborn (AGA-pregnancies). Thirty patients delivered growth restricted newborns at 32 weeks (i.r. 29-36w) with a median weight of 1160 gr (i.r. 1000-2065 gr) (IUGR-pregnancies). At mid-gestation (18 + 0 - 25 + 6 weeks + days of gestation) a significantly lower uterine blood flow volume per unit weight was observed between the two study groups and compared to controls: 142 ml/min/kg in IUGR-pregnancies, 217 ml/min/kg in AGA-pregnancies and 538 ml/min/kg in Control-pregnancies. These striking differences in blood flow volume were already present at mid-gestation, at a time when EFW was still normal. In late gestation (27 + 0 - 37 + 6 weeks + days of gestation), pregnancies with an abnormal uterine P.I. showed persistently low UtA flow (<50% of controls) even when corrected for fetal weight: 81 ml/min/kg in IUGR-pregnancies, 105 ml/min/kg in AGA-pregnancies, and 193 ml/min/kg in Control-pregnancies; p < 0.0001. Our findings are consistent with other recent studies regarding the association between reduced uterine blood flow volume and fetal growth restriction. However, the study brings new insight into the finding of abnormal uterine P.I. in normally grown fetuses typically dismissed as "falsely abnormal" or "false positive" findings. Our study suggests that blood flow volume measurement may serve as a new tool to assess this group of patients and possibly those with ischemic placental diseases that may provide some basis for therapeutic interventions.

Blood flow volume of uterine arteries in human pregnancies determined using 3D and bi-dimensional imaging, angio-Doppler, and fluid-dynamic modeling

The primary aim of this pilot study was to study uterine artery (UtA) blood flow volume in uneventful human pregnancies delivered at term, at mid and late gestation by means of 3D and bi-dimensional ultrasound imaging with angio-Doppler combined with fluid-dynamic modeling. Secondary aims were to correlate flow volume to placental site and to UtA Pulsatility Index (PI). Women with singleton, low-risk pregnancies were examined at mid and late gestation. The structure and course of the uterine artery (UtA) was studied in each patient by means of 3D-angio-Doppler and included vessel diameter D, blood flow velocity and PI (measured along the UtA). Fetal weight estimation and placental insertion site were assessed by ultrasound. A robust fluid-dynamic modeling was applied to calculate absolute flow and flow per unit fetal weight. Mean UtA diameter and blood flow velocity increased significantly (p < 0.0001) from mid-gestation to late gestation from 2.6 mm and 67.5 cm/s, to 3.0 mm and 85.3 cm/s, respectively, yielding an increasing absolute flow troughout gestation. h coefficient, derived by fluid-dynamic modeling to calculate mean velocity, increased significantly from 0.52 at mid-gestation to 0.57 at late gestation. UtA blood flow volume ml/min/kg-fetal weight was significantly higher at mid-gestation than at late gestation (535 ml/min/kg vs 193 ml/min/kg; p < 0.0001). In cases with strictly lateral placentas the ipsilateral UtA accommodates at mid and late gestation 63% and 67% of the total UtA flow. In central placentas UtA flow was evenly distributed between the two vessels. An inverse correlation was observed between PI and blood flow volume ml/min/kg (Pearson's coefficient r = -0.54). Our work confirms the technological and methodological limitations in the measurement of uterine artery blood flow. However, Doppler measurements supported by three-dimensional angio imaging of the uterine vessel, high resolution imaging and diameter measurement, and a robust mathematical model of local circulation adds a genuine new area of investigation into human uterine circulation during pregnancy.