Transmission line models to simulate the impedance of the uterine vasculature during the ovarian cycle and pregnancy

Interpretation of wave reflections in the umbilical arterial segment of the feto-placental circulation: computational modeling of the feto-placental arterial tree

Placental vascular abnormalities are associated with a host of pregnancy complications including placenta mediated fetal growth restriction (FGR). Umbilical arterial (UA) Doppler ultrasound velocity waveforms are widely used in the diagnosis of underlying placental vascular abnormalities in pregnancies with suspected FGR, which greatly help prevent stillbirth via ongoing fetal monitoring and timely delivery. However, the sensitivity of UA Doppler diagnosis diminishes late in gestation. Our goal was to present a generalized wave decomposition method to compute forward and reflected components from UA waveforms. A detailed anatomical based model was also developed to explain observed UA flow waveform and to explore how vascular properties affect the shape of flow wave components. Using pregnant mice and high frequency ultrasound microscopy, we obtained in utero Doppler and M- mode ultrasound measurements in 15 fetuses UA. Following ultrasound, the placentas were collected and perfused with contrast agent to obtain high-resolution 3D images of the feto-placental arteries. Model results indicate the significant role of terminal load impedance (capillary and/or veins) in creating positive or negative reflected waveforms. A negative reflected waveform is obtained when terminal impedance increases. This is consistent with the elongated and non-branching terminal villi that are proposed cause the highly abnormal UA waveforms found in early-onset FGR. The significance of these findings for the diagnostic utility of UA Doppler in human pregnancy is that the identification and measurement of wave reflections may aid in discriminating between healthy and abnormal placental vasculature in pregnancies with suspected late-onset FGR.

Computational modeling of the interactions between the maternal and fetal circulations in human pregnancy

In pregnancy, fetal growth is supported by its placenta. In turn, the placenta is nourished by maternal blood, delivered from the uterus, in which the vasculature is dramatically transformed to deliver this blood an ever increasing volume throughout gestation. A healthy pregnancy is thus dependent on the development of both the placental and maternal circulations, but also the interface where these physically separate circulations come in close proximity to exchange gases and nutrients between mum and baby. As the system continually evolves during pregnancy, our understanding of normal vascular anatomy, and how this impacts placental exchange function is limited. Understanding this is key to improve our ability to understand, predict, and detect pregnancy pathologies, but presents a number of challenges, due to the inaccessibility of the pregnant uterus to invasive measurements, and limitations in the resolution of imaging modalities safe for use in pregnancy. Computational approaches provide an opportunity to gain new insights into normal and abnormal pregnancy, by connecting observed anatomical changes from high-resolution imaging to function, and providing metrics that can be observed by routine clinical ultrasound. Such advanced modeling brings with it challenges to scale detailed anatomical models to reflect organ level function. This suggests pathways for future research to provide models that provide both physiological insights into pregnancy health, but also are simple enough to guide clinical focus. We the review evolution of computational approaches to understanding the physiology and pathophysiology of pregnancy in the uterus, placenta, and beyond focusing on both opportunities and challenges. This article is categorized under: Reproductive System Diseases >Computational Models.

Understanding abnormal uterine artery Doppler waveforms: A novel computational model to explore potential causes within the utero-placental vasculature

INTRODUCTION

Uterine artery (UtA) Doppler indices are one of the most commonly employed screening tests for pre-eclampsia worldwide. Abnormal indices appear to result from increased uterine vascular resistance, but anatomical complexity and lack of appropriate animal models mean that little is known about the relative contribution of each of the components of the uterine vasculature to the overall UtA Doppler waveform. Previous computational models suggested that trophoblast-mediated spiral artery remodeling has a dominant effect on the UtA Doppler waveform. However, these models did not incorporate the myometrial arterio-venous anastomoses, which have significant potential to affect utero-placental haemodynamics.

METHODS

We present a more anatomically complete computational model, explicitly incorporating a structural description of each component of the uterine vasculature, and crucially including myometrial arterio-venous anastomoses as parallel pathways for blood-flow away from the placental bed. Wave transmission theory was applied to the network to predict UtA waveforms.

RESULTS

Our model shows that high UtA resistance indices, combined with notching, reflect an abnormal remodeling of the entire uterine vasculature. Incomplete spiral artery remodeling alone is unlikely to cause abnormal UtA Doppler waveforms as increased resistance in these arteries can be 'buffered' by upstream anastomoses. Critically, our results indicate that the radial arteries, may have a more important effect on utero-placental flow dynamics, and the UtA Doppler waveform than previously thought.

CONCLUSIONS

This model suggests that to appropriately interpret UtA Doppler waveforms they must be considered to be reflecting changes in the entire system, rather than just the spiral arteries.

A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree

For the purpose of optimization of the whole arterial tree, a fast method for solving of one-dimensional model of blood flow is required. A semi-analytic transmission line method for solving a linearized one-dimensional model of blood flow in an arterial tree with viscoelastic walls is proposed. The transmission line method that solves the linearized model in the frequency domain and the method of characteristics that solves either linearized or non-linear one-dimensional models in the time domain are compared regarding accuracy and computational time. For this purpose, the benchmark problem of a 37-artery network with available experimental data is used. In the case of the linearized model, the results from the transmission line method and the method of characteristics are practically the same. The difference between the transmission line method solution of the linearized model and the method of characteristics solution of the non-linear model is much smaller than the error of either method of characteristics or transmission line method numerical solutions with respect to the experimental data. For typical applications, the transmission line method is at least two orders of magnitude faster than the method of characteristics.

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.

NUMERICAL SIMULATION AND VALIDITY OF A NOVEL METHOD FOR THE PREDICTION OF ARTERY STENOSIS VIA INPUT IMPEDANCE AND SUPPORT VECTOR MACHINE

The early detection and intervention of artery stenosis is very important to reduce the mortality of cardiovascular disease. A novel method for predicting artery stenosis was proposed by using the input impedance of the systemic arterial tree and support vector machine (SVM). Based on the built transmission line model of a 55-segment systemic arterial tree, the input impedance of the arterial tree was calculated by using a recursive algorithm. A sample database of the input impedance was established by specifying the different positions and degrees of artery stenosis. A SVM prediction model was trained by using the sample database. 10-fold cross-validation was used to evaluate the performance of the SVM. The effects of stenosis position and degree on the accuracy of the prediction were discussed. The results showed that the mean specificity, sensitivity and overall accuracy of the SVM are 80.2%, 98.2% and 89.2%, respectively, for the 50% threshold of stenosis degree. Increasing the threshold of the stenosis degree from 10% to 90% increases the overall accuracy from 82.2% to 97.4%. Increasing the distance of the stenosis artery from the heart gradually decreases the overall accuracy from 97.1% to 58%. The deterioration of the stenosis degree to 90% increases the prediction accuracy of the SVM to more than 90% for the stenosis of peripheral artery. The simulation demonstrated theoretically the feasibility of the proposed method for predicting artery stenosis via the input impedance of the systemic arterial tree and SVM.

NUMERICAL SIMULATION OF HUMAN SYSTEMIC ARTERIAL HEMODYNAMICS BASED ON A TRANSMISSION LINE MODEL AND RECURSIVE ALGORITHM

A novel recursive algorithm was proposed to calculate the input impedance of human systemic arterial tree, and to simulate the human systemic arterial hemodynamics with an 55 segment transmission line model. In calculation of input impedance, the structure of the arterial tree was expressed as a single linked list. An infinitesimal constant was used to replace 0 Hz frequency to calculate the DC and AC part of input impedance simultaneously. The input impedance at any point of the arterial tree can obtain easily by the proposed recursive algorithm. The results of input impedance are in accord with experimental data and other models' results. In addition, some comparisons were conducted about the effects of arterial compliance, length, internal radius and wall thickness on the input impedance of ascending aorta. The results showed input impedances of ascending aorta displayed significantly different characteristics for different kinds of parameters. Finally, the blood pressure and flow waveforms of all arterial segments were calculated and displayed in 3D. The arterial elasticity and viscosity were discussed by changing the Young's modulus and the phase difference, respectively. The simulation results showed that the blood pressure and flow waveforms of the arterial tree reflected accurately the main characteristic features of physiopathological changes, which demonstrated the effectiveness of the proposed model.

Signaling regulation of fetoplacental angiogenesis

During normal pregnancy, dramatically increased placental blood flow is critical for fetal growth and survival as well as neonatal birth weights and survivability. This increased blood flow results from angiogenesis, vasodilatation, and vascular remodeling. Locally produced growth factors including fibroblast growth factor 2 (FGF2) and vascular endothelial growth factor A (VEGFA) are key regulators of placental endothelial functions including cell proliferation, migration, and vasodilatation. However, the precise signaling mechanisms underlying such regulation in fetoplacental endothelium are less well defined, specifically with regard to the interactions amongst protein kinases (PKs), protein phosphatase, and nitric oxide (NO). Recently, we and other researchers have obtained solid evidence showing that different signaling mechanisms participate in FGF2- and VEGFA-regulated fetoplacental endothelial cell proliferation and migration as well as NO production. This review will briefly summarize currently available data on signaling mediating fetoplacental angiogenesis with a specific emphasis on PKs, ERK1/2, AKT1, and p38 MAPK and protein phosphatases, PPP2 and PPP3.