Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries

Adaptive-neuro-fuzzy-inference-system model for prediction of ultimate load of rectangular concrete-filled steel tubular columns

This study is devoted to the development of an Adaptive-Neuro-Fuzzy-Inference-System (ANFIS) model for the prediction of ultimate load of rectangular concrete-filled steel tubular structural members. The learning process of the model is performed by conducting a combination of backpropagation gradient descent and least-squares techniques. The performance of the model is examined by several quality metrics such as coefficient of determination (R2), Root-Mean-Squared-Error (RMSE), Mean-Absolute-Error (MAE), Index of Agreement (IA) and Slope of linear regression. Monte Carlo random sampling technique is employed to propagate input variations to the output response. Moreover, the performance of ANFIS is also compared with other machine learning models including Artificial Neural Network (ANN), Support Vector Machine (SVM), Gaussian Process Regression (GPR) and Ensemble. Results show that the ANFIS model yields higher prediction performance than other machine learning models, for both training and testing data points and regarding all quality metrics. For instance, using training data points, the ANFIS model exhibits a RMSE of 0.0283 compared to 0.0342, 0.0588, 0.0291, and 0.0464 using ANN, Ensemble, GPR, and SVM, respectively (the corresponding gain values are+17.3%,+51.9%,+2.8%, and+39.0%, respectively). On the other hand, using testing data points, the ANFIS model exhibits a RMSE of 0.0276 compared to 0.0393, 0.0987, 0.0403, and 0.0460 using ANN, Ensemble, GPR, and SVM, respectively (the corresponding values of gain are+29.8%,+72.1%,+31.5%, and+40.0%, respectively). The same observation can be made for other quality metrics. It can be concluded that the ANFIS model outperforms other models for both training and testing datasets. The ANFIS model is also compared with existing works in the past, showing its improvement in prediction results. Finally, sensitivity analysis is performed to determine the degree of effect of the input parameters on the ultimate load.

Uncertainty quantification of TMS simulations considering MRI segmentation errors

OBJECTIVE

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy.

APPROACH

The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field.

MAIN RESULTS

Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter, compartments. In contrast, E-field predictions are highly sensitive to possible CSF segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and white matter interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates.

SIGNIFICANCE

The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors.

Uncertainty quantification of TMS simulations considering MRI segmentation errors

OBJECTIVE

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy.

APPROACH

The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field.

MAIN RESULTS

Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter, compartments. In contrast, E-field predictions are highly sensitive to possible CSF segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and white matter interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates.

SIGNIFICANCE

The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors.