TY - JOUR AU - Horger, T.* AU - Oelker, A.* AU - Kuttler, C.* AU - Pérez-Velázquez, J. C1 - 28430 C2 - 33370 SP - 145-165 TI - Mathematical modeling of tumor-induced angiogenesis using porous medium diffusion. JO - Int. J. Biomath. Biostat. VL - 2 IS - 1 PB - Serials Publication PY - 2013 SN - 0973-7340 ER - TY - JOUR AU - Prigarin, S.M.* AU - Sandau, K.* AU - Kazmierczak, M. AU - Hahn, K. C1 - 28113 C2 - 32946 SP - 167-180 TI - Estimation of fractal dimension: A survey with numerical experiments and software description. JO - Int. J. Biomath. Biostat. VL - 2 IS - 1 PB - Serials Publications PY - 2013 SN - 0973-7340 ER - TY - JOUR AB - We drive a mathematical model of a part of the blood coagulation cascade set up in a perfusion experiment. Our purpose is to simulate the influence of blood flow and diffusion on the blood coagulation pathway. The resulting model consists of a system of partial differential equations taking into account the spatial distribution of the biochemical species. An important issue is inclusion of a dynamic boundary condition describing adhesion of activated platelets on a collagen coated top lid in the perfusion chamber. The validity of the model is established through criteria on the reaction diffusion and flow equations, which guarantee non negative concentrations at all times. The criteria is applied to the model of the blood coagulation cascade. AU - Andersen, N.M.* AU - Sorensen, M.P.* AU - Efendiyev, M.A. AU - Olsen, O.H.* AU - Ingwersen, S.H.* C1 - 5315 C2 - 27632 SP - 1-7 TI - Modelling of the blood coagulation cascade in an in vitro flow system. JO - Int. J. Biomath. Biostat. VL - 1 IS - 1 PB - IJBB PY - 2010 SN - 0973-7340 ER - TY - JOUR AB - We consider the stationary limit of a mathematical model that desribes gene regulation at the so-called mit-hindbrain boundary during neural development in vertebrates. The study of an approproate modified system provides us with solutions that resemble the situation of the original system and can be used as references for a subsequent numerical analysis in terms of a pseudo-spectral collocation point method. We discuss the resulting numerical solutions in terms of their biological relecance. AU - Ansorg, M. AU - Blöchl, F. AU - zu Castell, W. AU - Theis, F.J. AU - Wittmann, D.M. C1 - 5912 C2 - 27477 CY - New Delhi, India SP - 9-21 TI - Gene regulation at the Mid-Hindbrain Boundary: Study of a mathematical model in the stationary limit. JO - Int. J. Biomath. Biostat. VL - 1 IS - 1 PB - Serial Publications PY - 2010 SN - 0973-7340 ER - TY - JOUR AB - We present a criterion for preserving the positive cone for infinite systems of semi-linear diffusion-convection-reaction equations. AU - Efendiyev, M.A. AU - Lasser, R. AU - Sonner, S. C1 - 5317 C2 - 27634 SP - 47-52 TI - Necessary and sufficient conditions for an infinite system of parabolic equations preserving the positive cone. JO - Int. J. Biomath. Biostat. VL - 1 IS - 1 PB - IJBB PY - 2010 SN - 0973-7340 ER - TY - JOUR AB - We apply the trajectory dynamical systems approach to study the nonnegative solutions of a semilinear elliptic problem in an unbounded domains. The existence of the global attractor for the trajectory dynamical system associated with this problem is proved. The symmetrization and stabilization properties of nonnegative solutions as |x| ∞ are also established under new (weak) conditions in three dimensional case Ω ⊂ ℝ³ AU - Efendiyev, M.A. C1 - 6866 C2 - 29369 CY - New Delhi SP - 141-150 TI - Note on trajectory attractors for elliptic equations in unbounded domains. JO - Int. J. Biomath. Biostat. VL - 1 IS - 2 PB - Serials Publications PY - 2010 SN - 0973-7340 ER - TY - JOUR AB - Mitochondrial swelling due to permeability transition is an important biological phenomenon with a lot of open questions. We give a new mathematical approach to model the volume change during the process. As opposed to the existing models we do not use differential equations, just basic assumptions about the swelling of a single mitochondrion and its cumulative effect. The results accurately describe the experimental swelling curves and are in accordance with previous findings. They also provide more insight into the nature of the positive feedback in the process. Due to its simplicity the method can be used for other biochemical or population dynamical processes as well. AU - Eisenhofer, S. AU - Hense, B.A. AU - Toókos, F. AU - Zischka, H. C1 - 5316 C2 - 27633 SP - 53-62 TI - Modeling the volume change in mitochondria. JO - Int. J. Biomath. Biostat. VL - 1 IS - 1 PB - IJBB PY - 2010 SN - 0973-7340 ER - TY - JOUR AB - Diffusion Tensor Imaging (DTI) is a magnetic resonance technique which enables the in vivo visualisation and characterisation of nerve fibers in the human brain indicating diseases like Multiple Sclerosis or Alzheimer. Increasing the sensitivity by a reduction of the voxel size or by application of measurement parameters with better diffusion differentiation induces low signal to noise ratios (SNR) in the measured diffusion weighted images (DWI) which collect the information for DTI. Due to nonlinear noise propagation within the DTI formalism the fiber properties are modelled by biased non Gaussian random fields. We present a new denoising method for DTI with low SNR and explore it by Monte Carlo simulations based on a phantom and on human brain data with high resolution 1 mm3 voxels. The method combines voxelwise averaging, nonlinear spatial filtering and a modified Rician bias correction of the DWIs to reduce bias and noise in the estimated images of fiber properties. These procedures reduce the main part of the mean squared error, but due to sample size restrictions residual noise may remain. Therefore, (post)filtering is finally applied directly to those denoised images. The method is linked to the Delta Method formalizing the asymptotic Gaussian limit of nonlinear noise propagation. The simulations demonstrate the feasibility of a quantitative analysis of DTI data of the human brain with 1 mm3 resolution, measured at a clinical field strength of 3T, if thermal noise is the source of the dominating artifacts. In addition, the results support the design of new high resolution experiments. The method is not limited to the standard tensor model. AU - Hahn, K.R. AU - Prigarin, S.M.* AU - Rodenacker, K. AU - Hasan, K.M.* C1 - 5741 C2 - 27662 SP - 63-81 TI - Denoising for diffusion tensor imaging with low signal to noise ratios: Method and Monte Carlo validation. JO - Int. J. Biomath. Biostat. VL - 1 IS - 1 PB - IJBB PY - 2010 SN - 0973-7340 ER - TY - JOUR AB - Statistics has changed in the last decades. In this provisional essay, I collect some personal impressions, reflections, considerations, and informal remarks, as well as some examples concerning these changes. I shall express my conviction, that they are mainly caused by the IT revolution, which made formerly infeasible algorithms tractable, made new techniques feasible, and thus allowed for new methods. There was an exchange of ideas concerning this development at some workshops and conferences, in particular at EURANDOM and at the ‘Mathematisches Forschungsinstiut Oberwolfach’ (MFO). Statements of participants are included as well as remarks by others. This essay is intended as a contribution to the MFO- and EURANDOMdiscussions. AU - Winkler, G. C1 - 5190 C2 - 27397 SP - 113-128 TI - On recent changes in statistics. JO - Int. J. Biomath. Biostat. VL - 1 IS - 1 PB - IJBB PY - 2010 SN - 0973-7340 ER -