Multiscale Markov Model Research Articles

Exploring non-equilibrium molecular dynamics of mobile protons in the solid acid CsH2PO4 at the micrometer and microsecond scale.

We explicitly compute the non-equilibrium molecular dynamics of protons in the solid acid CsH2PO4 on the micrometer length scale via a multiscale Markov model: The molecular dynamics/matrix propagation (MDM) method. Within the MDM approach, the proton dynamics information of an entire molecular dynamics simulation can be condensed into a single M × M matrix (M is the number of oxygen atoms in the simulated system). Due to this drastic reduction in the complexity, we demonstrate how to increase the length and time scales in order to enable the simulation of inhomogeneities of CsH2PO4 systems at the nanometer scale. We incorporate explicit correlation of protonation dynamics with the protonation state of the neighboring proton sites and illustrate that this modification conserves the Markov character of the MDM method. We show that atomistic features such as the mean square displacement and the diffusion coefficient of the protons can be computed quantitatively from the matrix representation. Furthermore, we demonstrate the application potential of the scheme by computing the explicit dynamics of a non-equilibrium process in an 8 μm CsH2PO4 system during 5 ms.

A dynamic multi-scale Markov model based methodology for remaining life prediction

The ability to accurately predict the remaining life of partially degraded components is crucial in prognostics. In this paper, a performance degradation index is designed using multi-feature fusion techniques to represent deterioration severities of facilities. Based on this indicator, an improved Markov model is proposed for remaining life prediction. Fuzzy C-Means (FCM) algorithm is employed to perform state division for Markov model in order to avoid the uncertainty of state division caused by the hard division approach. Considering the influence of both historical and real time data, a dynamic prediction method is introduced into Markov model by a weighted coefficient. Multi-scale theory is employed to solve the state division problem of multi-sample prediction. Consequently, a dynamic multi-scale Markov model is constructed. An experiment is designed based on a Bently-RK4 rotor testbed to validate the dynamic multi-scale Markov model, experimental results illustrate the effectiveness of the methodology.

A segmentation concept for positron emission tomography imaging using multiresolution analysis

Positron emission tomography (PET) imaging is an emerging medical imaging modality. Due to its high sensitivity and ability to model function, it is effective in identifying active regions that may be associated with various types of tumours. Increasing numbers of patient scans have led to an urgent need for efficient data archival and the development of new image analysis techniques to aid clinicians in the diagnosis of disease. Additionally, to handle the large volumes of data generated using complex processing algorithms, it is becoming evident that co-processing solutions are essential. In this paper, an automated system for the segmentation of oncological PET data is developed. Initially, the Bayesian information criterion (BIC) is utilised for optimal segmentation level selection. Expectation maximisation (EM) based mixture modelling is then performed, using a k-means clustering procedure which varies voxel order for initialisation. A multiscale Markov model is then used to refine this segmentation by modelling spatial correlations between neighbouring image voxels. A field programmable gate array (FPGA) based co-processing solution is also proposed to offload the most complex computations onto hardware, in order to achieve high performance.

Fully automated segmentation of oncological PET volumes using a combined multiscale and statistical model

The widespread application of positron emission tomography (PET) in clinical oncology has driven this imaging technology into a number of new research and clinical arenas. Increasing numbers of patient scans have led to an urgent need for efficient data handling and the development of new image analysis techniques to aid clinicians in the diagnosis of disease and planning of treatment. Automatic quantitative assessment of metabolic PET data is attractive and will certainly revolutionize the practice of functional imaging since it can lower variability across institutions and may enhance the consistency of image interpretation independent of reader experience. In this paper, a novel automated system for the segmentation of oncological PET data aiming at providing an accurate quantitative analysis tool is proposed. The initial step involves expectation maximization (EM)-based mixture modeling using a k-means clustering procedure, which varies voxel order for initialization. A multiscale Markov model is then used to refine this segmentation by modeling spatial correlations between neighboring image voxels. An experimental study using an anthropomorphic thorax phantom was conducted for quantitative evaluation of the performance of the proposed segmentation algorithm. The comparison of actual tumor volumes to the volumes calculated using different segmentation methodologies including standard k-means, spatial domain Markov Random Field Model (MRFM), and the new multiscale MRFM proposed in this paper showed that the latter dramatically reduces the relative error to less than 8% for small lesions (7 mm radii) and less than 3.5% for larger lesions (9 mm radii). The analysis of the resulting segmentations of clinical oncologic PET data seems to confirm that this methodology shows promise and can successfully segment patient lesions. For problematic images, this technique enables the identification of tumors situated very close to nearby high normal physiologic uptake. The use of this technique to estimate tumor volumes for assessment of response to therapy and to delineate treatment volumes for the purpose of combined PET/CT-based radiation therapy treatment planning is also discussed.