In this paper we present a survey of various algorithms for computing matrix geometric means and derive new second-order optimization algorithms to compute the Karcher mean. These new algorithms are constructed using the standard definition of the Riemannian Hessian. The survey includes the ALM list of desired properties for a geometric mean, the analytical expression for the mean of two matrices, algorithms based on the centroid computation in Euclidean (flat) space, and Riemannian optimization techniques to compute the Karcher mean (preceded by a short introduction into differential geometry). A change of metric is considered in the optimization techniques to reduce the complexity of the structures used in these algorithms. Numerical experiments are presented to compare the existing and the newly developed algorithms. We conclude that currently first-order algorithms are best suited for this optimization problem as the size and/or number of the matrices increase. Copyright © 2012, Kent State University.

http://sma.epfl.ch/~anchpcommon/publications/pd_matrix_geometric_mean.pdf

A survey and comparison of contemporary algorithms for computing the matrix geometric mean

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2015.0641

Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

Background: Minimally invasive and alternative strategies for implantation have been anecdotally reported for contemporary continuous-flow left ventricular assist device (CF-LVAD) placement
 Methods: We reviewed our experience at a single center with alternative strategies for implantation of the HeartMate II and HeartWare CF-LVADs, in patients with advanced heart failure (HF) This featured article focuses on the associated surgical techniques and patient management pitfalls
 Results: For appropriately selected cases, our group believes that these alternative strategies allow for the development of novel and less traumatic surgical approaches for CF-LVAD implantation With reproducible outcomes, these approaches also promise the possibility of increasing the number of high-risk surgical patients who could benefit from CF-LVAD therapies
 Conclusions: This work has detailed a variety of less invasive alternative strategies for implantation of long-term LVADs These newer approaches have the potential for significant advancements in the field of cardiothoracic surgery Large-scale collaborative studies will be needed to clarify the potential advantages and disadvantages of these novel techniques on patient outcomes

/pdf/minimally-invasive-and-alternative-approaches-for-long-term-4nknuuaqhx.pdf

Minimally invasive and alternative approaches for long-term LVAD placement: the Vanderbilt strategy

Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics

Summary

Left ventricular assist devices (LVADs) are mechanical supports used in case of heart failure. Little is known as the height of the anastomosis in aorta might influence the hemodynamic. The aim of the study was to evaluate the fluid dynamic behavior due to the outflow graft placement of a continuous flow LVAD in ascending aorta and to identify the insertion site with the best hemodynamic profile.



Computational fluid dynamic studies were carried out to analyze 4 different anastomosis locations in a patient-specific aorta 3D model coupled with a lumped parameters model: 1 cm (case 1), 2 cm (case 2), 3 cm (case 3) and 4 cm (case 4) above the ST junction.



In cases 1 and 2, epiaortic vessels presented a steady flow, while in cases 3 and 4 the flow was whirling. Moreover, maximum velocity occurred before: brachiocephalic trunk (case 1), brachiocephalic and left carotid arteries (case 2), left carotid and left subclavian artery (case 3) and left subclavian vessel and upper wall of aortic arch (case 4). Maximum time averaged wall shear stress (TAWSS) was located in: the ascending aorta (cases 1 and 2), the inferior curvature of the arch (case 3); at the origin of epiaortic vessels (case 4). Furthermore, a flow recirculation (cases 1 and 2), a blood stagnation and chaotic flow (cases 3 and 4) occurred above the aortic valve.



The results suggested that the placement of the outflow graft at 2 cm above the ST junction gave the most favorable hemodynamic profile. Copyright © 2015 John Wiley & Sons, Ltd.

A computational fluid dynamics comparison between different outflow graft anastomosis locations of Left Ventricular Assist Device (LVAD) in a patient‐specific aortic model

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

BACKGROUND High levels of arterial oxygen pressures (PaO2) have been associated with increased mortality in extracorporeal cardiopulmonary resuscitation (ECPR), but there is limited information regarding possible mechanisms linking hyperoxia and death in this setting, notably with respect to its hemodynamic consequences. We aimed therefore at evaluating a possible association between PaO2, circulatory failure and death during ECPR. METHODS We retrospectively analyzed 44 consecutive cardiac arrest (CA) patients treated with ECPR to determine the association between the mean PaO2 over the first 24 h, arterial blood pressure, vasopressor and intravenous fluid therapies, mortality, and cause of deaths. RESULTS Eleven patients (25%) survived to hospital discharge. The main causes of death were refractory circulatory shock (46%) and neurological damage (24%). Compared to survivors, non survivors had significantly higher mean 24 h PaO2 (306 ± 121 mmHg vs 164 ± 53 mmHg, p < 0.001), lower mean blood pressure and higher requirements in vasopressors and fluids, but displayed similar pulse pressure during the first 24 h (an index of native cardiac recovery). The mean 24 h PaO2 was significantly and positively correlated with the severity of hypotension and the intensity of vasoactive therapies. Patients dying from circulatory failure died after a median of 17 h, compared to a median of 58 h for patients dying from a neurological cause. Patients dying from neurological cause had better preserved blood pressure and lower vasopressor requirements. CONCLUSION In conclusion, hyperoxia is associated with increased mortality during ECPR, possibly by promoting circulatory collapse or delayed neurological damage.

/pdf/hyperoxia-during-extracorporeal-cardiopulmonary-1ztc7n5ngu.pdf

Hyperoxia during extracorporeal cardiopulmonary resuscitation for refractory cardiac arrest is associated with severe circulatory failure and increased mortality.

Infection with the novel severe acute respiratory coronavirus-2 (SARS-CoV2) results in COVID-19, a disease primarily affecting the respiratory system to provoke a spectrum of clinical manifestations, the most severe being acute respiratory distress syndrome (ARDS). A significant proportion of COVID-19 patients also develop various cardiac complications, among which dysfunction of the right ventricle (RV) appears particularly common, especially in severe forms of the disease, and which is associated with a dismal prognosis. Echocardiographic studies indeed reveal right ventricular dysfunction in up to 40% of patients, a proportion even greater when the RV is explored with strain imaging echocardiography. The pathophysiological mechanisms of RV dysfunction in COVID-19 include processes increasing the pulmonary vascular hydraulic load and others reducing RV contractility, which precipitate the acute uncoupling of the RV with the pulmonary circulation. Understanding these mechanisms provides the fundamental basis for the adequate therapeutic management of RV dysfunction, which incorporates protective mechanical ventilation, the prevention and treatment of pulmonary vasoconstriction and thrombotic complications, as well as the appropriate management of RV preload and contractility. This comprehensive review provides a detailed update of the evidence of RV dysfunction in COVID-19, its pathophysiological mechanisms, and its therapy.

https://www.mdpi.com/2077-0383/10/12/2535/pdf

The Right Ventricle in COVID-19

Arterial tree hemodynamics can be simulated by means of several models of different level of complexity, depending on the outputs of interest and the desired degree of accuracy. In this work, several numerical comparisons of geometrical multiscale models are presented with the aim of evaluating the benefits of such complex dimensionally-heterogeneous models compared to other simplified simulations. More precisely, we present flow rate and pressure wave form comparisons between three-dimensional patient-specific geometries implicitly coupled with one-dimensional arterial tree networks and (i) a full one-dimensional arterial tree model and (ii) stand-alone three-dimensional fluid–structure interaction models with boundary data taken from precomputed full one-dimensional network simulations. On a slightly different context, we also focus on the set up and calibration of cardiovascular simulations. In particular, we perform sensitivity analyses of the main quantities of interest (flow rate, pressure, and solid wall displacement) with respect to the parameters accounting for the elastic and viscoelastic responses of the tissues surrounding the external wall of the arteries. Finally, we also compare the results of geometrical multiscale models in which the boundary solid rings of the three-dimensional geometries are fixed, with respect to those where the boundary interfaces are scaled to enforce the continuity of the vessels size with the surrounding one-dimensional arteries.

/pdf/numerical-comparison-and-calibration-of-geometrical-4eofg5o2tr.pdf

Numerical Comparison and Calibration of Geometrical Multiscale Models for the Simulation of Arterial Flows

Mechanical circulatory support,in particular ventricular assist devices(VAD),has been recently proposed as an alternative to transplantation in the treatment of terminal heart failure in the context of the lack of donors and raising number of patients on the waiting list. Although these systems have proved their efficiency through a rigorous patient selection, the complication rate remains high and experience shows that many of them are related to haemodynamic modifications due to VAD implantation. Furthermore, VAD themselves have been widely studied, while the flow near the anastomosis VAD-aorta is still not well-known, although many complications arise at this site. We present here the mathematical settings and some preliminary results of a numerical model of the anastomosis between the outflow cannula of left ventricular assist devices (LVAD) and the aorta.

Jean Bonnemain

Papers

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

Hyperoxia during extracorporeal cardiopulmonary resuscitation for refractory cardiac arrest is associated with severe circulatory failure and increased mortality.

The Right Ventricle in COVID-19

Numerical Comparison and Calibration of Geometrical Multiscale Models for the Simulation of Arterial Flows

Connecting Ventricular Assist Devices to the Aorta: a Numerical Model