The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Numerical assessment on the effective mechanical stimuli for matrix-associated metabolism in chondrocyte-seeded constructs

The self-regeneration capacity of articular cartilage is limited, due to its avascular and aneural nature. Loaded explants and cell cultures demonstrated that chondrocyte metabolism can be regulated via physiologic loading. However, the explicit ranges of mechanical stimuli that correspond to favourable metabolic response associated with extracellular matrix (ECM) synthesis are elusive. Unsystematic protocols lacking this knowledge produce inconsistent results. This study aims to determine the intrinsic ranges of physical stimuli that increase ECM synthesis and simultaneously inhibit nitric oxide (NO) production in chondrocyte-agarose constructs, by numerically re-evaluating the experiments performed by Tsuang et al. (2008). Twelve loading patterns were simulated with poro-elastic finite element models in ABAQUS. Pressure on solid matrix, von Mises stress, maximum principle stress and pore pressure were selected as intrinsic mechanical stimuli. Their development rates and magnitudes at the steady state of cyclic loading were calculated with MATLAB at the construct level. Concurrent increase in glycosaminoglycan and collagen was observed at 2300 Pa pressure and 40 Pa/s pressure rate. Between 0-1500 Pa and 0-40 Pa/s, NO production was consistently positive with respect to controls, whereas ECM synthesis was negative in the same range. A linear correlation was found between pressure rate and NO production (R = 0.77). Stress states identified in this study are generic and could be used to develop predictive algorithms for matrix production in agarose-chondrocyte constructs of arbitrary shape, size and agarose concentration. They could also be helpful to increase the efficacy of loading protocols for avascular tissue engineering. Copyright (c) 2010 John Wiley \& Sons, Ltd.

Ventricular-arterial coupling in a rat model of reduced arterial compliance provoked by hypervitaminosis D and nicotine

The vitamin D(3) and nicotine (VDN) model is one of isolated systolic hypertension (ISH) in which arterial calcification raises arterial stiffness and vascular impedance. The effects of VDN treatment on arterial and cardiac hemodynamics have been investigated; however, a complete analysis of ventricular-arterial interaction is lacking. Wistar rats were treated with VDN (VDN group, n = 9), and a control group (n = 10) was included without the VDN. At week 8, invasive indexes of cardiac function were obtained using a conductance catheter. Simultaneously, aortic pressure and flow were measured to derive vascular impedance and characterize ventricular-vascular interaction. VDN caused significant increases in systolic (138 +/- 6 vs. 116 +/- 13 mmHg, P < 0.01) and pulse (42 +/- 10 vs. 26 +/- 4 mmHg, P < 0.01) pressures with respect to control. Total arterial compliance decreased (0.12 +/- 0.08 vs. 0.21 +/- 0.04 ml/mmHg in control, P < 0.05), and pulse wave velocity increased significantly (8.8 +/- 2.5 vs. 5.1 +/- 2.0 m/s in control, P < 0.05). The arterial elastance and end-systolic elastance rose significantly in the VDN group (P < 0.05). Wave reflection was augmented in the VDN group, as reflected by the increase in the wave reflection coefficient (0.63 +/- 0.06 vs. 0.52 +/- 0.05 in control, P < 0.05) and the amplitude of the reflected pressure wave (13.3 +/- 3.1 vs. 8.4 +/- 1.0 mmHg in control, P < 0.05). We studied ventricular-arterial coupling in a VDN-induced rat model of reduced arterial compliance. The VDN treatment led to development of ISH and provoked alterations in cardiac function, arterial impedance, arterial function, and ventricular-arterial interaction, which in many aspects are similar to effects of an aged and stiffened arterial tree.

Are there accurate predictors of long-term vital and functional outcomes in cardiac surgical patients requiring prolonged intensive care?

BACKGROUND AND OBJECTIVE: The decision to maintain intensive treatment in cardiac surgical patients with poor initial outcome is mostly based on individual experience. The risk scoring systems used in cardiac surgery have no prognostic value for individuals. This study aims to assess (a) factors possibly related to poor survival and functional outcomes in cardiac surgery patients requiring prolonged (> or = 5 days) intensive care unit (ICU) treatment, (b) conditions in which treatment withdrawal might be justified, and (c) the patient's perception of the benefits and drawbacks of long intensive treatments. METHODS: The computerized data prospectively recorded for every patient in the intensive care unit over a 3-year period were reviewed and analyzed (n=1859). Survival and quality of life (QOL) outcomes were determined in all patients having required > or =5 consecutive days of intensive treatment (n=194/10.4%). Long-term survivors were interviewed at yearly intervals in a standardized manner and quality of life was assessed using the dependency score of Karnofsky. No interventions or treatments were given, withhold, or withdrawn as part of this study. RESULTS: In-hospital, 1-, and 3-year cumulative survival rates reached 91.3%, 85.6%, and 75.1%, respectively. Quality of life assessed 1 year postoperatively by the score of Karnofsky was good in 119/165 patients, fair in 32 and poor in 14. Multivariate logistic regression analysis of 19 potential predictors of poor outcome identified dialysis as the sole factor significantly (p=0.027) - albeit moderately - reducing long-term survival, and sustained neurological deficit as an inconstant predictor of poor functional outcome (p=0.028). One year postoperatively 0.63% of patients still reminded of severe suffering in the intensive station and 20% of discomfort. Only 7.7% of patients would definitely refuse redo surgery. CONCLUSIONS: This study of cardiac surgical patients requiring > or =5 days of intensive treatment did not identify factors unequivocally justifying early treatment limitation in individuals. It found that 1-year mortality and disability rates can be maintained at a low level in this subset of patients, and that severe suffering in the ICU is infrequent.

Noninvasive Doppler-derived myocardial performance index in rats with myocardial infarction: validation and correlation by conductance catheter

The rodent model of myocardial infarction (MI) is extensively used in heart failure studies. However, long-term follow-up of echocardiographic left ventricular (LV) function parameters such as the myocardial performance index (MPI) and its ratio with the fractional shortening (LVFS/MPI) has not been validated in conjunction with invasive indexes, such as those derived from the conductance catheter (CC). Sprague-Dawley rats with left anterior descending coronary artery ligation (MI group, n = 9) were compared with a sham-operated control group (n = 10) without MI. Transthoracic echocardiography (TTE) was performed every 2 wk over an 8-wk period, after which classic TTE parameters, especially MPI and LVFS/MPI, were compared with invasive indexes obtained by using a CC. Serial TTE data showed significant alterations in the majority of the noninvasive functional and structural parameters (classic and novel) studied in the presence of MI. Both MPI and LVFS/MPI significantly (P < 0.05 for all reported values) correlated with body weight (r = -0.58 and 0.76 for MPI and LVFS/MPI, respectively), preload recruitable stroke work (r = -0.61 and 0.63), LV end-diastolic pressure (LVEDP) (r = 0.82 and -0.80), end-diastolic volume (r = 0.61 and -0.58), and end-systolic volume (r = 0.46 and -0.48). Forward stepwise linear regression analysis revealed that, of all variables tested, LVEDP was the only independent determinant of MPI (r = 0.84) and LVFS/MPI (r = 0.83). We conclude that MPI and LVFS/MPI correlate strongly and better than the classic noninvasive TTE parameters with established, invasively assessed indexes of contractility, preload, and volumetry. These findings support the use of these two new noninvasive indexes for long-term analysis of the post-MI LV remodeling.

Effects of an aging vascular model on healthy and diseased hearts

The vitamin D(3) and nicotine (VDN) model is a model of isolated systolic hypertension (ISH) due to arterial calcification raising arterial stiffness and vascular impedance similar to an aged and stiffened arterial tree. We therefore analyzed the impact of this aging model on normal and diseased hearts with myocardial infarction (MI). Wistar rats were treated with VDN (n = 9), subjected to MI by coronary ligation (n = 10), or subjected to a combination of both MI and VDN treatment (VDN/MI, n = 14). A sham-treated group served as control (Ctrl, n = 10). Transthoracic echocardiography was performed every 2 wk, whereas invasive indexes were obtained at week 8 before death. Calcium, collagen, and protein contents were measured in the heart and the aorta. Systolic blood pressure, pulse pressure, thoracic aortic calcium, and end-systolic elastance as an index of myocardial contractility were highest in the aging model group compared with MI and Ctrl groups (P(VDN) < 0.05, 2-way ANOVA). Left ventricular wall stress and brain natriuretic peptide (P(VDNxMI) = not significant) were highest, while ejection fraction, stroke volume, and cardiac output were lowest in the combined group versus all other groups (P(VDNxMI) < 0.05). The combination of ISH due to this aging model and MI demonstrates significant alterations in cardiac function. This model mimics several clinical phenomena of cardiovascular aging and may thus serve to further study novel therapies.

Comparing oxygen transfer performance between three membrane oxygenators: effect of temperature changes during cardiopulmonary bypass

Recently, a new oxygenator (Dideco 903 [D903], Dideco, Mirandola, Italy) has been introduced to the perfusion community, and we set about testing its oxygen transfer performance and then comparing it to two other models. This evaluation was based on the comparison between oxygen transfer slope, gas phase arterial oxygen gradients, degree of blood shunting, maximum oxygen transfer, and diffusing capacity calculated for each membrane. Sixty patients were randomized into three groups of oxygenators (Dideco 703 [D703], Dideco; D903; and Quadrox, Jostra Medizintechnik AG, Hirrlingen, Germany) including 40/20 M/F of 68.6 +/- 11.3 years old, with a body weight of 71.5 +/- 12.1 kg, a body surface area (BSA) of 1.84 +/- 0.3 m(2), and a theoretical blood flow rate (index 2.4 times BSA) of 4.4 +/- 0.7 L/min. The maximum oxygen transfer (VO(2)) values were 313 mL O(2)/min (D703), 579 mL O(2)/min (D903), and 400 mL O(2)/min (Quadrox), with the D903 being the most superior (P < 0.05). Oxygen (O(2)) gradients were 320 mm Hg (D703), 235 mm Hg (D903), and 247 mm Hg (Quadrox), meaning D903 and Quadrox are more efficient versus the D703 (P < 0.05). Shunt fraction (Qs/Qt) and diffusing capacity (DmO(2)) were comparable (P = ns). Diffusing capacity values indexed to BSA (DmO(2)/m(2)) were 0.15 mL O(2)/min/mm Hg/m(2) (D703), 0.2 mL O(2)/min/mm Hg/m(2) (D903), and 0.18 mL O(2)/min/mm Hg/m(2) (Quadrox) with D903 outperforming D703 (P < 0.0005). During hypothermia (32.0 +/- 0.3 degrees C), there was a lower absolute and relative VO(2 )for all three oxygenators (P = ns). The O(2) gradients, DmO(2) and DmO(2)/m(2), were significantly lower for all oxygenators (P < 0.01). Also, Qs/Qt significantly rose for all oxygenators (P < 0.01). The oxygen transfer curve is characteristic to each oxygenator type and represents a tool to quantify oxygenator performance. Using this parameter, we demonstrated significant differences among commercially available oxygenators. However, all three oxygenators are considered to meet the oxygen needs of the patients.

The effect of a myocardial infarction on the normalized time-varying elastance curve

It has been suggested that the shape of the normalized time-varying elastance curve [E(n)(t(n))] is conserved in different cardiac pathologies. We hypothesize, however, that the E(n)(t(n)) differs quantitatively after myocardial infarction (MI). Sprague-Dawley rats (n = 9) were anesthetized, and the left anterior descending coronary artery was ligated to provoke the MI. A sham-operated control group (CTRL) (n = 10) was treated without the MI. Two months later, a conductance catheter was inserted into the left ventricle (LV). The LV pressure and volume were measured and the E(n)(t(n)) derived. Slopes of E(n)(t(n)) during the preejection period (alpha(PEP)), ejection period (alpha(EP)), and their ratio (beta = alpha(EP)/alpha(PEP)) were calculated, together with the characteristic decay time during isovolumic relaxation (tau) and the normalized elastance at end diastole (E(min)(n)). MI provoked significant LV chamber dilatation, thus a loss in cardiac output (-33%), ejection fraction (-40%), and stroke volume (-30%) (P < 0.05). Also, it caused significant calcium increase (17-fold), fibrosis (2-fold), and LV hypertrophy. End-systolic elastance dropped from 0.66 +/- 0.31 mmHg/microl (CTRL) to 0.34 +/- 0.11 mmHg/microl (MI) (P < 0.05). Normalized elastance was significantly reduced in the MI group during the preejection, ejection, and diastolic periods (P < 0.05). The slope of E(n)(t(n)) during the alpha(PEP) and beta were significantly altered after MI (P < 0.05). Furthermore, tau and end-diastolic E(min)(n) were both significantly augmented in the MI group. We conclude that the E(n)(t(n)) differs quantitatively in all phases of the heart cycle, between normal and hearts post-MI. This should be considered when utilizing the single-beat concept.