Random copolymer adsorption: Morita approximation compared to exact numerical simulations.

We study the adsorption of ideal random lattice copolymers with correlations in the sequences on homogeneous substrates with two different methods: An analytical solution of the problem based on the constrained annealed approximation introduced by Morita in 1964 and the generating function technique, and direct numerical simulations of lattice chains averaged over many realizations of random sequences. Both methods allow to calculate the free energy and different conformational characteristics of the adsorbed chain. The comparison of the results for random copolymers with different degree of correlations and different types of nonadsorbing monomers (neutral or repelling from the surface) shows not only qualitative but a very good quantitative agreement, especially in the cases of Bernoullian and quasialternating random sequences.

Developing and analyzing idealized models for molecular recognition.

We study equilibrium aspects of molecular recognition of two biomolecules using idealized model systems and methods from statistical physics. Starting from the basic experimental findings we demonstrate exemplarily how an idealized coarse-grained model for the investigation of molecular recognition of two biomolecules can be developed. In addition we provide details regarding two model systems for the recognition of a flexible and a rigid biomolecule respectively, the latter taking into account conformational changes. We focus particularly on the interplay and influence of the correlations of the residue distributions of the biomolecules on the recognition process.

Quantitative evaluation of free-form deformation registration for dynamic contrast-enhanced MR mammography.

In this paper, we present an evaluation study of a set of registration strategies for the alignment of sequences of 3D dynamic contrast-enhanced magnetic resonance breast images. The accuracy of the optimal registration strategies was determined on unseen data. The evaluation is based on the simulation of physically plausible breast deformations using finite element methods and on contrast-enhanced image pairs without visually detectable motion artifacts. The configuration of the finite element model was chosen according to its ability to predict in vivo breast deformations for two volunteers. We computed transformations for ten patients with 12 simulated deformations each. These deformations were applied to the postcontrast image to model patient motion occurring between pre- and postcontrast image acquisition. The original precontrast images were registered to the corresponding deformed postcontrast images. The performance of several registration configurations (rigid, affine, B-spline based nonrigid, single-resolution, multi-resolution, and volume-preserving) was optimized for five of the ten patients. The images were most accurately aligned with volume-preserving single-resolution nonrigid registration employing 40 or 20 mm control point spacing. When tested on the remaining five patients the optimal configurations reduced the average mean registration error from 1.40 to 0.45 mm for the whole breast tissue and from 1.20 to 0.32 mm for the enhancing lesion. These results were obtained on average within 26 (81) min for 40 (20) mm control point spacing. The visual appearance of the difference images from 30 patients was significantly improved after 20 mm volume-preserving single-resolution nonrigid registration in comparison to no registration or rigid registration. No substantial volume changes within the region of the enhancing lesions were introduced by this nonrigid registration.

Coarse-grained lattice model for investigating the role of cooperativity in molecular recognition.

Equilibrium aspects of the molecular recognition of rigid biomolecules are investigated using coarse-grained lattice models. The analysis is carried out in two stages. First, an ensemble of probe molecules is designed with respect to the target biomolecule. The recognition ability of the probe ensemble is then investigated by calculating the free energy of association. The influence of cooperative and anticooperative effects accompanying the association of the target and probe molecules is studied. Numerical findings are presented and compared to analytical results which can be obtained in the limit of dominating cooperativity and in the mean-field formulation of the models.

Multiscale analysis of MR-mammography data.

In this work we propose a method for automatically discriminating between different types of tissue in MR mammography datasets. This is accomplished by employing a wavelet-based multiscale analysis. After the data has been wavelet-transformed unsupervised machine learning methods are employed to identify typical patterns in the wavelet domain. To demonstrate the potential of the proposed approach we apply a filtering procedure that extracts the wavelet-based image information related to tumour tissue. In this way we obtain a robust segmentation of suspicious tissue in the MR image.

Evaluation of radiological features for breast tumour classification in clinical screening with machine learning methods.

OBJECTIVE: In this work, methods utilizing supervised and unsupervised machine learning are applied to analyze radiologically derived morphological and calculated kinetic tumour features. The features are extracted from dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) time-course data. MATERIAL: The DCE-MRI data of the female breast are obtained within the UK Multicenter Breast Screening Study. The group of patients imaged in this study is selected on the basis of an increased genetic risk for developing breast cancer. METHODS: The k-means clustering and self-organizing maps (SOM) are applied to analyze the signal structure in terms of visualization. We employ k-nearest neighbor classifiers (k-nn), support vector machines (SVM) and decision trees (DT) to classify features using a computer aided diagnosis (CAD) approach. RESULTS: Regarding the unsupervised techniques, clustering according to features indicating benign and malignant characteristics is observed to a limited extend. The supervised approaches classified the data with 74% accuracy (DT) and providing an area under the receiver-operator-characteristics (ROC) curve (AUC) of 0.88 (SVM). CONCLUSION: It was found that contour and wash-out type (WOT) features determined by the radiologists lead to the best SVM classification results. Although a fast signal uptake in early time-point measurements is an important feature for malignant/benign classification of tumours, our results indicate that the wash-out characteristics might be considered as important.

Validation of nonrigid image registration using finite-element methods: application to breast MR images.

This paper presents a novel method for validation of nonrigid medical image registration. This method is based on the simulation of physically plausible, biomechanical tissue deformations using finite-element methods. Applying a range of displacements to finite-element models of different patient anatomies generates model solutions which simulate gold standard deformations. From these solutions, deformed images are generated with a range of deformations typical of those likely to occur in vivo. The registration accuracy with respect to the finite-element simulations is quantified by co-registering the deformed images with the original images and comparing the recovered voxel displacements with the biomechanically simulated ones. The functionality of the validation method is demonstrated for a previously described nonrigid image registration technique based on free-form deformations using B-splines and normalized mutual information as a voxel similarity measure, with an application to contrast-enhanced magnetic resonance mammography image pairs. The exemplar nonrigid registration technique is shown to be of subvoxel accuracy on average for this particular application. The validation method presented here is an important step toward more generic simulations of biomechanically plausible tissue deformations and quantification of tissue motion recovery using nonrigid image registration. It will provide a basis for improving and comparing different nonrigid registration techniques for a diversity of medical applications, such as intrasubject tissue deformation or motion correction in the brain, liver or heart.

Real-space renormalization-group approach to field evolution equations.

An operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real-space renormalization group is introduced, in which cell overlapping is the key concept. Applications to (1+1)-dimensional PDEs are presented for linear and quadratic equations that are first order in time.

Coarse-grained lattice model for molecular recognition.

We present a simple model which allows us to investigate the equilibrium aspects of molecular recognition between rigid biomolecules on a generic level. Using a two-stage approach, which consists of a design and a testing step, the role of cooperativity and of varying bond strength in molecular recognition is investigated. Cooperativity is found to enhance selectivity. In complexes which require a high binding flexibility, a small number of strong bonds seems to be favored compared to a situation with many but weak bonds.

Influence of sequence correlations on the adsorption of random heteropolymers onto homogeneous planar surfaces.

Using a reference system approach, we develop an analytical theory for the adsorption of random heteropolymers with exponentially decaying and/or oscillating sequence correlations on planar homogeneous surfaces. We obtain a simple equation for the adsorption--desorption transition line. This result as well as the validity of the reference system approach is tested by a comparison with numerical lattice calculations.

Polymer adsorption onto random planar surfaces: interplay of polymer and surface correlations.

We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that it is preferable to have a small amount of strongly adsorbing sites or monomers rather than a greater amount of weakly adsorbing ones. The results are discussed with respect to their implications for the physics of molecular recognition.

Molecular recognition in a lattice model: an enumeration study.

We investigate the mechanisms underlying selective molecular recognition of single heteropolymers at chemically structured planar surfaces. To this end, we study systems with two-letter (HP) lattice heteropolymers by exact enumeration techniques. Selectivity for a particular surface is defined by an adsorption energy criterion. We analyze the distributions of selective sequences and the role of mutations. A particularly important factor for molecular recognition is the small-scale structure on the polymers.