3D single vessel fractional moving blood volume (3D-svFMBV): fully automated tissue perfusion estimation using ultrasound

Power Doppler ultrasound (PD-US) is the ideal modality to assess tissue perfusion as it is cheap, patient-friendly and does not require ionizing radiation. However, meaningful inter-patient comparison only occurs if differences in tissue-attenuation are corrected for. This can be done by standardizing the PD-US signal to a blood vessel assumed to have 100% vascularity. The original method to do this is called fractional moving blood volume (FMBV). We describe a novel, fully-automated method combining image processing, numerical modelling, and deep learning to estimate three-dimensional single vessel fractional moving blood volume (3D-svFMBV). We map the PD signals to a characteristic intensity profile within a single large vessel to define the standardization value at the high shear vessel margins. This removes the need for mathematical correction for background signal which can introduce error. The 3D-svFMBV was first tested on synthetic images generated using the characteristics of uterine artery and physiological ultrasound noise levels, demonstrating prediction of standardization value close to the theoretical ideal. Clinical utility was explored using 143 first-trimester placental ultrasound volumes. More biologically plausible perfusion estimates were obtained, showing improved prediction of pre-eclampsia compared with those generated with the semi-automated original 3D-FMBV technique. The proposed 3D-svFMBV method overcomes the limitations of the original technique to provide accurate and robust placental perfusion estimation. This not only has the potential to provide an early pregnancy screening tool but may also be used to assess perfusion of different organs and tumors

In silico modeling of oxygen-enhanced MRI of specific ventilation.

Specific ventilation imaging (SVI) proposes that using oxygen-enhanced 1H MRI to capture signal change as subjects alternatively breathe room air and 100% O2 provides an estimate of specific ventilation distribution in the lung. How well this technique measures SV and the effect of currently adopted approaches of the technique on resulting SV measurement is open for further exploration. We investigated (1) How well does imaging a single sagittal lung slice represent whole lung SV? (2) What is the influence of pulmonary venous blood on the measured MRI signal and resultant SVI measure? and (3) How does inclusion of misaligned images affect SVI measurement? In this study, we utilized two patient-based in silico models of ventilation, perfusion, and gas exchange to address these questions for normal healthy lungs. Simulation results from the two healthy young subjects show that imaging a single slice is generally representative of whole lung SV distribution, with a calculated SV gradient within 90% of that calculated for whole lung distributions. Contribution of O2 from the venous circulation results in overestimation of SV at a regional level where major pulmonary veins cross the imaging plane, resulting in a 10% increase in SV gradient for the imaging slice. A worst-case scenario simulation of image misalignment increased the SV gradient by 11.4% for the imaged slice

A review of feto-placental vasculature flow modelling

The placenta provides the vital nutrients and removal of waste products required for fetal growth and development. Understanding and quantifying the differences in structure and function between a normally functioning placenta compared to an abnormal placenta is vital to provide insights into the aetiology and treatment options for fetal growth restriction and other placental disorders. Computational modelling of blood flow in the placenta allows a new understanding of the placental circulation to be obtained. This structured review discusses multiple recent methods for placental vascular model development including analysis of the appearance of the placental vasculature and how placental haemodynamics may be simulated at multiple length scales

Proceedings of the 13th Engineering Mathematics and Applications Conference

EMAC2017 was the 13th biennial Engineering Mathematics and Applications Conference, and took place at University of Auckland, New Zealand from 29th November to 1st December 2017. EMAC is held under the auspices of the Engineering Mathematics Group which is a special interest group of the Australian and New Zealand Industrial and Applied Mathematics division of the Australian Mathematics Society. All of the articles included in the EMAC 2017 Proceedings have been peer reviewed by at least two referees and revised (when required) to satisfy the referees comments

Computational models of the pulmonary circulation: Insights and the move towards clinically directed studies

Biophysically-based computational models provide a tool for integrating and explaining experimental data, observations, and hypotheses. Computational models of the pulmonary circulation have evolved from minimal and efficient constructs that have been used to study individual mechanisms that contribute to lung perfusion, to sophisticated multi-scale and -physics structure-based models that predict integrated structure-function relationships within a heterogeneous organ. This review considers the utility of computational models in providing new insights into the function of the pulmonary circulation, and their application in clinically motivated studies. We review mathematical and computational models of the pulmonary circulation based on their application; we begin with models that seek to answer questions in basic science and physiology and progress to models that aim to have clinical application. In looking forward, we discuss the relative merits and clinical relevance of computational models: what important features are still lacking; and how these models may ultimately be applied to further increasing our understanding of the mechanisms occurring in disease of the pulmonary circulation

Pregnancy-specific uterine vascular reactivity: a data-driven computational model of shear-dependent, myogenic, and mechanical radial artery features.

`The entire maternal circulation adapts to pregnancy, and this adaption is particularly extensive in the uterine circulation where the major vessels double in size to facilitate an approximately 15-fold increase in blood supply to this organ over the course of pregnancy. Several factors may play a role in both the remodeling and biomechanical function of the uterine vasculature including the paracrine microenvironment, passive properties of the vessel wall, and active components of vascular function (incorporating the myogenic response and response to shear stress induced by intravascular blood flow). However, the interplay between these factors and how this plays out in an organ-specific manner to induce the extent of remodeling observed in the uterus is not well understood. Here we present an integrated assessment of the uterine radial arteries, likely rate limiters to the flow of oxygenated maternal blood to the placental surface, via computational modeling and pressure myography. We show that uterine radial arteries behave differently to other systemic vessels (higher compliance and shear-mediated constriction) and that their properties change with the adaptation to pregnancy (higher myogenic tone, higher compliance, and ability to tolerate higher flow rates before constricting). Together, this provides a useful tool to improve our understanding of the role of uterine vascular adaptation in normal and abnormal pregnancies and highlights the need for vascular bed-specific investigations of vascular function in health and disease. To our knowledge, this is the first data-driven computational model of autoregulation of uterine radial arteries, likely rate limiters of maternal blood flow to the placenta. The study demonstrates that uterine radial arteries behave differently from systemic vessels (higher compliance, shear-mediated constriction) and change in pregnancy (higher myogenic tone, higher compliance, tolerance of higher flow rates). This pregnancy-specific mathematical model of vascular reactivity allows interrogation of the functional significance of incomplete vascular adaption in pathology

Am J Physiol Heart Circ Physiol

`The entire maternal circulation adapts to pregnancy, and this adaption is particularly extensive in the uterine circulation where the major vessels double in size to facilitate an approximately 15-fold increase in blood supply to this organ over the course of pregnancy. Several factors may play a role in both the remodeling and biomechanical function of the uterine vasculature including the paracrine microenvironment, passive properties of the vessel wall, and active components of vascular function (incorporating the myogenic response and response to shear stress induced by intravascular blood flow). However, the interplay between these factors and how this plays out in an organ-specific manner to induce the extent of remodeling observed in the uterus is not well understood. Here we present an integrated assessment of the uterine radial arteries, likely rate limiters to the flow of oxygenated maternal blood to the placental surface, via computational modeling and pressure myography. We show that uterine radial arteries behave differently to other systemic vessels (higher compliance and shear-mediated constriction) and that their properties change with the adaptation to pregnancy (higher myogenic tone, higher compliance, and ability to tolerate higher flow rates before constricting). Together, this provides a useful tool to improve our understanding of the role of uterine vascular adaptation in normal and abnormal pregnancies and highlights the need for vascular bed-specific investigations of vascular function in health and disease. To our knowledge, this is the first data-driven computational model of autoregulation of uterine radial arteries, likely rate limiters of maternal blood flow to the placenta. The study demonstrates that uterine radial arteries behave differently from systemic vessels (higher compliance, shear-mediated constriction) and change in pregnancy (higher myogenic tone, higher compliance, tolerance of higher flow rates). This pregnancy-specific mathematical model of vascular reactivity allows interrogation of the functional significance of incomplete vascular adaption in pathology

Steady-state approximations for Hodgkin-Huxley cell models: Reduction of order for uterine smooth muscle cell model

Multi-scale mathematical bioelectrical models of organs such as the uterus, stomach or heart present challenges both for accuracy and computational tractability. These multi-scale models are typically founded on models of biological cells derived from the classic Hodkgin-Huxley (HH) formalism. Ion channel behaviour is tracked with dynamical variables representing activation or inactivation of currents that relax to steady-state dependencies on cellular membrane voltage. Timescales for relaxation may be orders of magnitude faster than companion ion channel variables or phenomena of physiological interest for the entire cell (such as bursting sequences of action potentials) or the entire organ (such as electromechanical coordination). Exploiting these time scales with steady-state approximations for relatively fast-acting systems is a well-known but often overlooked approach as evidenced by recent published models. We thus investigate feasibility of an extensive reduction of order for an HH-type cell model with steady-state approximations to the full dynamical activation and inactivation ion channel variables. Our effort utilises a published comprehensive uterine smooth muscle cell model that encompasses 19 ordinary differential equations and 105 formulations overall. The numerous ion channel submodels in the published model exhibit relaxation times ranging from order 10−1 to 105 milliseconds. Substitution of the faster dynamic variables with steady-state formulations demonstrates both an accurate reproduction of the full model and substantial improvements in time-to-solve, for test cases performed. Our demonstration here of an effective and relatively straightforward reduction method underlines the particular importance of considering time scales for model simplification before embarking on large-scale computations or parameter sweeps. As a preliminary complement to more intensive reduction of order methods such as parameter sensitivity and bifurcation analysis, this approach can rapidly and accurately improve computational tractability for challenging multi-scale organ modelling efforts. Author summary Mathematical modeling of physiological organ systems encompassing intracellular to organ-wide behaviour grapple with intrinsically multi-scaled systems in both space and time. Significant computational challenges arise with their numerical solution, often substantially constraining feasibility of in silico investigations. Naturally, streamlining and reducing the mathematical complexity of these models while maintaining accurate reproduction of experimental data is a persistent concern. We present a straightforward method for exploiting multiple time scales reducing the order of models by way of steady-state approximations at the cellular level. Applied to a uterine smooth muscle cell model, we obtain substantial improvements in time to solve by around a factor of two while accurately reproducing full model results. Our successful demonstration here highlights the importance and relative ease of the method—that is not altogether unknown but often overlooked—with potential application across a wide variety of multi-scale organ modeling efforts