We propose a new mathematical framework for estimating pulse arrival time (PAT). Existing methods of estimating PAT rely on local characteristic points or global parametric models: local characteristic point methods detect points such as foot points, max points, or max slope points, while global parametric methods fit a parametric form to the anacrotic phase of pulse signals. Each approach has its strengths and weaknesses; we take advantage of the favorable properties of both approaches in our method. To be more precise, we transform continuous pulse signals into scalar timing codes through three consecutive transformations, the last of which is a linear transformation. By training the linear transformation method on a subset of data, the proposed method yields results that are robust to noise. We apply this method to real photoplethysmography (PPG) signals and analyze the agreement between our results and those obtained using a conventional approach.

Various inverse algorithms have been proposed to estimate brain electrical activities with magnetoencephalography (MEG) and electroencephalography (EEG). To validate and compare the performances of inverse algorithms, many researchers have used artificially constructed EEG and MEG datasets. When the artificial sources are reconstructed on the cortical surface, accuracy of the source estimates has been difficult to evaluate. In this paper, we suggest a new measure to evaluate the reconstructed EEG/MEG cortical sources more accurately. To validate the usefulness of the proposed method, comparison between conventional and proposed evaluation metrics was conducted using artificial cortical sources simulated under different noise conditions. The simulation results demonstrated that only the proposed method could reflect the source space geometry regardless of the number of source peaks.

We propose a new method for personal identification using the derived vectorcardiogram (dVCG), which is derived from the limb leads electrocardiogram (ECG). The dVCG was calculated from the standard limb leads ECG using the precalculated inverse transform matrix. Twenty-one features were extracted from the dVCG, and some or all of these 21 features were used in support vector machine (SVM) learning and in tests. The classification accuracy was 99.53%, which is similar to the previous dVCG analysis using the standard 12-lead ECG. Our experimental results show that it is possible to identify a person by features extracted from a dVCG derived from limb leads only. Hence, only three electrodes have to be attached to the person to be identified, which can reduce the effort required to connect electrodes and calculate the dVCG.

For solving electroencephalographic forward problem, coupled method of finite element method (FEM) and fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed using meshfree method. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM adopts point collocation scheme. Suggested method is tested using simple equation using 1-, 2-, and 3-dimensional models, and error tendency according to node distance is studied. In addition, electroencephalographic forward problem is solved using spherical head model. Proposed hybrid method can produce well-approximated solution.

Automatically extracting breast tumor boundaries in ultrasound images is a difficult task due to the speckle noise, the low image contrast, the variance in shapes, and the local changes of image intensity. In this paper, an improved edge-based active contour model in a variational level set formulation is proposed for semi-automatically capturing ultrasonic breast tumor boundaries. First, we apply the phase asymmetry approach to enhance the edges, and then we define a new edge stopping function, which can increase the robustness to the intensity inhomogeneities. To extend the capture range of the method and provide good convergence to boundary concavities, we use the phase information to obtain an improved edge map, which can be used to calculate the gradient vector flow (GVF). Combining the edge stopping term and the improved GVF in the level set framework, the proposed method can robustly cope with noise, and it can extract the low contrast and/or concave boundaries well. Experiments on breast ultrasound images show that the proposed method outperforms the state-of-art methods.

Diffuse optical tomography is used to find the optical parameters of a turbid medium with infrared red light. The problem is mathematically formulated as a nonlinear problem to find the solution for the diffusion operator mapping the optical coefficients to the photon density distribution on the boundary of the region of interest, which is also represented by the Born expansion with respect to the unperturbed photon densities and perturbed optical coefficients. We suggest a new method of finding the solution by using the second-order Born approximation of the operator. The error analysis for the suggested method based on the second-order Born approximation is presented and compared with the conventional linearized method based on the first-order Born approximation. The suggested method has better convergence order than the linearized method, and this is verified in the numerical implementation.

Protein-protein interactions (PPIs) play a crucial role in cellular processes. In the present work, a new approach is proposed to construct a PPI predictor training a support vector machine model through a mutual information filter-wrapper parallel feature selection algorithm and an iterative and hierarchical clustering to select a relevance negative training set. By means of a selected suboptimum set of features, the constructed support vector machine model is able to classify PPIs with high accuracy in any positive and negative datasets.

A general computational model of the human lumbar spine and trunk muscles including optimization formulations was provided. For a given condition, the trunk muscle forces could be predicted considering the human physiology including the follower load concept. The feasibility of the solution could be indirectly validated by comparing the compressive force, the shear force, and the joint moment. The presented general computational model and optimization technology can be fundamental tools to understand the control principle of human trunk muscles.

The blood pressure patterns obtained from a linearly or stepwise deflating cuff exhibit personalized traits, such as fairly uniform peak patterns and regular beat geometry; it can support the diagnosis and monitoring of hypertensive patients with reduced sensitivity to fluctuations in Blood Pressure (BP) over time. Monitoring of personalized trait in Oscillometric Arterial Blood Pressure Measurements (OABPM) uses the Linear Discriminant Analysis (LDA) algorithm. The representation of personalized traits with features from the oscillometric waveforms using LDA algorithm includes four phases. Data collection consists of blood pressure data using auscultatory measurements and pressure oscillations data obtained from the oscillometric method. Preprocessing involves the normalization of various sized oscillometric waveforms to a uniform size. Feature extraction involves the use of features from oscillometric amplitudes, and trait identification involves the use of the LDA algorithm. In this paper, it presents a novel OABPM-based blood pressure monitoring system that can monitor personalized blood pressure pattern. Our approach can reduce sensitivity to fluctuations in blood pressure with the features extracted from the whole area in oscillometric arterial blood pressure measurement. Therefore this technique offers reliable blood pressure patterns. This study provides a cornerstone for the diagnosis and management of hypertension in the foreseeable future.

We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells and the rate of influx of IL-2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor dormancy.

This study investigates the effects of different solid models on predictions of brain shift for three craniotomies. We created a generic 3D brain model based on healthy human brain and modeled the brain parenchyma as single continuum and constrained by a practically rigid skull. We have used elastic model, hyperelastic 1st, 2nd, and 3rd Ogden models, and hyperelastic Mooney-Rivlin with 2- and 5-parameter models. A pressure on the brain surface at craniotomy region was applied to load the model. The models were solved with the finite elements package ANSYS. The predictions on stress and displacements were compared for three different craniotomies. The difference between the predictions of elastic solid model and a hyperelastic Ogden solid model of maximum brain displacement and maximum effective stress is relevant.

We formulate and discuss models for the spread of infectious diseases with variable population sizes and vaccinations on the susceptible individuals. First, we assume that the susceptible individuals are vaccinated continuously. We establish the threshold-like results for the existence and global stability of the disease-free and the endemic equilibriums for these systems. Especially, we prove the global stability of the endemic equilibriums by converting the systems into integrodifferential equations. Second, we suppose that vaccinations occur once per time period. We obtain the existence and global stability of the disease-free periodic solutions for such systems with impulsive effects. By a useful bifurcation theorem, we acquire the existence of the endemic periodic solutions when the disease-related deaths do not occur. At last, we compare the results with vaccinations and without vaccinations and illustrate our results by numerical simulations.

Within the last few decades, attempts have been made to characterize the underlying mechanisms of brain activity by analyzing neural signals recorded, directly or indirectly, from the human brain. Accordingly, inference of functional connectivity among neural signals has become an indispensable research tool in modern neuroscience studies aiming to explore how different brain areas are interacting with each other. Indeed, remarkable advances in computational sciences and applied mathematics even allow the estimation of causal interactions among multichannel neural signals. Here, we introduce the brief mathematical background of the use of causality inference in neuroscience and discuss the relevant mathematical issues, with the ultimate goal of providing applied mathematicians with the current state-of-the-art knowledge on this promising multidisciplinary topic.

MEG/EEG beamformer source imaging is a promising approach which can easily address spatiotemporal multi-dipole problems without a priori information on the number of sources and is robust to noise. Despite such promise, beamformer generally has weakness which is degrading localization performance for correlated sources and is requiring of dense scanning for covering all possible interesting (entire) source areas. Wide source space scanning yields all interesting area images, and it results in lengthy computation time. Therefore, an efficient source space scanning strategy would be beneficial in achieving accelerated beamformer source imaging. We propose a new strategy in computing beamformer to reduce scanning points and still maintain effective accuracy (good spatial resolution). This new strategy uses the distribution of correlation values between measurements and lead-field vectors. Scanning source points are chosen yielding higher RMS correlations than the predetermined correlation thresholds. We discuss how correlation thresholds depend on SNR and verify the feasibility and efficacy of our proposed strategy to improve the beamformer through numerical and empirical experiments. Our proposed strategy could in time accelerate the conventional beamformer up to over 40% without sacrificing spatial accuracy.