*Brainlesion ; 12658: 157-167, 2021.*

##### RESUMO

Glioblastoma ( GBM ) is arguably the most aggressive, infiltrative, and heterogeneous type of adult brain tumor. Biophysical modeling of GBM growth has contributed to more informed clinical decision-making. However, deploying a biophysical model to a clinical environment is challenging since underlying computations are quite expensive and can take several hours using existing technologies. Here we present a scheme to accelerate the computation. In particular, we present a deep learning ( DL )-based logistic regression model to estimate the GBM's biophysical growth in seconds. This growth is defined by three tumor-specific parameters: 1) a diffusion coefficient in white matter ( Dw ), which prescribes the rate of infiltration of tumor cells in white matter, 2) a mass-effect parameter ( Mp ), which defines the average tumor expansion, and 3) the estimated time ( T ) in number of days that the tumor has been growing. Preoperative structural multi-parametric MRI ( mpMRI ) scans from n = 135 subjects of the TCGA-GBM imaging collection are used to quantitatively evaluate our approach. We consider the mpMRI intensities within the region defined by the abnormal FLAIR signal envelope for training one DL model for each of the tumor-specific growth parameters. We train and validate the DL-based predictions against parameters derived from biophysical inversion models. The average Pearson correlation coefficients between our DL-based estimations and the biophysical parameters are 0.85 for Dw, 0.90 for Mp, and 0.94 for T, respectively. This study unlocks the power of tumor-specific parameters from biophysical tumor growth estimation. It paves the way towards their clinical translation and opens the door for leveraging advanced radiomic descriptors in future studies by means of a significantly faster parameter reconstruction compared to biophysical growth modeling approaches.

*IEEE Trans Biomed Eng ; 68(12): 3713-3724, 2021 12.*

##### RESUMO

It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called "mass effect"). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained T2-weighted and contrast-enhanced T1-weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and the volume fraction of tumor cells, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 × 10 -3 mm 2· d -1) is significantly less than those for the RD and RDM models (17.46 × 10 -3 mm 2· d -1 and 19.38 × 10 -3 mm 2· d -1, respectively). The error in the tumor volume fraction for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.

*IEEE Trans Med Imaging ; 40(1): 193-204, 2021 01.*

##### RESUMO

Our objective is the calibration of mathematical tumor growth models from a single multiparametric scan. The target problem is the analysis of preoperative Glioblastoma (GBM) scans. To this end, we present a fully automatic tumor-growth calibration methodology that integrates a single-species reaction-diffusion partial differential equation (PDE) model for tumor progression with multiparametric Magnetic Resonance Imaging (mpMRI) scans to robustly extract patient specific biomarkers i.e., estimates for (i) the tumor cell proliferation rate, (ii) the tumor cell migration rate, and (iii) the original, localized site(s) of tumor initiation. Our method is based on a sparse reconstruction algorithm for the tumor initial location (TIL). This problem is particularly challenging due to nonlinearity, ill-posedeness, and ill conditioning. We propose a coarse-to-fine multi-resolution continuation scheme with parameter decomposition to stabilize the inversion. We demonstrate robustness and practicality of our method by applying the proposed method to clinical data of 206 GBM patients. We analyze the extracted biomarkers and relate tumor origin with patient overall survival by mapping the former into a common atlas space. We present preliminary results that suggest improved accuracy for prediction of patient overall survival when a set of imaging features is augmented with estimated biophysical parameters. All extracted features, tumor initial positions, and biophysical growth parameters are made publicly available for further analysis. To our knowledge, this is the first fully automatic scheme that can handle multifocal tumors and can localize the TIL to a few millimeters.

##### Assuntos

Neoplasias Encefálicas , Glioblastoma , Imageamento por Ressonância Magnética Multiparamétrica , Neoplasias Encefálicas/diagnóstico por imagem , Calibragem , Glioblastoma/diagnóstico por imagem , Humanos , Imageamento por Ressonância Magnética*J Parallel Distrib Comput ; 149: 149-162, 2021 Mar.*

##### RESUMO

3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss-Newton-Krylov solver for diffeomorphic registration of two images. Our work extends the publicly available CLAIRE library to GPU architectures. Despite the importance of image registration, only a few implementations of large deformation diffeomorphic registration packages support GPUs. Our contributions are new algorithms to significantly reduce the run time of the two main computational kernels in CLAIRE: calculation of derivatives and scattered-data interpolation. We deploy (i) highly-optimized, mixed-precision GPU-kernels for the evaluation of scattered-data interpolation, (ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with optimized 8th-order finite differences, and (iii) compare with state-of-the-art CPU and GPU implementations. As a highlight, we demonstrate that we can register 2563 clinical images in less than 6 seconds on a single NVIDIA Tesla V100. This amounts to over 20× speed-up over the current version of CLAIRE and over 30× speed-up over existing GPU implementations.

*SIAM J Sci Comput ; 42(3): B549-B580, 2020.*

##### RESUMO

We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, multiparametric magnetic resonance imaging (MRI) scan of a glioblastoma patient. Tumor growth models are typically nonlinear parabolic partial differential equations (PDEs). Thus, we have to generate a second snapshot to be able to extract significant information from a single patient snapshot. We create this two-snapshot scenario as follows. We use an atlas (an average of several scans of healthy individuals) as a substitute for an earlier, pretumor, MRI scan of the patient. Then, using the patient scan and the atlas, we combine image-registration algorithms and parameter estimation algorithms to achieve a better estimate of the healthy patient scan and the tumor growth parameters that are consistent with the data. Our scheme is based on our recent work (Scheufele et al., Comput. Methods Appl. Mech. Engrg., to appear), but we apply a different and novel scheme where the tumor growth simulation in contrast to the previous work is executed in the patient brain domain and not in the atlas domain yielding more meaningful patient-specific results. As a basis, we use a PDE-constrained optimization framework. We derive a modified Picard-iteration-type solution strategy in which we alternate between registration and tumor parameter estimation in a new way. In addition, we consider an â 1 sparsity constraint on the initial condition for the tumor and integrate it with the new joint inversion scheme. We solve the sub-problems with a reduced space, inexact Gauss-Newton-Krylov/quasi-Newton method. We present results using real brain data with synthetic tumor data that show that the new scheme reconstructs the tumor parameters in a more accurate and reliable way compared to our earlier scheme.

*Annu Rev Biomed Eng ; 22: 309-341, 2020 06 04.*

##### RESUMO

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

##### Assuntos

Biofísica/métodos , Neoplasias Encefálicas/diagnóstico por imagem , Neoplasias Encefálicas/fisiopatologia , Processamento de Imagem Assistida por Computador , Algoritmos , Animais , Encéfalo/diagnóstico por imagem , Calibragem , Genoma Humano , Glioma , Humanos , Imageamento por Ressonância Magnética , Modelos Neurológicos , Modelos Teóricos , Neoplasias/metabolismo , Prognóstico*J Clin Med ; 9(5)2020 May 02.*

##### RESUMO

Optimal control theory is branch of mathematics that aims to optimize a solution to a dynamical system. While the concept of using optimal control theory to improve treatment regimens in oncology is not novel, many of the early applications of this mathematical technique were not designed to work with routinely available data or produce results that can eventually be translated to the clinical setting. The purpose of this review is to discuss clinically relevant considerations for formulating and solving optimal control problems for treating cancer patients. Our review focuses on two of the most widely used cancer treatments, radiation therapy and systemic therapy, as they naturally lend themselves to optimal control theory as a means to personalize therapeutic plans in a rigorous fashion. To provide context for optimal control theory to address either of these two modalities, we first discuss the major limitations and difficulties oncologists face when considering alternate regimens for their patients. We then provide a brief introduction to optimal control theory before formulating the optimal control problem in the context of radiation and systemic therapy. We also summarize examples from the literature that illustrate these concepts. Finally, we present both challenges and opportunities for dramatically improving patient outcomes via the integration of clinically relevant, patient-specific, mathematical models and optimal control theory.

*Med Image Comput Comput Assist Interv ; 12262: 551-560, 2020 Oct.*

##### RESUMO

We present a 3D fully-automatic method for the calibration of partial differential equation (PDE) models of glioblastoma (GBM) growth with "mass effect", the deformation of brain tissue due to the tumor. We quantify the mass effect, tumor proliferation, tumor migration, and the localized tumor initial condition from a single multiparameteric Magnetic Resonance Imaging (mpMRI) patient scan. The PDE is a reaction-advection-diffusion partial differential equation coupled with linear elasticity equations to capture mass effect. The single-scan calibration model is notoriously difficult because the precancerous (healthy) brain anatomy is unknown. To solve this inherently ill-posed and illconditioned optimization problem, we introduce a novel inversion scheme that uses multiple brain atlases as proxies for the healthy precancer patient brain resulting in robust and reliable parameter estimation. We apply our method on both synthetic and clinical datasets representative of the heterogeneous spatial landscape typically observed in glioblastomas to demonstrate the validity and performance of our methods. In the synthetic data, we report calibration errors (due to the ill-posedness and our solution scheme) in the 10%-20% range. In the clinical data, we report good quantitative agreement with the observed tumor and qualitative agreement with the mass effect (for which we do not have a ground truth). Our method uses a minimal set of parameters and provides both global and local quantitative measures of tumor infiltration and mass effect.

*Inverse Probl ; 36(3)2020 Mar.*

##### RESUMO

We propose domain decomposition preconditioners for the solution of an integral equation formulation of the acoustic forward and inverse scattering problems. We study both forward and inverse volume problems and propose preconditioning techniques to accelerate the iterative solvers. For the forward scattering problem, we extend the domain decomposition based preconditioning techniques presented for partial differential equations in "A restricted additive Schwarz preconditioner for general sparse linear systems", SIAM Journal on Scientific Computing, 21 (1999), pp. 792-797, to integral equations. We combine this domain decomposition preconditioner with a low-rank correction, which is easy to construct, forming a new preconditioner. For the inverse scattering problem, we use the forward problem preconditioner as a building block for constructing a preconditioner for the Gauss-Newton Hessian. We present numerical results that demonstrate the performance of both preconditioning strategies.

*Inverse Probl ; 36(4)2020 Apr.*

##### RESUMO

We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

*Comput Methods Appl Mech Eng ; 347: 533-567, 2019 Apr 15.*

##### RESUMO

We present SIBIA (Scalable Integrated Biophysics-based Image Analysis), a framework for joint image registration and biophysical inversion and we apply it to analyze MR images of glioblastomas (primary brain tumors). We have two applications in mind. The first one is normal-to-abnormal image registration in the presence of tumor-induced topology differences. The second one is biophysical inversion based on single-time patient data. The underlying optimization problem is highly non-linear and non-convex and has not been solved before with a gradient-based approach. Given the segmentation of a normal brain MRI and the segmentation of a cancer patient MRI, we determine tumor growth parameters and a registration map so that if we "grow a tumor" (using our tumor model) in the normal brain and then register it to the patient image, then the registration mismatch is as small as possible. This "coupled problem" two-way couples the biophysical inversion and the registration problem. In the image registration step we solve a large-deformation diffeomorphic registration problem parameterized by an Eulerian velocity field. In the biophysical inversion step we estimate parameters in a reaction-diffusion tumor growth model that is formulated as a partial differential equation (PDE). In SIBIA, we couple these two sub-components in an iterative manner. We first presented the components of SIBIA in "Gholami et al., Framework for Scalable Biophysics-based Image Analysis, IEEE/ACM Proceedings of the SC2017", in which we derived parallel distributed memory algorithms and software modules for the decoupled registration and biophysical inverse problems. In this paper, our contributions are the introduction of a PDE-constrained optimization formulation of the coupled problem, and the derivation of a Picard iterative solution scheme. We perform extensive tests to experimentally assess the performance of our method on synthetic and clinical datasets. We demonstrate the convergence of the SIBIA optimization solver in different usage scenarios. We demonstrate that using SIBIA, we can accurately solve the coupled problem in three dimensions (2563 resolution) in a few minutes using 11 dual-x86 nodes.

*Phys Rev E ; 99(6-1): 063313, 2019 Jun.*

##### RESUMO

Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such flows are challenging and expensive. Here, we propose a generic machine-learning-augmented reduced model for these flows. Our model replaces expensive parts of a numerical scheme with regression functions. Given the physical parameters of the particle, our model generalizes to arbitrary geometries and boundary conditions without the need to retrain the regression functions. It is approximately an order of magnitude faster than a state-of-the-art numerical scheme using the same number of degrees of freedom and can reproduce several features of the flow accurately. We illustrate the performance of our model on integral equation formulation of vesicle suspensions in two dimensions.

*J Math Biol ; 79(3): 941-967, 2019 08.*

##### RESUMO

In this article, we present a multispecies reaction-advection-diffusion partial differential equation coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so-called "mass effect", a term-of-art that refers to the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and a semi-Lagrangian method for advection. We also present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.

##### Assuntos

Algoritmos , Neoplasias Encefálicas/patologia , Simulação por Computador , Glioblastoma/patologia , Imageamento Tridimensional/métodos , Imageamento por Ressonância Magnética/métodos , Modelos Teóricos , Humanos , Interpretação de Imagem Assistida por Computador*Phys Biol ; 16(4): 041005, 2019 06 19.*

##### RESUMO

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

##### Assuntos

Matemática/métodos , Oncologia/métodos , Biologia de Sistemas/métodos , Biologia Computacional , Simulação por Computador , Humanos , Modelos Biológicos , Modelos Teóricos , Neoplasias/diagnóstico , Neoplasias/terapia , Análise de Célula Única/métodos*SIAM J Sci Comput ; 41(5): C548-C584, 2019.*

##### RESUMO

With this work we release CLAIRE, a distributed-memory implementation of an effective solver for constrained large deformation diifeomorphic image registration problems in three dimensions. We consider an optimal control formulation. We invert for a stationary velocity field that parameterizes the deformation map. Our solver is based on a globalized, preconditioned, inexact reduced space GaussâNewtonâKrylov scheme. We exploit state-of-the-art techniques in scientific computing to develop an eifective solver that scales to thousands of distributed memory nodes on high-end clusters. We present the formulation, discuss algorithmic features, describe the software package, and introduce an improved preconditioner for the reduced space Hessian to speed up the convergence of our solver. We test registration performance on synthetic and real data. We Demonstrate registration accuracy on several neuroimaging datasets. We compare the performance of our scheme against diiferent flavors of the Demons algorithm for diifeomorphic image registration. We study convergence of our preconditioner and our overall algorithm. We report scalability results on state-of-the-art supercomputing platforms. We Demonstrate that we can solve registration problems for clinically relevant data sizes in two to four minutes on a standard compute node with 20 cores, attaining excellent data fidelity. With the present work we achieve a speedup of (on average) 5× with a peak performance of up to 17× compared to our former work.

*SIAM J Sci Comput ; 39(6): B1064-B1101, 2017.*

##### RESUMO

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20× speedup for a two dimensional, real world multi-subject medical image registration problem.

*Neurosurgery ; 78(4): 572-80, 2016 Apr.*

##### RESUMO

BACKGROUND: Glioblastoma is an aggressive and highly infiltrative brain cancer. Standard surgical resection is guided by enhancement on postcontrast T1-weighted (T1) magnetic resonance imaging, which is insufficient for delineating surrounding infiltrating tumor. OBJECTIVE: To develop imaging biomarkers that delineate areas of tumor infiltration and predict early recurrence in peritumoral tissue. Such markers would enable intensive, yet targeted, surgery and radiotherapy, thereby potentially delaying recurrence and prolonging survival. METHODS: Preoperative multiparametric magnetic resonance images (T1, T1-gadolinium, T2-weighted, T2-weighted fluid-attenuated inversion recovery, diffusion tensor imaging, and dynamic susceptibility contrast-enhanced magnetic resonance images) from 31 patients were combined using machine learning methods, thereby creating predictive spatial maps of infiltrated peritumoral tissue. Cross-validation was used in the retrospective cohort to achieve generalizable biomarkers. Subsequently, the imaging signatures learned from the retrospective study were used in a replication cohort of 34 new patients. Spatial maps representing the likelihood of tumor infiltration and future early recurrence were compared with regions of recurrence on postresection follow-up studies with pathology confirmation. RESULTS: This technique produced predictions of early recurrence with a mean area under the curve of 0.84, sensitivity of 91%, specificity of 93%, and odds ratio estimates of 9.29 (99% confidence interval: 8.95-9.65) for tissue predicted to be heavily infiltrated in the replication study. Regions of tumor recurrence were found to have subtle, yet fairly distinctive multiparametric imaging signatures when analyzed quantitatively by pattern analysis and machine learning. CONCLUSION: Visually imperceptible imaging patterns discovered via multiparametric pattern analysis methods were found to estimate the extent of infiltration and location of future tumor recurrence, paving the way for improved targeted treatment.

##### Assuntos

Neoplasias Encefálicas/patologia , Glioblastoma/patologia , Adulto , Idoso , Área Sob a Curva , Neoplasias Encefálicas/cirurgia , Estudos de Coortes , Imagem de Tensor de Difusão , Feminino , Glioblastoma/cirurgia , Humanos , Imageamento por Ressonância Magnética , Masculino , Pessoa de Meia-Idade , Recidiva Local de Neoplasia/patologia , Recidiva Local de Neoplasia/cirurgia , Neuroimagem , Valor Preditivo dos Testes , Reprodutibilidade dos Testes , Estudos Retrospectivos*SIAM J Imaging Sci ; 9(3): 1154-1194, 2016.*

##### RESUMO

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss-)Newton-Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient.

*Neuro Oncol ; 18(3): 417-25, 2016 Mar.*

##### RESUMO

BACKGROUND: MRI characteristics of brain gliomas have been used to predict clinical outcome and molecular tumor characteristics. However, previously reported imaging biomarkers have not been sufficiently accurate or reproducible to enter routine clinical practice and often rely on relatively simple MRI measures. The current study leverages advanced image analysis and machine learning algorithms to identify complex and reproducible imaging patterns predictive of overall survival and molecular subtype in glioblastoma (GB). METHODS: One hundred five patients with GB were first used to extract approximately 60 diverse features from preoperative multiparametric MRIs. These imaging features were used by a machine learning algorithm to derive imaging predictors of patient survival and molecular subtype. Cross-validation ensured generalizability of these predictors to new patients. Subsequently, the predictors were evaluated in a prospective cohort of 29 new patients. RESULTS: Survival curves yielded a hazard ratio of 10.64 for predicted long versus short survivors. The overall, 3-way (long/medium/short survival) accuracy in the prospective cohort approached 80%. Classification of patients into the 4 molecular subtypes of GB achieved 76% accuracy. CONCLUSIONS: By employing machine learning techniques, we were able to demonstrate that imaging patterns are highly predictive of patient survival. Additionally, we found that GB subtypes have distinctive imaging phenotypes. These results reveal that when imaging markers related to infiltration, cell density, microvascularity, and blood-brain barrier compromise are integrated via advanced pattern analysis methods, they form very accurate predictive biomarkers. These predictive markers used solely preoperative images, hence they can significantly augment diagnosis and treatment of GB patients.

##### Assuntos

Neoplasias Encefálicas/patologia , Glioblastoma/mortalidade , Glioblastoma/patologia , Interpretação de Imagem Assistida por Computador , Adulto , Algoritmos , Barreira Hematoencefálica , Neoplasias Encefálicas/fisiopatologia , Estudos de Coortes , Feminino , Glioblastoma/genética , Humanos , Interpretação de Imagem Assistida por Computador/métodos , Aprendizado de Máquina , Imageamento por Ressonância Magnética/métodos , Masculino , Pessoa de Meia-Idade*J Math Biol ; 72(1-2): 409-33, 2016 Jan.*

##### RESUMO

We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor diffusion. We use a constrained optimization formulation with a reaction-diffusion model that results in a system of nonlinear partial differential equations. In our formulation, we estimate the parameters using partially observed, noisy tumor concentration data at two different time instances, along with white matter fiber directions derived from diffusion tensor imaging. The optimization problem is solved with a Gauss-Newton reduced space algorithm. We present the formulation and outline the numerical algorithms for solving the resulting equations. We test the method using a synthetic dataset and compute the reconstruction error for different noise levels and detection thresholds for monofocal and multifocal test cases.