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

Gleason, Rudolph L.; Sedaghati, Farbod

doi:10.1007/s10237-021-01555-0

Cited by 5 publications

(13 citation statements)

References 140 publications

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“…Given a set of modeling inputs, the modeling outputs are determined, namely

, and

at every location in the arterial network, from which centerline blood flow velocity,

, artery diameter waveforms,

, and wall shear stress waveforms,

, may be calculated. An implicit finite difference scheme was devised to solve the governing equations with the input parameters; see Gleason Jr. & Sedaghati, 2022 . We discretized the time domain into

=500 time steps per cardiac cycle, with

.…”

Section: Methodsmentioning

confidence: 99%

“…The lengths of all artery segments were taken from Gleason and Sedaghati (Gleason Jr. & Sedaghati, 2022 ). For the vessel diameters, we let each vascular segment grow radially to restore the mean wall shear stress (

) to a prescribed target values

.…”

Section: Methodsmentioning

confidence: 99%

“…For the nongravid uterus, we use Equation ( 5 ) to calculate the distensibility of each vessel in the vascular network. Following Gleason and Sedghati (Gleason Jr. & Sedaghati, 2022 ), for the gravid vascular networks, we let

where

denotes the gestational age,

and

are the fractional increases in diameter (

) and length (

) from the nongravid vasculature (i.e., at

) and the gravid time point of interest,

, and

are remodeling parameters, and

is the value of the expression in the square brackets at

= 1. We let

=2.2 and

=1.7 and let

= −0.85.…”

Section: Methodsmentioning

confidence: 99%

“…A validated 1D hemodynamics model that includes the growth and remodeling of the vascular and hemodynamic changes across gestation, comparing healthy pregnancy with early and late forms of preeclampsia, may provide a useful tool to better understand the development and progression of these complications and may reveal characteristics for improved early assessment of risk. We previously reported a mathematical framework of maternal vascular growth and remodeling and changes in hemodynamics in uncomplicated pregnancy (Gleason Jr. & Sedaghati, 2022 ). The purpose of this paper was to develop models that characterize early and late forms of preeclampsia, validate these models based on available results from the literature, and compare vascular and hemodynamic features across these illustrative simulations.…”

Section: Introductionmentioning

confidence: 99%

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A mathematical model of vascular and hemodynamics changes in early and late forms of preeclampsia

Sedaghati

Gleason

2023

Physiological Reports

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Preeclampsia–eclampsia syndrome is a leading cause of maternal mortality. The precise etiology of preeclampsia is still not well‐defined and different forms exist, including early and late forms or preeclampsia, which may arise via distinctly different mechanisms. Low‐dose aspirin administered at the end of the first trimester in women identified as high risk has been shown to reduce the incidence of early, but not late, preeclampsia; however, current risk factors show only fair predictive capability. There is a pressing need to develop accurate descriptions for the different forms of preeclampsia. This paper presents 1D fluid, solid, growth, and remodeling models for pregnancies complicated with early and late forms of preeclampsia. Simulations affirm a broad set of literature results that early forms of preeclampsia are characterized by elevated uterine artery pulsatility index (UA‐PI) and total peripheral resistance (TPR) and lower cardiac output (CO), with modestly increased mean arterial blood pressure (MAP) in the first half of pregnancy, with elevation of TPR and MAP beginning at 20 weeks. Conversely, late forms of preeclampsia are characterized by only slightly elevated UA‐PI and normal pre‐term TPR, and slightly elevated MAP and CO throughout pregnancy, with increased TPR and MAP beginning after 34 weeks. Results suggest that preexisting arterial stiffness may be elevated in women that develop both early forms and late forms of preeclampsia; however, data that verify these results are lacking in the literature. Pulse wave velocity increases in early‐ and late‐preeclampsia, coincident with increases in blood pressure; however, these increases are mainly due to the strain‐stiffening response of larger arteries, rather than arterial remodeling‐derived changes in material properties. These simulations affirm that early forms of preeclampsia may be associated with abnormal placentation, whereas late forms may be more closely associated with preexisting maternal cardiovascular factors; simulations also highlight several critical gaps in available data.

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“…Given a set of modeling inputs, the modeling outputs are determined, namely

, and

at every location in the arterial network, from which centerline blood flow velocity,

, artery diameter waveforms,

, and wall shear stress waveforms,

=500 time steps per cardiac cycle, with

.…”

Section: Methodsmentioning

confidence: 99%

) to a prescribed target values

.…”

Section: Methodsmentioning

confidence: 99%

where

denotes the gestational age,

and

are the fractional increases in diameter (

) and length (

) from the nongravid vasculature (i.e., at

) and the gravid time point of interest,

, and

are remodeling parameters, and

is the value of the expression in the square brackets at

= 1. We let

=2.2 and

=1.7 and let

= −0.85.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A mathematical model of vascular and hemodynamics changes in early and late forms of preeclampsia

Sedaghati

Gleason

2023

Physiological Reports

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“…Where μ is the apparent lymph viscosity. This framework is explained in details in our previous study 4 .…”

Section: Methodsmentioning

confidence: 99%

A 1D Model Characterizing the Role of Spatiotemporal Contraction Distributions on Lymph Transport

Sedaghati

Dixon

Gleason

2022

Preprint

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Background: Lymphedema is a condition in which the two primary functions of the lymphatic system, immunity and lymph transport, are compromised. Computational models of lymphatic function to characterize lymph transport have proved useful in quantifying changes in lymph transport in health and disease; however, much is unknown regarding the regulation of contractions throughout a lymphatic network. The purpose of this paper is to study the role of pacemaking cells and contractile wave propagation on lymph transport using a 1-D mathematical model. Method: A 1D fluid-solid modeling framework with constitutive relationships were employed to characterize the interaction between the contracting vessel wall and the lymph flow during contractions. The time-space distribution of contraction waves along the length of a three-lymphangion chain, was determined by prescribing the location of pacemaking cells and parameters that govern the contractile wave propagation, with the total contractile response at each location determined as the summation of the local electrical signals. Results: Spatiotemporal changes in radius and lymphangion ejection fraction from our illustrative simulations mimic well values reported in isolated lymphatics from the wild-type (WT) and Smmhc-CreERT2;Cx45fx/fx knock-out (KO) reported in the literature. The flow rate is 5.43 and 2.45 μL⁄hr in the WT and the KO (average) models, respectively. The average and the peak WSS in the WT model are 0.08 and 4 dyn⁄(cm^2 ) and -0.03 and 0.87 dyn⁄(cm^2 ) in the KO (average) models, respectively. Conclusions: The factors that govern the timing of lymphatic contractions remain largely unknown; but these factors likely play a central role in health and disease. This modeling framework captures well lymphatic contractile wave propagations and how it relates to lymph transport and may motivate novel assays and experimental endpoints to evaluate subtle changes in lymphatic pumping function in the development and progression of lymphedema.

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A 1D model characterizing the role of spatiotemporal contraction distributions on lymph transport

Sedaghati,

Dixon,

Gleason

2023

Sci Rep

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Lymphedema is a condition in which lymph transport is compromised. The factors that govern the timing of lymphatic contractions are largely unknown; however, these factors likely play a central role in lymphatic health. Computational models have proven useful in quantifying changes in lymph transport; nevertheless, there is still much unknown regarding the regulation of contractions. The purpose of this paper is to utilize computational modeling to examine the role of pacemaking activity in lymph transport. A 1D fluid–solid modeling framework was utilized to describe the interaction between the contracting vessel and the lymph flow. The distribution of contractions along a three-lymphangion chain in time and space was determined by specifying the pacemaking sites and parameters obtained from experimentation. The model effectively replicates the contractility patterns in experiments. Quantitatively, the flow rates were measured at 5.44 and 2.29 $${\upmu L}/\mathrm{h}$$ μ L / h , and the EF values were 78% and less than 33% in the WT and KO models, respectively, which are consistent with the literature. Applying pacemaking parameters in this modeling framework effectively captures lymphatic contractile wave propagations and their relation to lymph transport. It can serve as a motivation for conducting novel studies to evaluate lymphatic pumping function during the development of lymphedema.

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

Cited by 5 publications

References 140 publications

A mathematical model of vascular and hemodynamics changes in early and late forms of preeclampsia

A mathematical model of vascular and hemodynamics changes in early and late forms of preeclampsia

A 1D Model Characterizing the Role of Spatiotemporal Contraction Distributions on Lymph Transport

A 1D model characterizing the role of spatiotemporal contraction distributions on lymph transport

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