Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Focused fluid transfer through the mantle above subduction zones

Volcanic arcs above subduction zones are enriched in volatiles and fluid-mobile elements with respect to mid-oceanic ridge basalts. There is general consensus that this particular subduction zone signature is generated by fluid-induced extraction of these elements from subducted oceanic crust and its sedimentary cover. However, how these fluids are transferred through the mantle wedge to the locus of partial melting and what modification the fluids will experience is unresolved. Here we investigate the interaction of slab fluids with the mantle wedge through a series of high-pressure experiments. We explore two end-member processes of focused and porous reactive flow of hydrous slab melts through the mantle. Transfer by porous flow leads to the formation of hydrous minerals that sequester fluid-mobile elements and residual fluids characterized by trace element patterns inconsistent with typical arc lavas. In contrast, no hydrous minerals are formed in the reaction zone of experiments mimicking focused flow, and the typical trace element signature acquired during fluid extraction from the slab is preserved, indicating that this is an efficient process for element transfer through the mantle wedge.

THE RELATIONSHIP BETWEEN THE RHEOENCEPHALOGRAM AND CEREBRAL BLOOD FLOW

The rheoencephalogram (REG) is the change in the electrical impedance of the head that occurs with each heart beat. Without knowledge of the relationship between cerebral blood flow (Q) and the REG, the utility of the REG in the study of the cerebral vasculature is greatly limited. The hypothesis is that the relationship between the REG and Q when venous outflow is nonpulsatile is^ (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)^ where K is a proportionality constant and Q is the mean Q.^ Pulsatile CBF was measured in the goat via a chronically implanted electromagnetic flowmeter. Electrodes were implanted in the ipsilateral cerebral hemisphere, and the REG was measured with a two electrode impedance plethysmograph. Measurements were made with the animal's head elevated so that venous flow pulsations were not transmitted from the heart to the cerebral veins. Measurements were made under conditions of varied cerebrovascular resistance induced by altering blood CO(,2) levels and under conditions of high and low cerebrospinal fluid pressures. There was a high correlation (r = .922-.983) between the REG calculated from the hypothesized relationship and the measured REG under all conditions.^ Other investigators have proposed that the REG results from linear changes in blood resistivity proportional to blood velocity. There was little to no correlation between the measured REG and the flow velocity ( r = .022-.306). A linear combination of the flow velocity and the hypothesized relationship between the REG and Q did not predict the measured REG significantly better than the hypothesized relationship alone in 37 out of 50 experiments.^ Jacquy proposed an index (F) of cerebral blood flow calculated from amplitudes and latencies of the REG. The F index was highly correlated (r = .929) with measured cerebral blood flow under control and hypercapnic conditions, but was not as highly correlated under conditions of hypocapnia (r = .723) and arterial hypotension (r = .681).^ The results demonstrate that the REG is not determined by mean cerebral blood flow, but by the pulsatile flow only. Thus, the utility of the REG in the determination of mean cerebral blood flow is limited. ^

Pore fluid pressure at DSDP Leg 84 Holes

Evidence of considerable overpressuring of pore fluids in the sediment drilled during Leg 84 was obtained from direct measurement of pressure by two methods. The first involved measurement of back pressure when the annulus of the drill hole became constricted with unremoved drill cuttings or constriction was caused by plastic inflow of the drill hole walls. The second involved measurement of pressure ahead of the bit in conjunction with in situ water samples and heat flow. All measurements indicated abnormally high pore pressure even in slope deposits of the Middle America Trench off Guatemala.

Heat flow measurements on METEOR cruise M86/5

Mud volcanoes (MV) are sources of mass and energy, transported from deeper levels of the sediment pile to the surface. Together with fluid and gas, thermal energy is emitted through these structures. Therefore heat flow determination is a sensible tool to detect and quantify the amount of convective flow. In the Gulf of Cadiz several mud volcanoes can be found along major tectonic lines (SWIM faults). We employ geothermal measurements to observe the activity of mud volcanoes and possible leakage at the faults apart from pronounced structures.

Carbonate cements and fluid circulation of ODP Leg 116 samples

The carbonate cements found in Sites 717-719 of ODP Leg 116 correspond to the precipitation of inorganic calcite due to circulation of hot fluid associated with intraplate deformation in the central Indian Ocean. A first burst of hydrothermal activity may have occurred 7.5-9 Ma and a second burst less than 0.5 Ma. These fluids were probably derived from the basaltic basement and the immediately overlying sediments.

(Table 1) Characteristics of South Pole personnel according to forced expiratory flow (FEF25-75) response to altitude

The impact of acute altitude exposure on pulmonary function is variable. A large inter-individual variability in the changes in forced expiratory flows (FEFs) is reported with acute exposure to altitude, which is suggested to represent an interaction between several factors influencing bronchial tone such as changes in gas density, catecholamine stimulation, and mild interstitial edema. This study examined the association between FEF variability, acute mountain sickness (AMS) and various blood markers affecting bronchial tone (endothelin-1, vascular endothelial growth factor (VEGF), catecholamines, angiotensin II) in 102 individuals rapidly transported to the South Pole (2835 m). The mean FEF between 25 and 75% (FEF25-75) and blood markers were recorded at sea level and after the second night at altitude. AMS was assessed using Lake Louise questionnaires. FEF25-75 increased by an average of 12% with changes ranging from -26 to +59% from sea level to altitude. On the second day, AMS incidence was 36% and was higher in individuals with increases in FEF25-75 (41 vs. 22%, P = 0.05). Ascent to altitude induced an increase in endothelin-1 levels, with greater levels observed in individuals with decreased FEF25-75. Epinephrine levels increased with ascent to altitude and the response was six times larger in individuals with decreased FEF25-75. Greater levels of endothelin-1 in individuals with decreased FEF25-75 suggest a response consistent with pulmonary hypertension and/or mild interstitial edema, while epinephrine may be upregulated in these individuals to clear lung fluid through stimulation of beta2-adrenergic receptors.

Reduced order models for industrial thermo-fluid problems

A new method is presented to generate reduced order models (ROMs) in Fluid Dynamics problems of industrial interest. The method is based on the expansion of the flow variables in a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The method includes various ingredients that are new in this field. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. The resulting ROM is both computationally efficient(reconstructed flow fields require, in cases that do not present shock waves, less than 1 % of the time needed to compute a full CFD solution) and flexible(the projection window can avoid regions of large localized CFD errors).Also, for problems related with aerodynamics, POD modes are obtained from a set of snapshots calculated by a CFD method based on the compressible Navier Stokes equations and a turbulence model (which further more includes some unphysical stabilizing terms that are included for purely numerical reasons), but projection onto the POD manifold is made using the inviscid Euler equations, which makes the method independent of the CFD scheme. In addition, shock waves are treated specifically in the POD description, to avoid the need of using a too large number of snapshots. Various definitions of the residual are also discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors. The method is checked and discussed on several test problems that describe (i) heat transfer in the recirculation region downstream of a backwards facing step, (ii) the flow past a two-dimensional airfoil in both the subsonic and transonic regimes, and (iii) the flow past a three-dimensional horizontal tail plane. The method is both efficient and numerically robust in the sense that the computational effort is quite small compared to CFD and results are both reasonably accurate and largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications. Resumen Se presenta un nuevo método para generar modelos de orden reducido (ROMs) aplicado a problemas fluidodinámicos de interés industrial. El nuevo método se basa en la expansión de las variables fluidas en una base POD, calculada a partir de un cierto número de snapshots, los cuales se han obtenido gracias a simulaciones numéricas (CFD). A continuación, las amplitudes de los modos POD se calculan minimizando un residual global adecuadamente definido que combina las ecuaciones y las condiciones de contorno. El método incluye varios ingredientes que son nuevos en este campo de estudio. El residual puede calcularse utilizando únicamente un número limitado de puntos del campo fluido. Estos puntos puede encontrarse dispersos a lo largo del dominio computacional completo o sobre una ventana de proyección. El modelo ROM obtenido es tanto computacionalmente eficiente (en aquellos casos que no presentan ondas de choque reconstruir los campos fluidos requiere menos del 1% del tiempo necesario para calcular una solución CFD) como flexible (la ventana de proyección puede escogerse de forma que evite contener regiones con errores en la solución CFD localizados y grandes). Además, en problemas aerodinámicos, los modos POD se obtienen de un conjunto de snapshots calculados utilizando un código CFD basado en la versión compresible de las ecuaciones de Navier Stokes y un modelo de turbulencia (el cual puede incluir algunos términos estabilizadores sin sentido físico que se añaden por razones puramente numéricas), aunque la proyección en la variedad POD se hace utilizando las ecuaciones de Euler, lo que hace al método independiente del esquema utilizado en el código CFD. Además, las ondas de choque se tratan específicamente en la descripción POD para evitar la necesidad de utilizar un número demasiado grande de snapshots. Varias definiciones del residual se discuten, así como el número y distribución de los snapshots,el número de modos retenidos y el efecto de los errores debidos al CFD. El método se comprueba y discute para varios problemas de evaluación que describen (i) la transferencia de calor en la región de recirculación aguas abajo de un escalón, (ii) el flujo alrededor de un perfil bidimensional en regímenes subsónico y transónico y (iii) el flujo alrededor de un estabilizador horizontal tridimensional. El método es tanto eficiente como numéricamente robusto en el sentido de que el esfuerzo computacional es muy pequeño comparado con el requerido por el CFD y los resultados son razonablemente precisos y muy insensibles a la definición del residual, los errores debidos al CFD y al método CFD en sí mismo, el cual puede contener términos estabilizadores artificiales. Por lo tanto, el método puede utilizarse en aplicaciones prácticas de ingeniería.