Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning
Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-12-01
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| Series: | NeuroImage |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1053811922008266 |
| _version_ | 1811187336438874112 |
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| author | Hongming Li, PhD Zhi-De Deng, PhD Desmond Oathes, PhD Yong Fan, PhD |
| author_facet | Hongming Li, PhD Zhi-De Deng, PhD Desmond Oathes, PhD Yong Fan, PhD |
| author_sort | Hongming Li, PhD |
| collection | DOAJ |
| description | Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed. |
| first_indexed | 2024-04-11T14:00:32Z |
| format | Article |
| id | doaj.art-6f6feaf5c8f94072b1fd60a4583f6425 |
| institution | Directory Open Access Journal |
| issn | 1095-9572 |
| language | English |
| last_indexed | 2024-04-11T14:00:32Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | NeuroImage |
| spelling | doaj.art-6f6feaf5c8f94072b1fd60a4583f64252022-12-22T04:20:08ZengElsevierNeuroImage1095-95722022-12-01264119705Computation of transcranial magnetic stimulation electric fields using self-supervised deep learningHongming Li, PhD0Zhi-De Deng, PhD1Desmond Oathes, PhD2Yong Fan, PhD3Center for Biomedical Image Computation and Analytics, Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USAComputational Neurostimulation Research Program, Noninvasive Neuromodulation Unit, Experimental Therapeutics & Pathophysiology Branch, National Institute of Mental Health, NIH, MD 20892, USACenter for Neuromodulation in Depression and Stress, Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USACenter for Biomedical Image Computation and Analytics, Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA; Corresponding author.Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed.http://www.sciencedirect.com/science/article/pii/S1053811922008266Self-supervised learningDeep neural networksElectric field modelingTMS |
| spellingShingle | Hongming Li, PhD Zhi-De Deng, PhD Desmond Oathes, PhD Yong Fan, PhD Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning NeuroImage Self-supervised learning Deep neural networks Electric field modeling TMS |
| title | Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning |
| title_full | Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning |
| title_fullStr | Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning |
| title_full_unstemmed | Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning |
| title_short | Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning |
| title_sort | computation of transcranial magnetic stimulation electric fields using self supervised deep learning |
| topic | Self-supervised learning Deep neural networks Electric field modeling TMS |
| url | http://www.sciencedirect.com/science/article/pii/S1053811922008266 |
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