A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending.

Local arterial haemodynamics has been associated with the pathophysiology of several cardiovascular diseases. The stable spiral blood-flows that were observed in vivo in several vessels, may play a dual role in vascular haemodynamics, beneficial since it induces stability, reducing turbulence in the arterial tree, and accounts for normal organ perfusion, but detrimental in view of the imparted tangential velocities that are involved in plaque formation and development. Being a spiral flow considered representative of the local blood dynamics in certain vessels, a method is proposed to quantify the spiral structure of blood flow. The proposed function, computed along a cluster of particle trajectories, has been tested for the quantitative determination of the spiral blood flow in a three-dimensional, s-shaped femoral artery numerical model in which three degrees of stenosis were simulated in a site prone to atherosclerotic development. Our results confirm the efficacy of the Lagrangian analysis as a tool for vascular blood dynamics investigation. The proposed method quantified spiral motion, and revealed the progression in the degree of stenosis, in the presented case study. In the future, it could be used as a synthetic tool to approach specific clinical complications.

Three-dimensional numeric simulation of flow through an aortic bileaflet valve in a realistic model of aortic root.

A three-dimensional, realistic model of an aortic mechanical heart valve and Valsalva sinuses was developed to predict, by means of a numerical time dependent simulation, the flow field during a fraction of the systolic period. The numeric simulation was performed upon a model of valve similar to a Carbomedics 27 mm placed in a physiologic aortic root shaped model, in which no symmetry planes were exploited to reach a more realistic level. Input data for the simulation have been acquired during an experimental session on the same valve, according to the guidelines of testing protocol for prosthetic heart valves. Flow was assumed to be Newtonian and laminar at low regime and the leaflets fixed in the fully open position. The forward flow of the systolic phase was investigated, and a comparison with experimental results was performed at peak systole, the most representative point of the cardiac cycle. The results of this simulation furnished a reasonable indication (in terms of fluid dynamics) parameters downstream of the prosthetic device, especially in Valsalva sinuses, the role of which is proven to affect the valve's performance.

Beat-to-beat heart rate adaptation in pediatric and late adolescent patients with closed loop rate-responsive pacemakers.

The aim of this study was to evaluate the efficacy of physiological rate-responsive pacemakers (Closed Loop Stimulation--CLS) to pace pediatric and late adolescent patients undergoing rest, mental, standing, and exercise testing. Dual-chamber pacemaker is increasingly indicated for young patients. A new physiological pacing mode based on the indirect measure of ventricular contractility (CLS), has shown interesting results in adults, while no data on pediatric patients are available. RR intervals and beat-to-beat systolic and diastolic pressures were monitored in 12 pediatric patients (6 males, mean age 17 years [12-22 years]) who had a transvenous implant of Inos2+-CLS dual-chamber pacemaker (Biotronik GmbH, Berlin, Germany) and endocardial leads. All the patients showed correct electrical parameters at the implant and during the follow-ups. Paced RR intervals decreased significantly (F = 7.28, P = 0.01) from 0.85 +/- 0.08 seconds (rest) to 0.73 +/- 0.10 seconds (mental) and to 0.75 +/- 0.010 seconds (standing); systolic/diastolic pressure was significantly higher (F = 12.2, P = 0.002/F = 13.6, P = 0.001) in mental (134.4 +/- 19.9/74.4 +/- 8.1 mmHg) with respect to rest (115.1 +/- 18.3/61.0 +/- 6.1 mmHg), and standing (118.7 +/- 23.9/67.3 +/- 0.1 mmHg). During exercise the paced RR interval showed significant decrease of about 35% from baseline to maximum load (F = 24.90, P = 0.001) and systolic pressure increased significantly (F = 4.91, P = 0.019) by about 34% from baseline to maximum load. The comparison between paced and spontaneous rates showed very similar values and trend. In addition, CLS mode does not seem to overrun the spontaneous heart activity, when present. This is a study to evaluate CLS pacing in pediatric and late adolescent patients. The study shows that CLS pacing responds to both physical and non-physical stressors, providing physiological pacing rates, as previously observed in adults.

The power-law mathematical model for blood damage prediction: analytical developments and physical inconsistencies.

Blood trauma caused by medical devices is a major concern. Complications following the implantation/application of devices such as prosthetic heart valves, cannulae, blood pumps, tubing, and throttles lead to sublethal and lethal damage to platelets and erythrocytes. This damage is provided by the alterations in fluid dynamics, providing a mechanical load on the blood corpuscle's membrane by means of the shear stress. An appropriate quantification of the shear-induced hemolysis of artificial organs is thought to be useful in the design and development of such devices in order to minimize device-induced blood trauma. To date, a power-law mathematical relationship using the time of exposure of a blood corpuscle to a certain mechanical load and the shear stress itself (derived under the peculiar condition of uniform shear stress) has served as a basic model for the estimation of the damage to blood, investigated by means of numerical and/or experimental fluid dynamical techniques. The aim of the present article is to highlight the effect of a time-varying mechanical loading acting on blood cells based on the usual power-law model; furthermore, the effect of the loading history of a blood particle is discussed, showing how the past history of the shear acting on a blood corpuscle is not taken into account, as researchers have done until now. The need for a reassessment of the power-law model for potential blood trauma assessment is discussed by using a mathematical formulation based on the hypotheses of the existence of damage accumulation for blood with respect to time and with respect to shear stress, to be applied in complex flow fields such as the ones established in the presence of artificial organs.

Effect of autonomic stressors on rate control in pacemakers using ventricular impedance signal.

The aim of this study is to evaluate the heart rate adaptation obtained by a pacemaker, based on a measure of ventricular impedance in patients undergoing autonomic challenges. The evaluation procedure was based on the analysis of the mean value (MV) and heart rate variability (HRV) of RR and systolic pressure intervals, according to a set of neurovegetative stressors (controlled respiration in supine position and during active standing; mental stress; handgrip, and noninvasive sinusoidal stimulation of carotid baroreceptors). Each test lasted 5 minutes. Fifteen chronotropic incompetent patients first implanted, were studied three months after implantation. ECG, respiration activity, and noninvasive blood pressure were monitored. HRV was evaluated by spectral analysis. Variability in the low frequency (LF) and high frequency (HF) bands was compared by computing percentage and absolute powers. We found that baseline HR was 72.2 +/- 5.5 beats/min, in mental stress was 76.8 +/- 7.8 beats/min, in handgrip was 79.2 +/- 6.3 beats/min, and in active standing was 80.9 +/- 8.6 beats/min (P < 0.01, Friedman's test). During active standing, LF component was significantly higher with respect to baseline (25.7% of total power in standing; 9.4% in baseline, P < 0.01) and it was synchronous to the LF component of the arterial pressure variability. Carotid activation/deactivation by neck suction induced synchronous changes in the paced rates. In conclusion, closed loop strategy based on ventricular contractility continuously controls heart rate by tracking the sympathetic modulation to the heart.

Evolutive algorithms for beat-by-beat estimation of left ventricular mechanics.

Traditional methods to evaluate the ventricular mechanics need intraventricular pressure and volume recordings for multiple variably loaded beats. To do this, a complex and invasive procedure must be applied, that may decrease the clinical use. To overcome this limitation, a method to estimate the ventricular mechanics beat-by-beat is presented, modeling the ventricular pressure-volume relationship with a time-varying elastance function. The ability of the genetic algorithms (GAs) as identification technique is exploited. Applying GAs on surrogated data simulating variably loading conditions, the parameters of the time-varying elastance function, considered a measure of the contractility of the myocardial fibers are identified. These single-beat estimates are highly correlated with the end systolic pressure-volume relationship slope obtained by conventional multiple-beat analysis. The main advantage in using GAs for single beat analysis may lie, in the perspective of an use for in vivo investigations, both in their stochastic nature, and in the guaranteed better performance with respect to other search techniques on problems involving noisy signals. Future studies will approach the reduction in GAs computational costs, for a real time in vivo application.

Prediction of atrial fibrillation from surface ECG: review of methods and algorithms.

The study aims to review the mathematical methods developed for the prediction of atrial fibrillation by analysis of surface electrocardiographic records in paroxysmal or post-cardiosurgery patients. A risk stratification based on ECG analysis would be very useful either to optimise the prophylactic antiarrhythmic treatment in high risk patients, or to limit drugs administration in low risk subjects. The works published so far managed to achieve good results in terms of sensitivity and specificity. However, since these methods are not completely reliable yet, their clinical application is still limited. The present study is divided in sections about time domain, frequency domain, premature complexes detection, heart rate variability, and non linear ECG analysis based methods.

Evaluation of the surface-averaged load exerted on a blood element by the Reynolds shear stress field provided by artificial cardiovascular devices.

Implantable prosthetic devices can often affect the recipient's hemostasis, with possible hemolysis and thrombus formation. Since such devices can produce turbulent flow, it is important to characterize it as accurately as possible, by means of the Reynolds stress tensor. Some parameters related to the latter have been often used to provide a quantity related to the possible damage to blood constituents: the TSS(max), for instance, has been associated with hemolysis. It can be expressed as TSS(max)=(sigma(1)-sigma(3))/2, sigma(1) and sigma(3) being the highest and lowest principal normal stresses (PNSs) in each point of the flow. In the present work, the average value of the shear stress over a spherical surface, representative of a blood component, is derived. All three PNSs (sigma(1), sigma(2) and sigma(3)) are found to have an equal role in the determination of this parameter, since the relative formula shows a marked symmetry with respect to the PNSs. The average shear stress level, for a given (sigma(1), sigma(3)) pair (hence, for a given TSS(max)), has a minimum and maximum value, depending on the particular sigma(2) value yielded by the local structure of the turbulent flow field. A numerical investigation on more complex geometries shows similar results. The role of the intermediate PNS is thus shown for the first time to have a physical relevance. The presented results can be useful whenever a spatial averaging of the shear field is important to be assessed, such as in the case of platelet activation. A new parameter is thus proposed, which can be correlated with prosthetic devices complications.

The linear ablation of atrial fibrillation in the right atrium: can the isthmus ablation improve its efficacy?

OBJECTIVES: The aims of this study were to compare the efficacy of a 2- versus a 3 RF lesions ablation procedure in the RA in patients with paroxysmal AF, and to map right atrial activation during AF. BACKGROUND: RF catheter-mediated ablation lines mimicking the Maze operation have been proposed as a novel curative approach for AF. The relationship between this type of ablation and right atrial mapping has not been extensively studied. METHODS: Twenty-four patients with recurrent, drug-refractory, paroxysmal AF underwent an extensive mapping of the RA before attempting linear lesion RF ablation. Patients were divided into two groups: 15 patients received two linear lesions (Group 1), 9 patients three linear lesions (Group 2). RESULTS: One-month success rate AF did not recur in 40% of Group 1 patients (6/15) and in 66% (6/9) of Group 2 patients. 27% of patients in Group 1 and 11% of patients in Group 2 had recurrences controlled by drugs. No benefit in 33% of Group 1 patients and 22% of Group 2. Long-term follow-up In the absence of any drug treatment, no AF recurrences were observed in 26% of Group 1 patients (FU: 23 to 47 months) and 55% of Group 2 (FU: 14 to 23 months). No complications were reported. CONCLUSIONS: Right atrial linear ablation is safe and may be proposed for AF treatment in selected patients.

Monodimensional estimation of maximum Reynolds shear stress in the downstream flow field of bileaflet valves.

BACKGROUND AND AIM OF THE STUDY: Turbulent flow generated by prosthetic devices at the bloodstream level may cause mechanical stress on blood particles. Measurement of the Reynolds stress tensor and/or some of its components is a mandatory step to evaluate the mechanical load on blood components exerted by fluid stresses, as well as possible consequent blood damage (hemolysis or platelet activation). Because of the three-dimensional nature of turbulence, in general, a three-component anemometer should be used to measure all components of the Reynolds stress tensor, but this is difficult, especially in vivo. The present study aimed to derive the maximum Reynolds shear stress (RSS) in three commercially available prosthetic heart valves (PHVs) of wide diffusion, starting with monodimensional data provided in vivo by echo Doppler. METHODS: Accurate measurement of PHV flow field was made using laser Doppler anemometry; this provided the principal turbulence quantities (mean velocity, root-mean-square value of velocity fluctuations, average value of cross-product of velocity fluctuations in orthogonal directions) needed to quantify the maximum turbulence-related shear stress. RESULTS: The recorded data enabled determination of the relationship, the Reynolds stresses ratio (RSR) between maximum RSS and Reynolds normal stress in the main flow direction. The RSR was found to be dependent upon the local structure of the flow field. CONCLUSION: The reported RSR profiles, which permit a simple calculation of maximum RSS, may prove valuable during the post-implantation phase, when an assessment of valve function is made echocardiographically. Hence, the risk of damage to blood constituents associated with bileaflet valve implantation may be accurately quantified in vivo.

Atrial signal analysis and defibrillation threshold assessment in chronic persistent and reinduced atrial fibrillation.

INTRODUCTION: Induced versus spontaneous atrial fibrillation (AF) is of interest for assessing atrial defibrillation threshold reproducibility. METHODS AND RESULTS: Twenty-one patients with chronic AF underwent internal cardioversion with assessment of atrial defibrillation threshold at baseline and at reinduced AF. High right atrial (HRA) and coronary sinus (CS) bipolar recordings were analyzed to measure the mean local atrial period, its coefficient of variation, the 5th (P5) and 95th (P95) percentiles of atrial intervals, and the percentage of points lying at the baseline (number of occurrences), and to quantify AF organization. Atrial defibrillation threshold was comparable in baseline and reinduced AF in terms of leading-edge voltage and delivered energy. Baseline and reinduced AF were comparable with regard to overall signal parameters (both in HRA and CS) and the presence of an organized arrhythmia pattern. As for individual variables, P5 increased while P95 and coefficient of variation decreased in reinduced AF compared with spontaneous AF (statistical significance was achieved for all these parameters in HRA, but only for coefficient of variation and P95 in CS). CONCLUSION: Sustained AF reinduced after cardioversion of chronic AF is comparable with baseline AF in terms of atrial defibrillation threshold, atrial cycle length, and pattern of organization. Therefore, a clinical model based on reinduction of sustained AF after cardioversion is suitable for studying the effects of a series of interventions on atrial defibrillation threshold. However, because this model does not yield a form of AF with comparable indices of local refractoriness (e.g., P5), it is not recommended when analyzing local electrophysiologic properties.