Estimation of aortic stiffness by finger photoplethysmography using enhanced pulse wave analysis and machine learning.

Introduction: Aortic stiffness plays a critical role in the evolution of cardiovascular diseases, but the assessment requires specialized equipment. Photoplethysmography (PPG) and single-lead electrocardiogram (ECG) are readily available in healthcare and wearable devices. We studied whether a brief PPG registration, alone or in combination with single-lead ECG, could be used to reliably estimate aortic stiffness. Methods: A proof-of-concept study with simultaneous high-resolution index finger recordings of infrared PPG, single-lead ECG, and finger blood pressure (Finapres) was performed in 33 participants [median age 44 (range 21-66) years, 19 men] and repeated within 2 weeks. Carotid-femoral pulse wave velocity (cfPWV; two-site tonometry with SphygmoCor) was used as a reference. A brachial single-cuff oscillometric device assessed aortic pulse wave velocity (aoPWV; Arteriograph) for further comparisons. We extracted 136 established PPG waveform features and engineered 13 new with improved coupling to the finger blood pressure curve. Height-normalized pulse arrival time (NPAT) was derived using ECG. Machine learning methods were used to develop prediction models. Results: The best PPG-based models predicted cfPWV and aoPWV well (root-mean-square errors of 0.70 and 0.52 m/s, respectively), with minor improvements by adding NPAT. Repeatability and agreement were on par with the reference equipment. A new PPG feature, an amplitude ratio from the early phase of the waveform, was most important in modelling, showing strong correlations with cfPWV and aoPWV (r = -0.81 and -0.75, respectively, both P < 0.001). Conclusion: Using new features and machine learning methods, a brief finger PPG registration can estimate aortic stiffness without requiring additional information on age, anthropometry, or blood pressure. Repeatability and agreement were comparable to those obtained using non-invasive reference equipment. Provided further validation, this readily available simple method could improve cardiovascular risk evaluation, treatment, and prognosis.

Computational cardiac physiology for new modelers: Origins, foundations, and future.

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Computational Analysis of Flow Structures in Turbulent Ventricular Blood Flow Associated With Mitral Valve Intervention.

Cardiac disease and clinical intervention may both lead to an increased risk for thrombosis events due to a modified blood flow in the heart, and thereby a change in the mechanical stimuli of blood cells passing through the chambers of the heart. Specifically, the degree of platelet activation is influenced by the level and type of mechanical stresses in the blood flow. In this article we analyze the blood flow in the left ventricle of the heart through a computational model constructed from patient-specific data. The blood flow in the ventricle is modelled by the Navier-Stokes equations, and the flow through the mitral valve by a parameterized model which represents the projected opening of the valve. A finite element method is used to solve the equations, from which a simulation of the velocity and pressure of the blood flow is constructed. The intraventricular blood flow is complex, in particular in diastole when the inflow jet from the atrium breaks down into turbulent flow on a range of scales. A triple decomposition of the velocity gradient tensor is then used to distinguish between rigid body rotational flow, irrotational straining flow, and shear flow. The triple decomposition enables the separation of three fundamentally different flow structures, that each generates a distinct type of mechanical stimulus on the blood cells in the flow. We compare the results in a simulation where a mitral valve clip intervention is modelled, which leads to a significant modification of the intraventricular flow. Further, we perform a sensitivity study of the results with respect to the positioning of the clip. It was found that the shear in the simulation cases treated with clips increased more compared to the untreated case than the rotation and strain did. A decrease in valve opening area of 64% in one of the cases led to a 90% increase in rotation and strain, but a 150% increase in shear. The computational analysis opens up for improvements in models of shear-induced platelet activation, by offering an algorithm to distinguish shear from other modalities in intraventricular blood flow.

High shear stress amplitude in combination with prolonged stimulus duration determine induction of osteoclast formation by hematopoietic progenitor cells.

To date, it is unclear how fluid dynamics stimulate mechanosensory cells to induce an osteoprotective or osteodestructive response. We investigated how murine hematopoietic progenitor cells respond to 2 minutes of dynamic fluid flow stimulation with a precisely controlled sequence of fluid shear stresses. The response was quantified by measuring extracellular adenosine triphosphate (ATP), immunocytochemistry of Piezo1, and sarcoplasmic/endoplasmic Ca2+ reticulum ATPase 2 (SERCA2), and by the ability of soluble factors produced by mechanically stimulated cells to modulate osteoclast differentiation. We rejected our initial hypothesis that peak wall shear stress rate determines the response of hematopoietic progenitor cells to dynamic fluid shear stress, as it had only a minor correlation with the abovementioned parameters. Low stimulus amplitudes corresponded to activation of Piezo1, SERCA2, low concentrations of extracellular ATP, and inhibition of osteoclastogenesis and resorption area, while high amplitudes generally corresponded to osteodestructive responses. At a given amplitude (3 Pa) and waveform (square), the duration of individual stimuli (duty cycle) showed a strong correlation with the release of ATP and osteoclast number and resorption area. Collectively, our data suggest that hematopoietic progenitor cells respond in a viscoelastic manner to loading, since a combination of high shear stress amplitude and prolonged duty cycle is needed to trigger an osteodestructive response. PLAIN LANGUAGE SUMMARY: In case of painful joints or missing teeth, the current intervention is to replace them with an implant to keep a high-quality lifestyle. When exercising or chewing, the cells in the bone around the implant experience mechanical loading. This loading generally supports bone formation to strengthen the bone and prevent breaking, but can also stimulate bone loss when the mechanical loading becomes too high around orthopedic and dental implants. We still do not fully understand how cells in the bone can distinguish between mechanical loading that strengthens or weakens the bone. We cultured cells derived from the bone marrow in the laboratory to test whether the bone loss response depends on (i) how fast a mechanical load is applied (rate), (ii) how intense the mechanical load is (amplitude), or (iii) how long each individual loading stimulus is applied (duration). We mimicked mechanical loading as it occurs in the body, by applying very precisely controlled flow of fluid over the cells. We found that a mechanosensitive receptor Piezo1 was activated by a low amplitude stimulus, which usually strengthens the bone. The potential inhibitor of Piezo1, namely SERCA2, was only activated by a low amplitude stimulus. This happened regardless of the rate of application. At a constant high amplitude, a longer duration of the stimulus enhanced the bone-weakening response. Based on these results we deduce that a high loading amplitude tends to be bone weakening, and the longer this high amplitude persists, the worse it is for the bone.

A partition of unity approach to fluid mechanics and fluid-structure interaction.

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.

Portable simulation framework for diffusion MRI.

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite element discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite element discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite element software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds.

The Bloch-Torrey partial differential equation can be used to describe the evolution of the transverse magnetization of the imaged sample under the influence of diffusion-encoding magnetic field gradients inside the MRI scanner. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The variable thickness of the three-dimensional domains is included in the weak formulation established on the manifolds. We conducted a numerical study of the proposed approach by simulating the diffusion MRI signals from the extracellular space (a thin layer medium) and from neurons (a thin tube medium), comparing the results with the reference signals obtained using a standard three-dimensional finite element discretization. We show good agreements between the simulated signals using our proposed method and the reference signals for a wide range of diffusion MRI parameters. The approximation becomes better as the diffusion time increases. The method helps to significantly reduce the required simulation time, computational memory, and difficulties associated with mesh generation, thus opening the possibilities to simulating complicated structures at low cost for a better understanding of diffusion MRI in the brain.

3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE FEM Model.

Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.

Patient-Specific Left Ventricular Flow Simulations From Transthoracic Echocardiography: Robustness Evaluation and Validation Against Ultrasound Doppler and Magnetic Resonance Imaging.

The combination of medical imaging with computational fluid dynamics (CFD) has enabled the study of 3-D blood flow on a patient-specific level. However, with models based on gated high-resolution data, the study of transient flows, and any model implementation into routine cardiac care, is challenging. This paper presents a novel pathway for patient-specific CFD modelling of the left ventricle (LV), using 4-D transthoracic echocardiography (TTE) as input modality. To evaluate the clinical usability, two sub-studies were performed. First, a robustness evaluation was performed, where repeated models with alternating input variables were generated for six subjects and changes in simulated output quantified. Second, a validation study was carried out, where the pathway accuracy was evaluated against pulsed-wave Doppler (100 subjects), and 2-D through-plane phase-contrast magnetic resonance imaging measurements over seven intraventricular planes (6 subjects). The robustness evaluation indicated a model deviation of <12%, with highest regional and temporal deviations at apical segments and at peak systole, respectively. The validation study showed an error of <11% (velocities <10 cm/s) for all subjects, with no significant regional or temporal differences observed. With the patient-specific pathway shown to provide robust output with high accuracy, and with the pathway dependent only on 4-D TTE, the method has a high potential to be used within future clinical studies on 3-D intraventricular flow patterns. To this, future model developments in the form of e.g., anatomically accurate LV valves may further enhance the clinical value of the simulations.

Adaptive unified continuum FEM modeling of a 3D FSI benchmark problem.

In this paper, we address a 3D fluid-structure interaction benchmark problem that represents important characteristics of biomedical modeling. We present a goal-oriented adaptive finite element methodology for incompressible fluid-structure interaction based on a streamline diffusion-type stabilization of the balance equations for mass and momentum for the entire continuum in the domain, which is implemented in the Unicorn/FEniCS software framework. A phase marker function and its corresponding transport equation are introduced to select the constitutive law, where the mesh tracks the discontinuous fluid-structure interface. This results in a unified simulation method for fluids and structures. We present detailed results for the benchmark problem compared with experiments, together with a mesh convergence study.