Stephanus A. van Gils

Efficacy, nephrotoxicity and ototoxicity of aminoglycosides, mathematically modelled for modelling-supported therapeutic drug monitoring

Therapeutic drug monitoring (TDM) of aminoglycosides has been a topic during the last thirty years. There is a tendency that - because of the once-daily regimen - TDM is considered not necessary anymore. Although once daily dosing has the potential for decreased toxicity, long-term usage can cause severe nephro- and ototoxicity. Furthermore, inadequate plasma concentrations can lead to treatment failure. This work is devoted to the development and application of the first mathematical model of aminoglycosides, which simulates in relation to the pharmacokinetics both their effects on bacteria as well as their nephrotoxicity and cochleotoxicity. Our software system is suitable for TDM. Based on theoretical considerations, a multi-compartment mathematical model in a numerical program in Matlab is derived that incorporates the antimicrobial effects of aminoglycosides, the saturable and active uptake into kidney cells, the reversible nephrotoxicity and the irreversible cochleotoxicity. Using fictitious person data, and an assumed pharmacokinetic and dynamic parameter set obtained from the literature, we simulated the drug concentrations, antibacterial effects, and toxicity over time in virtual patients to illustrate the benefits of optimized, efficacious dosage regimens that minimize (acceptable) nephro- and auditory ototoxicity. Our model confirms that extended-interval dosing seems the most appropriate to achieve this goal. By this manner, the present mathematical model contributes to an increase in our knowledge of how to obtain an optimized dosing strategy for individual patients. With the developed program, we are able to demonstrate that optimal aminoglycoside dosing still needs a sophisticated system of TDM.

Travelling waves in a singularly perturbed sine-Gordon equation

We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves correspond to the so-called fluxons and their linear stability is determined by calculating the Evans function. Surface resistance corresponds to a singular perturbation term in the governing equation, which specifically complicates the computation of the corresponding Evans function. Both the flow of quasi-particles across and along the junction stabilise the waves.

Comparing epileptiform behavior of mesoscale detailed models and population models of neocortex.

Two models of the neocortex are developed to study normal and pathologic neuronal activity. One model contains a detailed description of a neocortical microcolumn represented by 656 neurons, including superficial and deep pyramidal cells, four types of inhibitory neurons, and realistic synaptic contacts. Simulations show that neurons of a given type exhibit similar, synchronized behavior in this detailed model. This observation is captured by a population model that describes the activity of large neuronal populations with two differential equations with two delays. Both models appear to have similar sensitivity to variations of total network excitation. Analysis of the population model reveals the presence of multistability, which was also observed in various simulations of the detailed model.

Modeling focal epileptic activity in the Wilson-cowan model with depolarization block.

Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson–Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson–Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures.

Multiscale Segmentation via Bregman Distances and Nonlinear Spectral Analysis

In biomedical imaging reliable segmentation of objects (e.g. from small cells up to large organs) is of fundamental importance for automated medical diagnosis. New approaches for multi-scale segmentation can considerably improve performance in case of natural variations in intensity, size and shape. This paper aims at segmenting objects of interest based on shape contours and automatically finding multiple objects with different scales. The overall strategy of this work is to combine nonlinear segmentation with scales spaces and spectral decompositions recently introduced in literature. For this we generalize a variational segmentation model based on total variation using Bregman distances to construct an inverse scale space. This offers the new model to be accomplished by a scale analysis approach based on a spectral decomposition of the total variation. As a result we obtain a very efficient, (nearly) parameter-free multiscale segmentation method that comes with an adaptive regularization parameter choice. The added benefit of our method is demonstrated by systematic synthetic tests and its usage in a new biomedical toolbox for identifying and classifying circulating tumor cells. Due to the nature of nonlinear diffusion underlying, the mathematical concepts in this work offer promising extensions to nonlocal classification problems.

Exploiting pallidal plasticity for stimulation in Parkinson’s disease

OBJECTIVEnContinuous application of high-frequency deep brain stimulation (DBS) often effectively reduces motor symptoms of Parkinsons disease patients. While there is a growing need for more effective and less traumatic stimulation, the exact mechanism of DBS is still unknown. Here, we present a methodology to exploit the plasticity of GABAergic synapses inside the external globus pallidus (GPe) for the optimization of DBS.nnnAPPROACHnAssuming the existence of spike-timing-dependent plasticity (STDP) at GABAergic GPe-GPe synapses, we simulate neural activity in a network model of the subthalamic nucleus and GPe. In particular, we test different DBS protocols in our model and quantify their influence on neural synchrony.nnnMAIN RESULTSnIn an exemplary set of biologically plausible model parameters, we show that STDP in the GPe has a direct influence on neural activity and especially the stability of firing patterns. STDP stabilizes both uncorrelated firing in the healthy state and correlated firing in the parkinsonian state. Alternative stimulation protocols such as coordinated reset stimulation can clearly profit from the stabilizing effect of STDP. These results are widely independent of the STDP learning rule.nnnSIGNIFICANCEnOnce the model settings, e.g., connection architectures, have been described experimentally, our model can be adjusted and directly applied in the development of novel stimulation protocols. More efficient stimulation leads to both minimization of side effects and savings in battery power.

On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations

AbstractWe consider the perturbed Hamiltonian systemn

Computational modeling of Adelta-fiber-mediated nociceptive detection of electrocutaneous stimulation

u_t = partial _x delta H(u) - varepsilon P(u)