Скачать или смотреть Stochastic Modeling of Post-Stroke Memory Recovery Using Weekly Memory Data (No.1398, 10/20/2025)

Stochastic Modeling of Post-Stroke Memory Recovery Using Weekly Memory Data (No.1398, 10/20/2025)

Gerald C. Hsu
EclaireMD Foundation

Category: Methodology

his article presents a stochastic probability analysis of memory recovery following a hemorrhagic stroke on June 21, 2025. It evaluates post-stroke recovery patterns using probability theory, contrasting with the author's deterministic Viscoplastic Energy Theory (VMT) and Topological Data Analysis (TDA) models. The dataset spans 17 weeks of daily memory tests, comprising 140 trials per week. It includes one output variable (percentage of correct answers) and five input variables: Systolic Blood Pressure (SBP), Pulse Pressure (PP), Heart Rate (HR), Sleep Hours, and Walking Steps.

Stochastic analysis frames recovery as a probabilistic process influenced by complex neural, vascular, and behavioral factors. Each weekly result is modeled as a Binomial process, x ∼ Binomial(n=140, p), where p is the probability of success. This approach is sound as each test item represents a Bernoulli trial. A Bayesian framework was used to update the unknown probability p weekly. Assuming an uninformative prior Beta(1, 1), the posterior distribution becomes p | x ∼ Beta(α = 1 + x, β = 1 + n − x). From this, the posterior mean E[p] and variance Var[p] are calculated, allowing for the computation of probabilities exceeding recovery thresholds, such as P(p ≥ 0.95). Sustained recovery was defined as p ≥ 0.95 for four consecutive weeks.

A logistic regression was applied to the weekly posterior mean probabilities to identify contributors among the five input variables: logit(p_week) = β₀ + β₁·SBP + β₂·PP + β₃·HR + β₄·SleepH + β₅·Steps. This hybrid model quantifies uncertainty while identifying influential factors.

The Bayesian posterior probabilities revealed a clear transition from uncertainty to stability. The probability of sustained recovery, P(p ≥ 0.95), rose from 0.00 at Week 1 to 0.97 by Week 7 and 0.999 by Week 9, when memory test scores reached 100%. This indicates high certainty of sustained recovery from Week 7 onward. The logistic regression confirmed that walking activity was the strongest correlate with memory improvement. Heart rate showed a mild positive correlation, while SBP and PP had minimal influence. The model demonstrated a moderate fit (McFadden R² = 0.17) and good accuracy (Brier score = 0.068).

The stochastic model’s findings confirm what was already apparent from visual data inspection and deterministic analyses using VMT and TDA: a monotonic rise in recovery probability reaching stability by Week 9. The model’s strength lies in formally quantifying the reduction in uncertainty and providing clear probability thresholds for recovery. However, it did not reveal new insights beyond those identified through intuitive pattern recognition and prior deterministic methods. The practical conclusions remained similar, despite the model’s higher computational complexity.

In conclusion, the stochastic analysis provides a robust probabilistic complement to deterministic models within the GH-Method: Math-Physical Medicine framework. The posterior probability of full recovery (p ≥ 0.95) transitioned from near zero to near certainty by Week 9, with walking activity being the most significant behavioral correlate. While theoretically elegant, the stochastic model primarily validated and quantified conclusions already reached through other methods. It offers a valuable quantitative language for expressing certainty in recovery, reflecting how the brain's neural reorganization gradually moves from randomness to stable function. This work reflects an intellectual journey from mathematics and engineering to medicine, applying concepts studied decades ago to the author's own biomedical recovery.

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