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Quantification of atherosclerotic plaque components using in vivo MRI and supervised classifiers

In this work we aimed to study the possibility of using supervised classifiers to quantify the main components of carotid atherosclerotic plaque in vivo on the basis of multisequence MRI data. MRI data consisting of five MR weightings were obtained from 25 symptomatic subjects. Histological micrographs of endarterectomy specimens from the 25 carotids were used as a standard of reference for training and evaluation. The set of subjects was divided in a training set (12 subjects) and an evaluation set (13 subjects). Four different classifiers and two human MRI readers determined the percentages of calcified tissue, fibrous tissue, lipid core, and intraplaque hemorrhage on the subject level for all subjects in the evaluation set. Quantification of the relatively small amounts of calcium could not be done with statistical significance by either the classifiers or the MRI readers. For the other tissues a simple Bayesian classifier (Bayes) performed better than the other classifiers and the MRI readers. All classifiers performed better than the MRI readers in quantifying the sum of hemorrhage and lipid proportions. The MRI readers overestimated the hemorrhage proportions and tended to underestimate the lipid proportions. In conclusion, this pilot study demonstrates the benefits of algorithmic classifiers for quantifying plaque components. Magn Reson Med, 2006.

A probabilistic analysis of local search

We present a theoretical average-case analysis of a 2-opt algorithm for the traveling salesman problem. First, we give a model which allows us to compute the required number of steps and the distribution of final solutions found by a best improvement algorithm. This model is empirically validated for a restricted version of the 2-opt neighborhood. Secondly, we present a semi-empirical analysis of the average-case performance of an iterated 2-opt and Lin-Kernighan algorithm based on empirically obtained parameters.

Some Complexity Aspects of Secondary School Timetabling Problems

We consider timetabling problems of secondary schools, in which the students can choose their own curricula. Besides finding a time slot and classroom assignment, every student must be assigned to a subject group for each subject in his curriculum. This problem is NP-hard for several independent reasons. In this paper we investigate the borderline between easy and hard subproblems. In particular, we show that the addition of blocks of size two, i.e. two lessons to be taught at consecutive time slots, or the addition of a constraint on the subject group size changes a subproblem from polynomially solvable to NP-hard.

On the local structure of recursion operators for symmetries

For a class of Hamiltonian systems with a suitable recursion operator for symmetries it is shown that there exists a local coordinate system in which the Hamiltonian, the symplectic form and the recursion operator all have a special (diagonal) form.

Modelling the temperature evolution of bone under high intensity focused ultrasound.

Magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) has been clinically shown to be effective for palliative pain management in patients suffering from skeletal metastasis. The underlying mechanism is supposed to be periosteal denervation caused by ablative temperatures reached through ultrasound heating of the cortex. The challenge is exact temperature control during sonication as MR-based thermometry approaches for bone tissue are currently not available. Thus, in contrast to the MR-HIFU ablation of soft tissue, a thermometry feedback to the HIFU is lacking, and the treatment of bone metastasis is entirely based on temperature information acquired in the soft tissue adjacent to the bone surface. However, heating of the adjacent tissue depends on the exact sonication protocol and requires extensive modelling to estimate the actual temperature of the cortex. Here we develop a computational model to calculate the spatial temperature evolution in bone and the adjacent tissue during sonication. First, a ray-tracing technique is used to compute the heat production in each spatial point serving as a source term for the second part, where the actual temperature is calculated as a function of space and time by solving the Pennes bio-heat equation. Importantly, our model includes shear waves that arise at the bone interface as well as all geometrical considerations of transducer and bone geometry. The model was compared with a theoretical approach based on the far field approximation and an MR-HIFU experiment using a bone phantom. Furthermore, we investigated the contribution of shear waves to the heat production and resulting temperatures in bone. The temperature evolution predicted by our model was in accordance with the far field approximation and agreed well with the experimental data obtained in phantoms. Our model allows the simulation of the HIFU treatments of bone metastasis in patients and can be extended to a planning tool prior to MR-HIFU treatments.

Vulnerability to atrial fibrillation under stretch can be explained by stretch-activated channels

Experimental studies show an increased vulnerability to atrial fibrillation (AF) in acutely dilated atria. By application of a stretch-activated channel (SAC) blocker, vulnerability to AF decreases significantly, indicating a role for SACs in the initiation of AF. Using a computer model of cardiac electromechanics, we investigate the hypothesis that increased vulnerability to AF may be attributed to SACs.In our model, the human atria are represented by a triangular mesh obtained from MRI data. Electrophysiology is modeled by thirteen ionic membrane currents, including the stretch-activated current Isac and intracellular calcium handling. Mechanical behavior is modeled by a series elastic, a contractile, and a parallel elastic element. The contractile force is related to the intracellular concentration of free calcium as well as to the sarcomere length. To mimic acute dilatation, overall stretch is applied to the atria. Due to contraction of some areas, stretch increases in other areas, leading to a variation in Isac conductance. In the presence of Isac, the membrane potential depolarizes, which causes inactivation of the sodium channels and results in conduction slowing or block. Inducibility of AF increases under stretch, which is explained by an increased dispersion in atrial effective refractory period (AERP), conduction slowing and local conduction block. Our observations explain the large differences in intra- atrial conduction measured in experiments and provide insight in the vulnerability to AF in dilated atria.

Symmetries of the massive Thirring model

For a Hamiltonian system every non‐Hamiltonian symmetry gives rise to a recursion operator for symmetries. Using this method two recursion operators for symmetries of the massive Thirring model are constructed. The structure of the Lie algebra of symmetries generated by these operators is given.

Computing the stochastic dynamics of phosphorylation networks.

Cells of all organisms share the ability to respond to various extracellular signals. Depending on the cell type and the organism, these signals may include hormones secreted by other cells or changes in nutrient concentrations. The signals are processed by an intricate network of protein-protein interactions, including phosphorylation and de-phosphorylation events. As some signaling proteins are only present in low concentrations, random fluctuations may affect the dynamics of the network. The mathematical modeling of networks with significant random fluctuations requires the use of stochastic methods. The stochastic dynamics of a chemical reaction system are described by the Chemical Master Equation. Often the numerical evaluation of this equation is problematic. The first problem is that many systems have an infinite number of possible states; leaving simulations of individual trajectories as the only alternative. To circumvent this problem, we focus on a class of systems that have a finite state space. More specifically, we focus on networks of phosphorylation cycles without taking into account the synthesis and degradation of proteins. The second problem is that memory requirements cause a practical limit to the size of systems that can be evaluated. In this paper, we discuss how these limitations can be overcome using parallel computation and methods dealing efficiently with the available memory. These methods were implemented in a parallel C++ program. We discuss two networks for which the stochastic dynamics were evaluated using this program: a single phosphorylation cycle and an oscillating MAP-kinase cascade.

Normal forms for a class of formulas

We consider a class of formulas which consist of real functions a1,...,aN, their derivatives, and zero or more occurrences of an integration operator I. Formulas of this type arise in some part of mathematical physics. Due to integration by parts, various formulas have the same meaning for all (suitable) functions a1,...,aN. Anormal form and a normalization algorithm are given.

Single-variable reaction systems: deterministic and stochastic models.

Biochemical reaction networks are often described by deterministic models based on macroscopic rate equations. However, for small numbers of molecules, intrinsic noise can play a significant role and stochastic methods may thus be required. In this work, we analyze the differences and similarities between a class of macroscopic deterministic models and corresponding mesoscopic stochastic models. We derive expressions that provide a clear and intuitive view upon the behavior of the stochastic model. In particular, these expressions show the dependence of both the dynamics and the stationary distribution of the stochastic model on the number of molecules in the system. As expected, most properties of the stochastic model correspond well with those in the deterministic model if the number of molecules is large enough. However, for some properties, both models are inconsistent, even if the number of molecules in the stochastic model tends to infinity. Throughout this paper, we use a bistable autophosphorylation cycle as a running example. For such a bistable system, we give an explicit proof that the rate of convergence to the stationary distribution (or the second eigenvalue of the transition matrix) depends exponentially on the number of molecules.