Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We describe sufficient conditions for the strong consistency and asymptotic normality of both methods and investigate their finite sample properties in a variety of examples.

ECG-triggered muscular counterpulsation for treatment of low cardiac output

BACKGROUND: Skeletal muscular counterpulsation (MCP) has been used as a new noninvasive technique for treatment of low cardiac output. The MCP method is based on ECG-triggered skeletal muscle stimulation. The purpose of the present study was to evaluate acute hemodynamic changes induced by MCP in the experimental animal. METHODS: Eight anaesthetized pigs (43+/-4 kg) were studied at rest and after IV â-blockade (10 mg propranolol) before and after MCP. Muscular counterpulsation was performed on both thighs using trains (75 ms duration) of multiple biphasic electrical impulses with a width of 1 ms and a frequency of 200 Hz at low (10 V) and high (30 V) amplitude. ECG-triggering was used to synchronize stimulation to a given time point. LV pressure-volume relations were determined using the conductance catheter. After baseline measurements, MCP was carried out for 10 minutes at low and high stimulation amplitude. The optimal time point for MCP was determined from LV pressure-volume loops using different stimulation time points during systole and diastole. Best results were observed during end-systole and, therefore, this time point was used for stimulation. RESULTS: Under control conditions, MCP was associated with a significant decrease in pulmonary vascular resistance (-18%), a decrease in systemic vascular resistance (-11%) and stroke work index (-4%), whereas cardiac index (+2%) and ejection fraction (+6%) increased slightly. Pressure-volume loops showed a leftward shift with a decrease in end-systolic volume. After â-blockade, cardiac function decreased (HR, MAP, EF, dP/dt max), but it improved with skeletal muscle stimulation (HR +10% and CI +17%, EF +5%). There was a significant decrease in pulmonary (-19%) and systemic vascular resistance (-29%). CONCLUSIONS: In the animal model, ECG-triggered skeletal muscular counterpulsation is associated with a significant improvement in cardiac function at baseline and after IV â-blockade. Thus, MCP represents a new, non-invasive technique which improves cardiac function by diastolic compression of the peripheral arteries and veins, with a decrease in systemic vascular resistance and increase in cardiac output.

Comparison of three methods for driven pile capacity

A significant cost for foundations is the design and installation of piles when they are required due to poor ground conditions. Not only is it important that piles be designed properly, but also that the installation equipment and total cost be evaluated. To assist in the evaluation of piles a number of methods have been developed. In this research three of these methods were investigated, which were developed by the Federal Highway Administration, the US Corps of Engineers and the American Petroleum Institute (API). The results from these methods were entered into the program GRLWEAPTM to assess the pile drivability and to provide a standard base for comparing the three methods. An additional element of this research was to develop EXCEL spreadsheets to implement these three methods. Currently the Army Corps and API methods do not have publicly available software and must be performed manually, which requires that data is taken off of figures and tables, which can introduce error in the prediction of pile capacities. Following development of the EXCEL spreadsheet, they were validated with both manual calculations and existing data sets to ensure that the data output is correct. To evaluate the three pile capacity methods data was utilized from four project sites from North America. The data included site geotechnical data along with field determined pile capacities. In order to achieve a standard comparison of the data, the pile capacities and geotechnical data from the three methods were entered into GRLWEAPTM. The sites consisted of both cohesive and cohesionless soils; where one site was primarily cohesive, one was primarily cohesionless, and the other two consisted of inter-bedded cohesive and cohesionless soils. Based on this limited set of data the results indicated that the US Corps of Engineers method more closely compared with the field test data, followed by the API method to a lesser degree. The DRIVEN program compared favorably in cohesive soils, but over predicted in cohesionless material.

Noninvasive measurement of cardiac output during exercise by inert gas rebreathing technique

Reduced exercise tolerance and dyspnea during exercise are hallmarks of heart failure syndrome. Exercise capacity and various parameters of cardiopulmonary response to exercise are of important prognostic value. All the available parameters only indirectly reflect left ventricular dysfunction and hemodynamic adaptation to an increased demand. Noninvasive assessment of cardiac output, especially during an incremental exercise stress test, would allow the direct measure of cardiac reserve and may become the gold standard for prognostic evaluation in the future.

Corticospinal output and loss of force during motor fatigue

The objective of this study was to analyze central motor output changes in relation to contraction force during motor fatigue. The triple stimulation technique (TST, Magistris et al. in Brain 121(Pt 3):437-450, 1998) was used to quantify a central conduction index (CCI = amplitude ratio of central conduction response and peripheral nerve response, obtained simultaneously by the TST). The CCI removes effects of peripheral fatigue from the quantification. It allows a quantification of the percentage of the entire target muscle motor unit pool driven to discharge by a transcranial magnetic stimulus. Subjects (n = 23) performed repetitive maximal voluntary contractions (MVC) of abductor digiti minimi (duration 1 s, frequency 0.5 Hz) during 2 min. TST recordings were obtained every 15 s, using stimulation intensities sufficient to stimulate all cortical motor neurons (MNs) leading to the target muscle, and during voluntary contractions of 20% of the MVC to facilitate the responses. TST was also repetitively recorded during recovery. This basic exercise protocol was modified in a number of experiments to further characterize influences on CCI of motor fatigue (4 min exercise at 50% MVC; delayed fatigue recovery during local hemostasis, "stimulated exercise" by 20 Hz trains of 1 s duration at 0.5 Hz during 2 min). In addition, the cortical silent period was measured during the basic exercise protocol. Force fatigued to approximately 40% of MVC in all experiments and in all subjects. In all subjects, CCI decreased during exercise, but this decrease varied markedly between subjects. On average, CCI reductions preceded force reductions during exercise, and CCI recovery preceded force recovery. Exercising at 50% for 4 min reduced muscle force more markedly than CCI. Hemostasis induced by a cuff delayed muscle force recovery, but not CCI recovery. Stimulated exercise reduced force markedly, but CCI decreased only marginally. Summarized, force reduction and reduction of the CCI related poorly quantitatively and in time, and voluntary drive was particularly critical to reduce the CCI. The fatigue induced reduction of CCI may result from a central inhibitory phenomenon. Voluntary muscle activation is critical for the CCI reduction, suggesting a primarily supraspinal mechanism.