Corina S. Drapaca

Deformation-based mapping of volume change from serial brain MRI in the presence of local tissue contrast change

This paper is motivated by the analysis of serial structural magnetic resonance imaging (MRI) data of the brain to map patterns of local tissue volume loss or gain over time, using registration-based deformation tensor morphometry. Specifically, we address the important confound of local tissue contrast changes which can be induced by neurodegenerative or neurodevelopmental processes. These not only modify apparent tissue volume, but also modify tissue integrity and its resulting MRI contrast parameters. In order to address this confound we derive an approach to the voxel-wise optimization of regional mutual information (RMI) and use this to drive a viscous fluid deformation model between images in a symmetric registration process. A quantitative evaluation of the method when compared to earlier approaches is included using both synthetic data and clinical imaging data. Results show a significant reduction in errors when tissue contrast changes locally between acquisitions. Finally, examples of applying the technique to map different patterns of atrophy rate in different neurodegenerative conditions is included.

A nonlinear viscoelastic fractional derivative model of infant hydrocephalus

Infant communicating hydrocephalus is a clinical condition where the cerebral ventricles become enlarged causing the developing brain parenchyma of the newborn to be displaced outwards into the soft, unfused skull. In this paper, a hyperelastic, fractional derivative viscoelastic model is derived to describe infant brain tissue under conditions consistent with the development of hydrocephalus. An incremental numerical technique is developed to determine the relationship between tissue deformation and applied pressure gradients. Using parameter values appropriate for infant parenchyma, it is shown that pressure gradients of the order of 1 mm Hg are sufficient to cause hydrocephalus. Predicting brain tissue deformations resulting from pressure gradients is of interest and relevance to the treatment and management of hydrocephalus, and to the best of our knowledge, this is the first time that results of this nature have been established.

Segmentation of tissue boundary evolution from brain MR image sequences using multi-phase level sets

In this paper, we focus on the automated extraction of the cerebrospinal fluid-tissue boundary, particularly around the ventricular surface, from serial structural MRI of the brain acquired in imaging studies of aging and dementia. This is a challenging segmentation problem because of the common occurrence of peri-ventricular lesions which locally alter the appearance of white matter. We examine a level set approach which evolves a 4D description of the ventricular surface over time. This has the advantage of allowing constraints on the contour in the temporal direction, improving the consistency of the extracted object over time. The 3D MR images of the entire brain are first aligned using global rigid registration. We then follow the approach proposed by Chan and Vese which is based on the Mumford and Shah model and implemented using the Osher and Sethian level set method. We have extended this to the 4D case to propagate a 4D contour toward the tissue boundaries through the evolution of a 5D implicit function. For convergence we use region-based information provided by the image rather than the gradient of the image. This model is then adapted to allow intensity contrast changes between time frames in the MRI sequence. Results on time sequences of 3D brain MR images are presented and discussed.

A Nonlinear Total Variation-Based Denoising Method With Two Regularization Parameters

The aim of the present paper is to study the effect of the regularization parameter used in the numerical implementation of the Rudin-Osher-Fatemi denoising model. By using two different regularization parameters in the numerical scheme of the Rudin-Osher-Fatemi model, we will show experimentally that when a particular relationship between the sizes of these parameters holds, the quality of the denoised image and the speed of convergence of the numerical scheme are both much improved in comparison with the classic numerical scheme of the Rudin-Osher-Fatemi model where only one regularization parameter is used.

Aging impact on brain biomechanics with applications to hydrocephalus

Hydrocephalus is a neurological disorder whose clinical symptoms and treatment outcome are correlated with patient age. In Wilkie et al. (2010, A theoretical study of the effect of intraventricular pulsations on the pathogenesis of hydrocephalus. Appl. Math. Comput., 215, 3181-3191), the fractional Zener model was used to investigate the role of cerebrospinal fluid pressure pulsations in the development of hydrocephalus in infants and adults. In this paper, we determine the mechanical parameters of the fractional Zener model for the infant and adult brains using age-dependent shear complex modulus data (Thibault, K. L. & Margulies, S. S. (1998) Age-dependent material properties of the porcine cerebrum: effect on pediatric inertial head injury criteria. J. Biomech., 31, 1119-1126). The displacement of brain tissue under conditions representing the onset of hydrocephalus are then calculated. The infant brain was found to produce tissue displacements that are unphysical for our model geometry and a new boundary condition is proposed to replace the stress-free outer boundary condition used in Wilkie et al. (2010). The steadystate elastic modulus is identified as the parameter of interest in the development of hydrocephalus: it is found to increase from the infant value of 621 Pa to the young adult value of 955 Pa and we hypothesize that it then decreases with age. The low steady-state elastic modulus of the infant brain (and possibly the aged brain) increases the tissues susceptibility to large deformations and thus to the ventricular expansion characteristic of hydrocephalus.

A Combined Level Set/Mesh Warping Algorithm for Tracking Brain and Cerebrospinal Fluid Evolution in Hydrocephalic Patients

Hydrocephalus is a neurological disease which occurs when normal cerebrospinal fluid (CSF) circulation is impeded within the cranial cavity. As a result, the brain ventricles enlarge, and the tissue compresses, causing physical and mental problems. Treatment has been mainly through CSF flow diversion by surgically implanting a CSF shunt in the brain ventricles or by performing an endoscopic third ventriculostomy (ETV). However, the patient response to either treatment continues to be poor. Therefore, there is an urgent need to design better therapy protocols for hydrocephalus. An important step in this direction is the development of predictive computational models of the mechanics of hydrocephalic brains. In this paper, we propose a combined level set/mesh warping algorithm to track the evolution of the ventricles in the hydrocephalic brain. Our combined level set/mesh warping method is successfully used to track the evolution of the brain ventricles in two hydrocephalic patients.

A theoretical study of the effect of intraventricular pulsations on the pathogenesis of hydrocephalus

Hydrocephalus, a condition which affects thousands of people annually in the US alone, arises as a result of a build-up of cerebrospinal fluid (CSF) in the brains ventricular cavity due to an imbalance between the rates of CSF production and absorption. Although the earliest known instances of hydrocephalus date back to the time of Hippocrates, the pathophysiology of hydrocephalus is still poorly understood, and is the subject of active debate in the literature. Recently, the pulsations of the cerebrospinal fluid have been suggested as a possible mechanism for ventricular expansion. In this paper, we attempt to determine the significance of these pulsations in the development of hydrocephalus by simulating their mechanical effects on the brain. The brain parenchyma is modelled as a fractional Zener viscoelastic solid, which extends the work previously presented in Sivaloganathan et al. [S. Sivaloganathan, M. Stastna, G. Tenti, J. Drake, A viscoelastic model of the brain parenchyma with pulsatile ventricular pressure, Appl. Math. Comput. 165 (2005) 687-698]. Explicit solutions for the displacement and stresses are obtained by solving the boundary value problems corresponding to the cases of infant and adult hydrocephalus. As expected, when the cranial vault is a rigid container, as in adult hydrocephalus, very small displacements are predicted.

Droplet squeezing through a narrow constriction: Minimum impulse and critical velocity

Models of a droplet passing through narrow constrictions have wide applications in science and engineering. In this paper, we report our findings on the minimum impulse (momentum change) of pushing a droplet through a narrow circular constriction. The existence of this minimum impulse is mathematically derived and numerically verified. The minimum impulse happens at a critical velocity when the time-averaged Young-Laplace pressure balances the total minor pressure loss in the constriction. Finally, numerical simulations are conducted to verify these concepts. These results could be relevant to problems of energy optimization and studies of chemical and biomedical systems.

A Fractional Pressure-Volume Model of Cerebrospinal Fluid Dynamics in Hydrocephalus

Hydrocephalus is a serious neurological disorder characterized by abnormalities in the cerebrospinal fluid (CSF) circulation, resulting in an excessive accumulation of CSF in the ventricles of the brain, brain compression and sometimes an increase in the intracranial pressure. It is believed that hydrocephalus may be caused by increased CSF production, or by obstruction of CSF circulation or of the venous outflow system. Therefore, the treatment is based on CSF flow diversion. Given that the response of patients who have been treated continues to be poor, there is an urgent need to design better therapy protocols for hydrocephalus. An important step in this direction is the development of predictive mathematical models that better explain the fundamental science behind this clinical condition. One of the first mathematical models of CSF pressure-volume compensation introduced by Marmarou in the 1970s provides a theoretical basis for studying hydrocephalus. However, the model fails to fully capture the complex CSF dynamics. In this paper we propose a generalization of Marmarou’s model using fractional calculus. We use a modified Adomian decomposition method to solve analytically the proposed fractional order nonlinear differential equation. Our results show temporal multi-scaling behavior of the CSF dynamics.

Leakage Evaluation by Virtual Entropy Generation (VEG) Method

Leakage through microscale or nanoscale cracks is usually hard to observe, difficult to control, and causes significant economic loss. In the present research, the leakage in a pipe was evaluated by the virtual entropy generation (VEG) method. In virtual entropy generation method, the “measured entropy generation” is forced to follow the “experimental second law of thermodynamics”. Taking the leakage as the source virtual entropy generation, a new pipe leakage evaluation criterion was analytically derived, which indicates that the mass leakage rate should be smaller than the pressure drop rate inside a pipe. A numerical study based on computational fluid dynamics showed the existence of an unrealistic virtual entropy generation at a high mass leakage rate. Finally, the new criterion was used in the evaluation of leakage available in the literature. These results could be useful for leakage control or industry criteria design in the future.