A formalism for sequential estimation of neural membrane time constant and input–output curve towards selective and closed-loop transcranial magnetic stimulation <sup>*</sup>
Bibliographic record
Abstract
Abstract Objective. To obtain a formalism for real-time concurrent sequential estimation of neural membrane time constant and input–output (IO) curve with transcranial magnetic stimulation (TMS). Approach. First, the neural membrane response and depolarization factor, which leads to motor evoked potentials with TMS are analytically computed and discussed. Then, an integrated model is developed which combines the neural membrane time constant and IO curve. Identifiability of the proposed integrated model is discussed. A condition is derived, which assures estimation of the proposed integrated model. Finally, sequential parameter estimation (SPE) of the neural membrane time constant and IO curve is described through closed-loop optimal sampling and open-loop uniform sampling TMS. Without loss of generality, this paper focuses on a specific case of commercialized TMS pulse shapes. The proposed formalism and SPE method are directly applicable to other pulse shapes. Main results. The results confirm satisfactory estimation of the membrane time constant and IO curve parameters. By defining a stopping rule based on five times consecutive convergence of the estimation parameters with a tolerances of 0.01, the membrane time constant and IO curve parameters are estimated with 82 TMS pulses with absolute relative estimation errors (AREs) of less than 4% with the optimal sampling SPE method. At this point, the uniform sampling SPE method leads to AREs up to 16%. The uniform sampling method does not satisfy the stopping rule due to the large estimation variations. Significance. This paper provides a tool for real-time closed-loop SPE of the neural time constant and IO curve, which can contribute novel insights in TMS studies. SPE of the membrane time constant enables selective stimulation, which can be used for advanced brain research, precision medicine and personalized medicine.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".