Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Validation of statistical shape model based reconstruction of the proximal femur - A morphology study

Seventeen bones (sixteen cadaveric bones and one plastic bone) were used to validate a method for reconstructing a surface model of the proximal femur from 2D X-ray radiographs and a statistical shape model that was constructed from thirty training surface models. Unlike previously introduced validation studies, where surface-based distance errors were used to evaluate the reconstruction accuracy, here we propose to use errors measured based on clinically relevant morphometric parameters. For this purpose, a program was developed to robustly extract those morphometric parameters from the thirty training surface models (training population), from the seventeen surface models reconstructed from X-ray radiographs, and from the seventeen ground truth surface models obtained either by a CT-scan reconstruction method or by a laser-scan reconstruction method. A statistical analysis was then performed to classify the seventeen test bones into two categories: normal cases and outliers. This classification step depends on the measured parameters of the particular test bone. In case all parameters of a test bone were covered by the training population's parameter ranges, this bone is classified as normal bone, otherwise as outlier bone. Our experimental results showed that statistically there was no significant difference between the morphometric parameters extracted from the reconstructed surface models of the normal cases and those extracted from the reconstructed surface models of the outliers. Therefore, our statistical shape model based reconstruction technique can be used to reconstruct not only the surface model of a normal bone but also that of an outlier bone.

The ability of the Gaussian-2, Gaussian-3, Complete Basis Set–QB3, and Complete Basis Set–APNO model chemistries to model the geometries of small water clusters

The Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO methods have been used to calculate geometries of neutral clusters of water, (H2O)n, where n = 2–6. The structures are in excellent agreement with those determined from experiment and those predicted from previous high-level calculations. These methods also provide excellent thermochemical predictions for water clusters, and thus can be used with confidence in evaluating the structures and thermochemistry of water clusters.

Efficacy of telavancin against penicillin-resistant pneumococci and Staphylococcus aureus in a rabbit meningitis model and determination of kinetic parameters

The penetration of telavancin was 2% into inflamed meninges and ca. 1 per thousand into noninflamed meninges after two intravenous injections (30 mg/kg of body weight). In experimental meningitis, telavancin was significantly superior to vancomycin combined with ceftriaxone against a penicillin-resistant pneumococcal strain. Against a methicillin-sensitive staphylococcal strain, telavancin was slightly but not significantly superior to vancomycin.

A Cox Model for Biostatistics of the Future

Professor Sir David R. Cox (DRC) is widely acknowledged as among the most important scientists of the second half of the twentieth century. He inherited the mantle of statistical science from Pearson and Fisher, advanced their ideas, and translated statistical theory into practice so as to forever change the application of statistics in many fields, but especially biology and medicine. The logistic and proportional hazards models he substantially developed, are arguably among the most influential biostatistical methods in current practice. This paper looks forward over the period from DRC's 80th to 90th birthdays, to speculate about the future of biostatistics, drawing lessons from DRC's contributions along the way. We consider "Cox's model" of biostatistics, an approach to statistical science that: formulates scientific questions or quantities in terms of parameters gamma in probability models f(y; gamma) that represent in a parsimonious fashion, the underlying scientific mechanisms (Cox, 1997); partition the parameters gamma = theta, eta into a subset of interest theta and other "nuisance parameters" eta necessary to complete the probability distribution (Cox and Hinkley, 1974); develops methods of inference about the scientific quantities that depend as little as possible upon the nuisance parameters (Barndorff-Nielsen and Cox, 1989); and thinks critically about the appropriate conditional distribution on which to base infrences. We briefly review exciting biomedical and public health challenges that are capable of driving statistical developments in the next decade. We discuss the statistical models and model-based inferences central to the CM approach, contrasting them with computationally-intensive strategies for prediction and inference advocated by Breiman and others (e.g. Breiman, 2001) and to more traditional design-based methods of inference (Fisher, 1935). We discuss the hierarchical (multi-level) model as an example of the future challanges and opportunities for model-based inference. We then consider the role of conditional inference, a second key element of the CM. Recent examples from genetics are used to illustrate these ideas. Finally, the paper examines causal inference and statistical computing, two other topics we believe will be central to biostatistics research and practice in the coming decade. Throughout the paper, we attempt to indicate how DRC's work and the "Cox Model" have set a standard of excellence to which all can aspire in the future.

Model-based control of neuromuscular block using mivacurium: design and clinical verification

BACKGROUND: Short-acting agents for neuromuscular block (NMB) require frequent dosing adjustments for individual patient's needs. In this study, we verified a new closed-loop controller for mivacurium dosing in clinical trials. METHODS: Fifteen patients were studied. T1% measured with electromyography was used as input signal for the model-based controller. After induction of propofol/opiate anaesthesia, stabilization of baseline electromyography signal was awaited and a bolus of 0.3 mg kg-1 mivacurium was then administered to facilitate endotracheal intubation. Closed-loop infusion was started thereafter, targeting a neuromuscular block of 90%. Setpoint deviation, the number of manual interventions and surgeon's complaints were recorded. Drug use and its variability between and within patients were evaluated. RESULTS: Median time of closed-loop control for the 11 patients included in the data processing was 135 [89-336] min (median [range]). Four patients had to be excluded because of sensor problems. Mean absolute deviation from setpoint was 1.8 +/- 0.9 T1%. Neither manual interventions nor complaints from the surgeons were recorded. Mean necessary mivacurium infusion rate was 7.0 +/- 2.2 microg kg-1 min-1. Intrapatient variability of mean infusion rates over 30-min interval showed high differences up to a factor of 1.8 between highest and lowest requirement in the same patient. CONCLUSIONS: Neuromuscular block can precisely be controlled with mivacurium using our model-based controller. The amount of mivacurium needed to maintain T1% at defined constant levels differed largely between and within patients. Closed-loop control seems therefore advantageous to automatically maintain neuromuscular block at constant levels.