Acceleration of PDE-Based Biological Simulation Through the Development of Neural Network Metamodels

Burzawa, Lukasz; Li, Linlin; Wang, Xu; Tepole, Adrián Buganza; Umulis, David M.

doi:10.1007/s40139-020-00216-8

Cited by 6 publications

(5 citation statements)

References 42 publications

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“…With the development of imaging science, especially the continuous innovation of X-ray computed tomography (CT) imaging technology, the microstructure and the subtle pathological changes of the lung can be fully displayed. e use of imaging to detect and diagnose pulmonary fungal infections is a critical research topic in this field [5]. e 2006 Diagnostic Criteria and Treatment Principles for Invasive Pulmonary Fungal Infections (Draft) listed the characteristic imaging manifestations of pulmonary aspergillus infectious disease and fungal pneumonia as the main clinical indicators of the diagnostic criteria, but other findings of the characteristic images have not been defined yet [6].…”

Section: Introduction E Incidence Of Invasive Pulmonary Fungal Infect...mentioning

confidence: 99%

Diagnosis of Bronchial and Pulmonary Fungal Infection Using Gradient Weighted Denoising Algorithm-Based CT Images

Li-hua

Zhang

2022

Scientific Programming

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Based on computed tomography (CT) with a gradient weighted denoising algorithm, the image denoising technique was applied to diagnose bronchial and pulmonary fungal infection to discuss the features of CT images and the efficiency of the denoising algorithm. Therefore, it could assist clinicians in disease treatment. The clinical data and imaging data of 100 patients with invasive pulmonary fungal infection were collected in the hospital. All of them were rolled into a natural denoising CT group (routine group) and gradient weighted denoising algorithm-based image denoising group (algorithm group). The images from the routine group were processed by the routine natural denoising method, and the images from the algorithm group were denoised with the gradient weighted denoising algorithm. The results showed that the algorithm group had greater denoising efficiency and less denoising time compared with the routine group ( P < 0.05 ). The diagnostic sensitivity, specificity, and accuracy of the denoised images from the algorithm group were higher markedly than the above three indicators of the routine group ( P < 0.05 ). For bronchopulmonary infections, the sensitivity, specificity, and accuracy of the PDE model for CT denoised images were 99.00%, 96.87%, and 98.33%, the positive rate of chest CT examination was 86.2%, which was higher markedly than the rate of ordinary CT examination (70.5%), and the difference was statistically substantial ( P < 0.05 ). Besides, the mean absolute error (MAE), peak signal to noise ratio (PSNR), and mean structural similarity index measure (MSSIM) of the algorithm group were better than those of the unprocessed images and the routine group ( P < 0.05 ). Moreover, the algorithm group had a good visual effect. In conclusion, the gradient weighted denoising algorithm could effectively remove the noise and bar artifacts in CT images and well retain the edge details of CT images, thereby improving the quality of CT images. Therefore, it was suitable for clinical diagnosis and had practical application value.

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Section: Introduction E Incidence Of Invasive Pulmonary Fungal Infect...mentioning

confidence: 99%

Diagnosis of Bronchial and Pulmonary Fungal Infection Using Gradient Weighted Denoising Algorithm-Based CT Images

Li-hua

Zhang

2022

Scientific Programming

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“…Machine learning and in particular neural networks have emerged as powerful tools in biophysics to discover patterns from data, perform optimization, and accelerate computationally expensive physics solvers (Peng et al, 2020). Our previous work in this regard already showed the ability of long short-term memory (LSTM) a special type of neural network model specifically designed to work with sequential data which allowed it to capture accurately the dynamics of 1D reaction-diffusion systems (Burzawa et al, 2020). In this work we leverage the multilayer perceptron (MLP) type of neural network due to the output data was on a spherical domain that does not maintain the sequential feature.…”

Section: Discussionmentioning

confidence: 99%

Determining the role of advection in patterning by bone morphogenetic proteins through neural network model-based acceleration of a 3D finite element model of the zebrafish embryo

Wang

Chai

et al. 2022

Front. Syst. Biol.

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Embryonic development is a complex phenomenon that integrates genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogens guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes the morphogen patterns in three-dimensional (3D) space, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo, nor how the patterns are controlled over time. Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP-mediated DV patterning. The layer of epithelial cells begins to thin as they spread toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members through advection. We developed a Finite Element Model (FEM) that incorporates all stages of zebrafish embryonic development data and solves the advection-diffusion-reaction Partial Differential Equations (PDE) in a growing domain. We use the model to investigate mechanisms in underlying BMP-driven DV patterning during epiboly. Solving the PDE is computationally expensive for parameter exploration. To overcome this obstacle, we developed a Neural Network (NN) metamodel of the 3D embryo that is accurate and fast and provided a nonlinear map between high-dimensional input and output that replaces the direct numerical simulation of the PDEs. From the modeling and acceleration by the NN metamodels, we identified the impact of advection on patterning and the influence of the dynamic expression level of regulators on the BMP signaling network.

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“…While sub-cell-level representations of the biophysical and biochemical processes in tissues has several advantages (e.g., allowing direct representation of cells with different phenotypes), such representations suffer from the same problems as those described for turbulence. For many practical applications, both the number of degrees of freedom and the presence of nonlinearities make the direct computation of the continuum mechanics at the microscale level impractical [2]. Hence, upscaling methods have been developed and employed to allow resolution in spatial and temporal domains where it is needed, while providing accurate but more economical methods for domains where resolution is not a priority.…”

Section: Objectives and Outlinementioning

confidence: 99%

“…Upscaling can be accomplished via a number of approaches ranging from formal averaging methods to various numerical schemes; a review of these methods (with an emphasis on nonlinear problems) has been reported in [1,2,3]. Regardless of the approach, the process of eliminating the microscale variables in coarse-grained problems is known generally as the closure problem.…”

Section: Introductionmentioning

confidence: 99%

“…The number of different approaches pursued here is vast. It includes the use of simple neural networks [12], recurrent neural networks [13], deep neural networks with dimension reduction via diffusion maps [14], recurrent neural network architectures with dimension reduction accomplished via an autoencoder scheme [15], multilayer perceptrons for generating reduced-order metamodels [2], and direct / constrained equation learning methods [16]. Because these models are designed to learn the appropriate macroscale behavior from an appropriate suite of ML approaches, the end result is frequently high-fidelity predictive ability from the generated network, but usually without the generation of an explicit macroscale equation for the process.…”

Section: Introductionmentioning

confidence: 99%

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Explicit physics-informed neural networks for non-linear upscaling closure: the case of transport in tissues

Taghizadeh,

Byrne,

Wood

2021

Preprint

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In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in a multiscale tissue. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space.Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are two outcomes of this work of particular note: 1) we find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometry of the two example tissue types; and 2) the approach results in an upscaled PDE with an effectiveness factor that is predicted (implicitly) via the trained neural network. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling

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Acceleration of PDE-Based Biological Simulation Through the Development of Neural Network Metamodels

Cited by 6 publications

References 42 publications

Diagnosis of Bronchial and Pulmonary Fungal Infection Using Gradient Weighted Denoising Algorithm-Based CT Images

Diagnosis of Bronchial and Pulmonary Fungal Infection Using Gradient Weighted Denoising Algorithm-Based CT Images

Determining the role of advection in patterning by bone morphogenetic proteins through neural network model-based acceleration of a 3D finite element model of the zebrafish embryo

Explicit physics-informed neural networks for non-linear upscaling closure: the case of transport in tissues

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