Theoretically Optimal Duty Cycles for Chest and Abdominal Compression during External Cardiopulmonary Resuscitation

Objective: To use an electronic model of human circulation to compare the hemodynamic effects of different durations of chest compression during external CPR, both with, and without interposed abdominal compression (IAC). Methods: An electrical analog model of human circulation was studied on digital computer workstations using SPICE, a general-purpose circuit simulation program. In the model the heart and blood vessels were represented as resistive-capacitive networks, pressures as voltages, blood flow as electric current, blood inertia as inductance, and cardiac and venous valves as diodes. External pressurization of the heart and great vessels, as would occur in IAC-CPR, was simulated by the alternate application of damped rectangular voltage pulses, first between intrathoracic vascular capacitances and ground, and then between intra-abdominal vascular capacitances and ground. With this model, compression frequencies of 60, 80, and 100 cycles/min and duty cycles ranging from 10% to 90%, both with and without IAC, were compared. Results: There was little difference in hemodynamics when the overall compression frequency was varied between 60 and 100 cycles/min; but the effects of duty cycle were substantial. During both standard CPR and IAC-CPR, total flow and coronary flow were greatest at chest compression durations equal to 30% of cycle time. Interposed abdominal compression substantially improved simulated systemic blood flow and perfusion pressure at all duty cycles, compared with standard CPR without abdominal compression. Mean arterial pressure \u3e 75 mm Hg and artificial cardiac output \u3e 2.0 L/min could be generated by 30% duty cycle compression with IAC. Coronary perfusion in the model is clearly optimized at 30% chest compression (i.e., high-impulse chest compression technique). Conclusion: Combined high-impulse chest compressions and IACs maximize blood flow during CPR in the electrical analog model of human circulation

Modelling Overnight and Daytime Returns Using a Multivariate GARCH-Copula Model

We introduce a multivariate GARCH-Copula model to describe joint dynamics of overnight and daytime returns for multiple assets. The conditional mean and variance of individual overnight and daytime returns depend on their previous realizations through a variant of GARCH specification, and two Student’s t copulas describe joint distributions of both returns respectively. We employ both constant and time-varying correlation matrices for the t copulas and with the time-varying case the dependence structure of both returns depends on their previous dependence structures through a DCC specification. We estimate the model by a two-step procedure, where marginal distributions are estimated in the first step and copulas in the second. We apply our model to overnight and daytime returns of SPDR ETFs of nine major sectors and briefly illustrate its use in risk management and asset allocation. Our empirical results show higher mean, lower variance, fatter tails and lower correlations for overnight returns than daytime returns. Daytime returns are significantly negatively correlated with previous overnight returns. Moreover, daytime returns depend on previous overnight returns in both conditional variance and correlation matrix (through a DCC specification). Most of our empirical findings are consistent with the asymmetric information argument in the market microstructure literature. With respect to econometric modelling, our results show a DCC specification for correlation matrices of t copulas significantly improves the fit of data and enables the model to account for time-varying dependence structure.

Severe Loss Probabilities in Portfolio Credit Risk Models

We derive explicit sharp bounds on the distribution of the number of defaults from a pool of obligors with common probability of default and default correlation. These bounds are extremely wide, implying that default probabilities and default correlations only very loosely determine probabilities of severe portfolio losses. Our results quantify and thereby reinforce Gordy’s (2002) statement that “Capital decisions ... depend on higher moments”.Portfolio Credit Risk Models

Statistical analysis of joint short-term and long-term survival in resuscitation research

Objective: To develop statistical tools that utilize combined initial survival data and post-resuscitation survival data to test the null hypothesis that true, population-wide outcomes following experimental CPR interventions are not different from control. Method: A new test statistic, d2, for evaluating Type 1 error is derived from a bivariate, two-dimensional analysis of categorical initial resuscitation and post-resuscitation survival data, which are statistically independent because they are obtained during non-overlapping periods of time. The d2 test statistic, which is distributed as a chi-squared distribution, is derived from first principles and validated using Monte Carlo methods of computer simulation for thousands of clinical trials. Results: Under the null hypothesis, the normalized difference in the proportions of patients surviving the initial resuscitation period and the normalized difference in the proportions of such short-term survivors that also survive the post-resuscitation period are jointly distributed in a two-dimensional space as a bivariate standard normal distribution, against which observed intervention and control outcomes can be compared in a test of statistical significance. Typically this two-dimensional approach has greater statistical power to detect true differences, compared to conventional one-dimensional tests. Smaller group sizes (Ns) are usually required to reach statistical significance when both initial survival and post-resuscitation survival are considered together. Such two-dimensional analysis is easily extended to meta-analysis of multiple trials. Conclusions: A straightforward, easy-to-use bivariate test for Type I errors in statistical inference can be done for resuscitation studies reporting both short-term and long-term survival data. Acceptance of such two-dimensional tests of the null hypothesis, as proposed by Hallstrom, can save time, money, effort, and disappointment in the difficult and sometimes frustrating field of resuscitation researc

Circulatory Adjuncts: Newer Methods of Cardiopulmonary Resuscitation

Current standard CPR only provides about one fifth of normal forward blood flow and only about one quarter of the blood flow that is theoretically possible with advanced external techniques. Two such techniques are now approved as optional alternatives in resuscitation guidelines. This chapter reviews modern understanding of the physiology of blood flow during CPR and practical aspects of utilizing more advanced resuscitation methods. When properly performed these methods produce statistically significant increases in survival

Quantitative prediction of body surface potentials from myocardial action potentials using a summed dipole model

This paper demonstrates quantitatively, using streamlined mathematics, how the transmembrane ionic currents in individual cardiac muscle cells act to produce the body surface potentials of the electrocardiogram (ECG). From fundamental principles of electrostatics, anatomy, and physiology, one can characterize the strength of apparent dipoles along a wavefront of depolarization in a local volume of myocardium. Net transmembrane flow of ionic current in actively depolarizing or repolarizing tissue induces extracellular current flow, which sets up a field of electrical potential that resembles that of a dipole. The local dipole strength depends upon the tissue cross section, the tissue resistivity, the resting membrane potential, the membrane capacitance, the volume fraction of intracellular fluid, the time rate of change of the action potential, and the cell radius. There are no unknown, free parameters. There are no arbitrary scale factors. Body surface potentials are a function of the summed local dipole strengths, directions, and distances from the measuring point. Calculations of body surface potentials can be made for the scenarios of depolarization (QRS complex), repolarization (T wave) and localized acute injury (ST segment shifts) and agree well with experimentally measured potentials. This simplified predictive dipole theory provides a solution to the forward problem of electrocardiography that explains from a physiological perspective how the collective depolarization and repolarization of individual cardiac muscle cells create body surface potentials in health and disease

Generalized Fractals for Computer Generated Art: Preliminary Results

This paper explores new types of fractals created by iteration of the functions xn+1 = f1(xn, yn) and yn+1 = f2(xn, yn) in a general plane, rather than in the complex plane. Iteration of such functions generates orbits with novel fractal patterns. Especially interesting are N-th order polynomials, raised to a positive or negative integer power, p. Such functions create novel fractal patterns, including budding, spiked, striped, dragon head, and bat-like forms. The present faculty working paper shows how to create a rich variety of complex and fascinating fractals using this generalized approach, which is accessible to students with high school level skills in mathematics and coding

Relative effectiveness of interposed abdominal compression CPR: sensitivity analysis and recommended compression rates

Interposed abdominal compression (IAC)-CPR incorporates alternating chest and abdominal compressions to generate enhanced artificial circulation during cardiac arrest. The technique has been generally successful in improving blood flow and survival compared to standard CPR; however some questions remain. Objective: To determine why does IAC-CPR produce more apparent benefit in some subjects than in others? and what is the proper compression rate, given that there are actually two compressions (chest and abdomen) in each cycle? Method: Computer models provide a means to search for subtle effects in complex systems. The present study employs a validated 12-compartment mathematical model of the human circulation to explore the effects upon systemic perfusion pressure of changes in 35 different variables, including vascular resistances, vascular compliances, and rescuer technique. CPR with and without IAC was modeled. Results and conclusions: Computed results show that the effect of 100 mmHg abdominal compressions on systemic perfusion pressure is relatively constant (about 16 mmHg augmentation). However, the effect of chest compression depends strongly upon chest compression frequency and technique. When chest compression is less effective, as is often true in adults, the addition of IAC produces relatively dramatic augmentation (e.g. from 24 to 40 mmHg). When chest compression is more effective, the apparent augmentation with IAC is relatively less (e.g. from 60 yo 76 mmHg). The optimal frequency for uninterrupted IAC-CPR is near 50 complete cycles per minute with very little change in efficacy over the range of 20 to 100 cycles/min. In theory, the modest increase in systemic perfusion pressure produced by IAC can make up in part for poor or ineffective chest compressions in CPR. IAC appears relatively less effective in circumstances when chest pump output is high

Drug Induced Changes in Ventricular Defibrillation Threshold

Abstract not availabl