Analytical modeling of the instantaneous maximal transvalvular pressure gradient in aortic stenosis

In presence of aortic stenosis, a jet is produced downstream of the aortic valve annulus during systole. The vena contracta corresponds to the location where the cross-sectional area of the flow jet is minimal. The maximal transvalvular pressure gradient (TPG_max) is the difference between the static pressure in the left ventricle and that in the vena contracta. TPG_max is highly time-dependent over systole and is known to depend upon the transvalvular flow rate, the effective orifice area (EOA) of the aortic valve and the cross-sectional area of the left ventricular outflow tract. However, it is still unclear how these parameters modify the TPG_max waveform. We thus derived an explicit analytical model to describe the instantaneous TPG_max across the aortic valve during systole. This theoretical model was validated with in vivo experiments obtained in 19 pigs with supravalvular aortic stenosis. Instantaneous TPG_max was measured by catheter and its waveform was compared with the one determined from the derived equation. Our results showed a very good concordance between the measured and predicted instantaneous TPG_max. Total relative error and mean absolute error were on average 9.4±4.9% and 2.1±1.1 mmHg, respectively. The analytical model proposed and validated in this study provides new insight into the behaviour of the TPG_max and thus of the aortic pressure at the level of vena contracta. Because the static pressure at the coronary inlet is similar to that at the vena contracta, the proposed equation will permit to further examine the impact of aortic stenosis on coronary blood flow.     

Comparison of stenosis models for usage in the estimation of pressure gradient across aortic coarctation

Non-invasive estimation of the pressure gradient in cardiovascular stenosis has much clinical importance in assisting the diagnosis and treatment of stenotic diseases. In this research, a systematic comparison is conducted to investigate the accuracy of a group of stenosis models against the MRI- and catheter-measured patient data under the aortic coarctation condition. Eight analytical stenosis models, including six from the literature and two proposed in this study, are investigated to examine their prediction accuracy against the clinical data. The two improved models proposed in this study consider comprehensively the Poiseuille loss, the Bernoulli loss in its exact form, and the entrance effect, of the blood flow. Comparison of the results shows that one of the proposed models demonstrates a cycle-averaged mean prediction error of −0.15 ± 3.03 mmHg, a peak-to-peak prediction error of −1.8 ± 6.89 mmHg, which is the best among the models studied.     

Subject-specific multiscale modeling of aortic valve biomechanics

A Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range (\(0.36-0.87\)) with a strong correlation with the organ length-scale radial strain (\(R^{2}= 0.95\)); conversely, circumferential cell strains spanned a very narrow range (\(0.75-0.88\)) showing no correlation with the circumferential strain at the organ level (\(R^{2}= 0.02\)). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.

     

Consistent trilayer biomechanical modeling of aortic valve leaflet tissue

Aortic valve tissue exhibits highly nonlinear, anisotropic, and heterogeneous material behavior due to its complex microstructure. A thorough understanding of these characteristics permits us to develop numerical models that can shed insight on the function of the aortic valve in health and disease. Herein, we take a closer look at consistently capturing the observed physical response of aortic valve tissue in a continuum mechanics framework. Such a treatment is the first step in developing comprehensive multiscale and multiphysics models.We highlight two important aspects of aortic valve tissue behavior: the role of the collagen fiber microstructure and the native prestressing. We propose a model that captures these two features as well as the heterogeneous layer-scale topology of the tissue. We find the model can reproduce the experimentally observed multiscale mechanical behavior in a manner that provides intuition on the underlying mechanics.     

Measurement of a gradient of oxygen partial pressure across the intact root

Summary Oxygen partial pressures in the vacuolar sap of root cells have been measured using oxygen sensitive polarographic microelectrodes. A significant gradient in oxygen partial pressure was observed across intact sunflower roots growing in air saturated culture solution. The relevance of this finding to the mechanism of salt transfer across the root and in particular to the Crafts-Broyer theory is discussed.     

Patient-specific modeling of biomechanical interaction in transcatheter aortic valve deployment

The objective of this study was to develop a patient-specific computational model to quantify the biomechanical interaction between the transcatheter aortic valve (TAV) stent and the stenotic aortic valve during TAV intervention. Finite element models of a patient-specific stenotic aortic valve were reconstructed from multi-slice computed tomography (MSCT) scans, and TAV stent deployment into the aortic root was simulated. Three initial aortic root geometries of this patient were analyzed: (a) aortic root geometry directly reconstructed from MSCT scans, (b) aortic root geometry at the rapid right ventricle pacing phase, and (c) aortic root geometry with surrounding myocardial tissue. The simulation results demonstrated that stress, strain, and contact forces of the aortic root model directly reconstructed from MSCT scans were significantly lower than those of the model at the rapid ventricular pacing phase. Moreover, the presence of surrounding myocardium slightly increased the mechanical responses. Peak stresses and strains were observed around the calcified regions in the leaflets, suggesting the calcified leaflets helped secure the stent in position. In addition, these elevated stresses induced during TAV stent deployment indicated a possibility of tissue tearing and breakdown of calcium deposits, which might lead to an increased risk of stroke. The potential of paravalvular leak and occlusion of coronary ostia can be evaluated from simulated post-deployment aortic root geometries. The developed computational models could be a valuable tool for pre-operative planning of TAV intervention and facilitate next generation TAV device design.     

Estimation of changes in instantaneous aortic blood flow by the analysis of arterial blood pressure

The purpose of this study was to introduce and validate a new algorithm to estimate instantaneous aortic blood flow (ABF) by mathematical analysis of arterial blood pressure (ABP) waveforms. The algorithm is based on an autoregressive with exogenous input (ARX) model. We applied this algorithm to diastolic ABP waveforms to estimate the autoregressive model coefficients by requiring the estimated diastolic flow to be zero. The algorithm incorporating the coefficients was then applied to the entire ABP signal to estimate ABF. The algorithm was applied to six Yorkshire swine data sets over a wide range of physiological conditions for validation. Quantitative measures of waveform shape (standard deviation, skewness, and kurtosis), as well as stroke volume and cardiac output from the estimated ABF, were computed. Values of these measures were compared with those obtained from ABF waveforms recorded using a Transonic aortic flow probe placed around the aortic root. The estimation errors were compared with those obtained using a windkessel model. The ARX model algorithm achieved significantly lower errors in the waveform measures, stroke volume, and cardiac output than those obtained using the windkessel model (P < 0.05).     

Evaluating predation pressure on green treefrog larvae across a habitat gradient

The effect of a predator on the abundance of a prey species depends upon the predators abundance and its ability to capture that prey. The objectives of this research were to evaluate the community structure of predators of green treefrog (Hyla cinerea) tadpoles across habitat types and evaluate the effectiveness of individual predators on H. cinerea tadpoles. Correspondence and cluster analyses of predator frequencies across 23 aquatic habitats indicated that the majority of variance in predator communities was due to a division between permanent and temporary habitats. Experimental work demonstrated that survival of the smallest H. cinerea tadpoles was significantly lower than survival of medium and large tadpoles with the most effective predators, indicating that H. cinerea tadpoles attain a refuge from predation at larger body sizes. We combined the effectiveness of predators in experiments with the abundance of each predator species from the predator community survey to demonstrate that predation pressure on H. cinerea tadpoles is higher in temporary ponds. This pattern may explain in part why this species generally breeds successfully only in permanent habitats. It also confirms that discussions about an increasing gradient of predation pressure from temporary to permanent aquatic habitats should be restricted to individual prey species for which such a gradient has been demonstrated.     

Computation of aortic pulse wave velocity and aortic pulse wave velocity and aortic extensibility from pressure gradient measurements.

This study is concerned with the computation of aortic pulse wave velocity based on simultaneous recordings of the aortic pressure gradient and first-time derivative of aortic pressure. These variables were recorded by means of a double-lumen catheter introduced in the aorta of four anesthetized closed chest dogs, and connected to critically damped manometer systems. Results of aortic pulse wave velocity were then compared: (i) to the true phase velocity obtained from spectra of apparent phase velocity, and (ii) to the pulse wave velocity computed from the time shift between maximum slopes of the pressure wave. From the aortic valves to 37 cm down the aortic trunk, pulse wave velocity increased from 410-460 cm/s to approximately 600-800 cm/s. Based on the wave propagation equation presented of Bramwell and Hill (Bramwell, J.C., and Hill, A. V. 1922. Proc. R. Soc. 93, 298-306), volumetric extensibility coefficients were computed from pulse wave velocity data. Results indicated that, from the aortic valves to 37 cm down to the aorta, the mean volumetric extensibility decreased from 0.43-0.56% deltaV/cm H2O to 0.16-0.25% deltaV/cm H2O (1 cm H2O = 94.1 N/m2).     

Diastolic gradient of pressure and the effective artificial mitral valve section area in terms of its dysfunction

A seven-year experience of treatment of 126 patients with mitral heart disease who were implanted monocuspid MIKS and bicuspid MEDINZh-2 and ROSKARDIKS prostheses (Russia) is presented. The comparative assessment of hemodynamic efficiency and the analysis of the rate of the occurrence of dysfunction of these mechanical prostheses revealed that the MIKS and MEDINZh-2 implants have advantages of hemodynamic characteristics over ROSKARDIKS, despite the priority of the standard size. It was shown that the initially low diastolic pressure gradient on the mitral valve prosthesis and the initially larger area of the prosthetic effective mitral valve aperture are of crucial importance for preventing valve complications and reducing the number of open heart reoperations.     

Strain transfer through the aortic valve

The complex structural organization of the aortic valve (AV) extracellular matrix (ECM) enables large and highly nonlinear tissue level deformations. The collagen and elastin (elastic) fibers within the ECM form an interconnected fibrous network (FN) and are known to be the main load-bearing elements of the AV matrix. The role of the FN in enabling deformation has been investigated and documented. However, there is little data on the correlation between tissue level and FN-level strains. Investigating this correlation will help establish the mode of strain transfer (affine or nonaffine) through the AV tissue as a key feature in microstructural modeling and will also help characterize the local FN deformation across the AV sample in response to applied tissue level strains. In this study, the correlation between applied strains at tissue level, macrostrains across the tissue surface, and local FN strains were investigated. Results showed that the FN strain distribution across AV samples was inhomogeneous and nonuniform, as well as anisotropic. There was no direct transfer of the deformation applied at tissue level to the fibrous network. Loading modes induced in the FN are different than those applied at the tissue as a result of different local strains in the valve layers. This nonuniformity of local strains induced internal shearing within the FN of the AV, possibly exposing the aortic valve interstitial cells (AVICs) to shear strains and stresses.     

Asymptomatic papillary fibroelastoma of the aortic valve

A previously healthy 63-year-old woman with multiple risk factors for coronary artery disease was referred to the outpatient clinic with a three-month history of atypical chest pain. At physical examination no abnormalities could be detected and the ECG was completely normal. At transthoracic echocardiography and transoesophageal echocardiography a mass, 1 cm in diameter and attached to the right coronary cusp of the aortic valve, was detected. The mass had the echocardiographic appearance of a nonhomogeneous, round, dense, mobile structure, typical features of a fibroelastoma (figure 1). On dipyridamole-thallium scintigraphy, no coronary insufficiency could be demonstrated. Since cardiac papillary fibroelastomas are associated with a risk of thromboembolic events, the patient underwent complete tumour excision by a simple shave excision (figure 2).     

Techniques of aortic valve repair

Similar to mitral repair, newer methods of aortic valve reconstruction are achieving excellent outcomes with an 85% to 90% freedom from valve-related complications at 10 years. The goal of this review is to illustrate these newer and more stable techniques of aortic valve repair. Most patients with aortic insufficiency from either trileaflet or bicuspid aortic valves are candidates for repair, in addition to selected patients with mixed aortic stenosis/insufficiency and aortic root aneurysms. Initially, aggressive commissural annuloplasty is performed to reduce measured valve diameter to 19 to 21 mm. Leaflet prolapse is corrected with plication stitches placed in the free edge of each leaflet adjacent to the Nodulus Arantius. In this regard, the leaflet free edge functions as the chorda tendinea of the aortic valve, and shortening with plication stitches raises the leaflet to a proper "effective height." Leaflet defects are augmented with gluteraldehyde-fixed autologous pericardium, and mild-to-moderate strategically placed spicules of calcium are removed with the cavitron ultrasonic surgical aspirator. Using these methods, most insufficient aortic valves, and many with mixed lesions, can be satisfactorily repaired. Six cases are illustrated in this review, spanning the spectrum of pathologies from annular dilatation without leaflet defects, to standard congenital bicuspid valve with prolapse, to trileaflet prolapse, to unusual bicuspid pathology with calcification, to a moderately calcified trileaflet valve with mixed lesions, and to aortic root aneurysms with severe aortic insufficiency. All valves were repaired using the techniques described above with trivial residual leak and minimal gradients. All repairs have been followed with yearly echocardiography, and valve reconstruction with these methods is now quite stable with excellent late outcomes. Most insufficient aortic valves now can undergo stable repair with minimal late valve-related complications. Greater application of aortic valve repair seems indicated.     

Balloon dilatation of the aortic valve for inoperable aortic stenosis.

The place of balloon dilatation of the aortic valve in the treatment of calcific aortic stenosis is controversial. Thirty two patients (mean age 76) in whom valve replacement was contraindicated were followed up for three to 24 months (mean 8); 25 were in functional class III or IV according to the New York Heart Association''s classification. Major complications of the procedure occurred in four patients. Echocardiography and Doppler studies were performed before operation and before discharge in 28 patients, and the area of the valve was measured again six to 50 (mean 23) weeks after operation in 11 patients. The peak to peak aortic pressure gradient fell from a mean of 65 (SD 24) to 46 (20) mm Hg, but the area of the aortic valve, measured by Doppler echocardiography, in 18 patients showed a modest but significant increase, from 0.61 (0.16) to 0.74 (0.23) cm2. One month after dilatation, 29 patients were alive, of whom 17 had improved symptoms. Only two had lasting clinical benefit. Sixteen patients died, 12 of a cardiac cause. The estimated one year survival rate was 49%. Six patients underwent or required valve replacement because of persisting symptoms. In view of its limited long term efficacy balloon dilatation of the aortic valve should be used only for patients with severe symptoms whose life expectancy is limited by other disease or who are considered to be unsuitable for valve replacement. It may have a role in improving the condition of patients who present with cardiogenic shock or pulmonary oedema before valve replacement is undertaken.