PRĀṆA–PD: A Prāṇa-Regulated Adaptive Network Architecture for Studying Multisystem Dysfunction and Functional Recovery in Parkinson's Disease

Satyavrat Nirala¹
Draft v2.0 for co-author, clinical and statistical review. Corresponding author and affiliations to be added.

Abstract

Background. Parkinson's disease (PD) is conventionally characterised by motor signs, yet respiratory, autonomic, gastrointestinal, bladder, speech and swallowing problems are common and strongly affect independence and quality of life. Formal frameworks that treat these domains as an interacting system, with individual profiles, are scarce. The Praśna Upaniṣad (III.3–III.12) describes five functionally distinct Prāṇas under the coordination of a principal Prāṇa, offering an organising scheme that can be translated into testable hypotheses.

Objective. To formalise the five-Prāṇa scheme as a measurable, falsifiable dynamical-systems model of multisystem function in PD, to specify an adaptive rehabilitation objective under safety constraints, and to test the model's computability and identifiability in simulation before any clinical use.

Methods. We replaced the untestable assumption that "Prāṇa approaches zero" with a bounded coordination reserve \(\rho\in[0,1]\). Five normalised functional-capacity variables \(\mathbf x(t)\) evolve according to \(\dot{\mathbf x}=[\mathbf A_L+\rho\mathbf A_C-\mathbf D]\mathbf x+\mathbf h+\mathbf B\mathbf u+\mathbf G\mathbf E+\mathbf w\), with \(\mathbf A_C\) a graph Laplacian over five hypothesised domain pairs, diagonal impairment \(\mathbf D\) calibrated to clinical scores, a seven-category intervention vector \(\mathbf u\), and a clinician-reviewed proportional controller with a quadratic objective \(J\) including a safety term. We simulated three illustrative profiles (motor-, autonomic/GI-, and speech/swallowing-dominant) under usual care, adaptive rehabilitation, and adaptive rehabilitation plus a hypothetical adjunct (200 seeds per cell, one intercurrent illness at week 20). We separately simulated cohorts with known coupling to test whether the coupling matrix can be recovered from noisy weekly measurements.

Results. The implementation was reproduced independently in TypeScript and Python (agreement to four decimals on nine deterministic scenarios). Under the placeholder input matrix, the adaptive arm lowered \(J\) by 49–60 % versus usual care and raised the weakest-domain capacity, with the largest safety benefit in the speech/swallowing profile (safety cost 7.27 → 0.25). The adjunct arm was indistinguishable from the adaptive arm because its assumed effect was set small. In synthetic cohorts, the sign of all five coupling links was recovered in every replicate; two links were approximately unbiased at \(n=200\), while three were overestimated by 60–90 %. Increasing \(\rho\) improved the weakest domain but lowered mean function, formalising the position that stronger coupling is not uniformly better.

Conclusions. PRĀṆA–PD is a computable and individualisable research hypothesis. The simulated benefits are consequences of assumed parameters and are not evidence of efficacy. Coupling estimation requires recorded disturbances, instrumental-variable correction and simulation-based calibration before real-data interpretation. An 18-month programme of measurement development, observational validation and feasibility testing is proposed. The model makes no claim to cure PD, to restore neurons, or to alter disease progression.

Keywords: Parkinson's disease; non-motor symptoms; dynamical systems; network physiology; rehabilitation; Ayurveda; Praśna Upaniṣad; control theory; identifiability.

1. Introduction

PD is associated with loss of dopaminergic neurons and altered circuit function, and it affects systems beyond movement, including olfaction, bowel and bladder function, blood-pressure regulation, speech and swallowing [1,2]. Two people with the same diagnosis can have strikingly different functional profiles; one may be limited mainly by gait, another by constipation and orthostatic symptoms, another by dysarthria and dysphagia. Guideline care recognises this through multidisciplinary input, including Parkinson's-specific physiotherapy, occupational therapy and speech-language therapy according to individual need [3]. What is lacking is a shared quantitative language that represents the interactions among domains and supports hypothesis-driven study of whether coordinated, individualised rehabilitation improves several domains together.

Classical Indian thought offers an organising vocabulary. In the Praśna Upaniṣad, Prāṇa assigns duties to the other vital functions, as a ruler assigns officials, and the text then distinguishes Prāṇa, Apāna, Samāna, Vyāna and Udāna by function [4]. We do not claim these are anatomical or neurological entities. We treat the scheme as a source of five functional domains and a coordination principle, each translated into variables that modern instruments can measure, and each open to refutation.

An earlier formulation proposed \(\lim\mathcal P(t)=0\) as disease advances. That statement cannot be tested as a description of PD, because Prāṇa is not an observable, and because PD does not degrade all systems uniformly. We therefore replaced it with a bounded, operationally defined coordination reserve and with domain-specific impairment, and we model selective disruption of both systems and their connections.

2. Theory

2.1 Domains and state variables

Five functional domains are defined, each with its own measurement set (Table 1). The state \(\mathbf x(t)\in[0,1]^5\) holds normalised capacities, where 1 is a chosen healthy reference and 0 the lower end of the assessment scale. They are research scores, not quantities of Prāṇa. Respiratory-sensory regulation (Prāṇa) is deliberately separated from speech, swallowing and airway protection (Udāna), to avoid counting overlapping respiratory measurements twice.

2.2 Master equation

Dynamics are written as

with \(\mathbf A_L=-\mathbf\Lambda\) (relaxation rates), \(\mathbf h=\mathbf\Lambda\mathbf 1\) (tonic homeostatic drive), \(\mathbf A_C\) the Laplacian of non-negative weights \(w_{ij}\) on five hypothesised pairs (Prāṇa–Udāna, Apāna–Samāna, Samāna–Vyāna, Vyāna–Udāna, Prāṇa–Vyāna), \(\mathbf D=\operatorname{diag}(d_i)\), \(d_i=\lambda_i s_i/(1-s_i)\), and \(s_i\in[0,1)\) the clinical impairment score. Three properties follow directly. (i) With \(\mathbf D=\mathbf 0\), \(\mathbf u=\mathbf 0\), \(\mathbf E=\mathbf 0\), the healthy state \(\mathbf x=\mathbf 1\) is an equilibrium. (ii) Because \(\mathbf A_C\mathbf 1=\mathbf 0\), coordination redistributes function between domains without creating or destroying it. (iii) With \(\rho=0\), an untreated domain settles at \(x_i^\ast=1-s_i\). The term \(\mathbf h\) is an explicit addition to the originally proposed form: without it the unforced system has only the trivial equilibrium \(\mathbf x=\mathbf 0\).

A dynamic coupling mask gives \(\mathbf A(t)=\mathbf A_L+\mathbf C(t)\odot\mathbf A_C-\mathbf D(t)\), allowing individual links to weaken independently. Excess synchronisation can itself be maladaptive, so the goal is regulated, not maximal, coupling.

2.3 Adaptive rehabilitation objective

Let \(\mathbf x^\ast=\mathbf x_0+g(\mathbf 1-\mathbf x_0)\) be an individualised target closing a fraction \(g\) of each domain's gap. At each review, \(\mathbf u=\operatorname{sat}[\mathbf K(\mathbf x^\ast-\hat{\mathbf x})]\), where \(\hat{\mathbf x}\) is the noisy measured state, \(\mathbf K=\kappa\,\mathbf B^{\top}/\bar b\) over six non-medical categories (medical care is held fixed by the treating clinician and is never driven by the controller), and \(\operatorname{sat}\) clips to the safe range \([0,1]\). Performance is

where \(\theta_i\) are clinical safety floors. \(\mathbf Q\), \(\mathbf R\), \(\lambda\) and \(\theta\) must be elicited from patients and clinicians; the defaults used here are placeholders.

3. Methods

3.1 Simulation

The system was integrated by Euler–Maruyama with step 0.1 week (process noise \(\sigma_w=0.01\), measurement noise \(\sigma_m=0.03\)), over 52 weeks with a review every four weeks, state clipped to [0,1]. Three illustrative profiles (impairment scores in Table 2) were run under (a) usual care (fixed background medical intensity 0.5, no adaptive layer), (b) adaptive rehabilitation, and (c) adaptive rehabilitation with a hypothetical Ayurvedic-adjunct channel whose effect size in \(\mathbf B\) is deliberately small. A single three-week intercurrent illness at week 20 acted through \(\mathbf G\mathbf E\). Coupling weights were 0.07–0.10 per week, \(\rho(0)=0.8\), declining 0.0005 per week. Each cell used 200 random seeds. All coefficients are illustrative and were not fitted to data.

3.2 Implementation checks

The model was implemented twice, in TypeScript (web simulator) and Python/NumPy (reference), by separate code paths. Nine noise-free scenarios (3 profiles × 3 arms) were compared on mean final capacity and total \(J\).

3.3 Identifiability experiment

We generated synthetic cohorts (\(n=60\) and \(200\); weekly measurements over 52 weeks; random patient-specific impairment, one recorded intercurrent illness per patient; process noise 0.02; measurement noise 0.015) with known coupling \(\rho w_{ij}\). The estimator regresses weekly state increments on interval-midpoint states with patient-specific own-decay, a shared coupling term per hypothesised pair, and the recorded disturbance as a regressor. Because measurement error in regressors biases ordinary least squares toward zero, regressors were instrumented with the state two time-points earlier (two-stage least squares in the spirit of Anderson and Hsiao [14]). Eight replicate cohorts were run per size. We report bias and spread without tuning to the truth.

4. Results

4.1 Implementation agreement

The two implementations agreed to four decimal places on all nine scenarios (e.g. profile B, usual care: mean final capacity 0.5459, \(J\)=17.3757 in both).

4.2 Adaptive rehabilitation versus usual care (simulation)

Relative to usual care, adaptive rehabilitation reduced total \(J\) by 51 % (A), 49 % (B) and 60 % (C). In every profile the weakest domain remained the originally most impaired one, and its final capacity stayed below 0.35, so the controller improved the profile without removing the principal deficit. The adaptive controller directed effort toward the most impaired domain's matching intervention category (movement for A, nutrition for B, speech/swallowing for C), the individualisation the model is intended to capture. The adjunct arm was indistinguishable from adaptive rehabilitation (profile A: 7.40 vs 7.40, within one SD; B: 9.99 vs 10.07, within about 0.6 SD; C: 9.29 vs 9.28). This is not a finding about Ayurvedic adjuncts. It follows from the small adjunct effect assumed in \(\mathbf B\), and it shows that, with plausible effect sizes and measurement noise, an add-on of this magnitude would be hard to detect in a feasibility-scale study.

4.3 Coordination reserve

Steady-state analysis under usual care showed a trade-off. For profile A, increasing \(\rho\) from 0 to 1 raised the weakest-domain capacity from 0.278 to 0.373 and lowered mean capacity from 0.706 to 0.654. Profiles B and C showed the same direction with smaller magnitude. This is expected from the Laplacian structure and formalises the principle that coordination is useful for the weakest links but is not a general amplifier.

4.4 Identifiability of coupling

The identification route was developed iteratively on this simulator, and the steps are informative. A naïve pooled least-squares estimator recovered coupling strengths that were severely biased: omitting patient-specific own-decay and omitting the recorded disturbance biased the estimates, and measurement noise drove ordinary least squares toward zero (estimates near 0 or negative). Adding patient-specific decay, the recorded disturbance and instrumental variables recovered the correct sign for all links; two links became approximately unbiased. A systematic upward bias of 60–90 % in three links did not resolve with sample size and its cause is not established. Candidate causes include discretisation of the weekly interval, the interaction between instrumentation and the strong common disturbance, and boundary clipping. We therefore treat the estimator as a prototype and recommend that any real-data estimate be accompanied by a simulation-based calibration run under the study's own sampling design.

5. Discussion

What the model offers. It converts a qualitative five-function scheme into a bounded, computable system with domain-specific impairment, explicit couplings that can be switched off one at a time, and an auditable objective that trades functional gain against burden and safety. It is individualisable by construction: the same equations produce different priorities for the motor-, autonomic- and speech-dominant profiles.

What it does not show. The superiority of adaptive rehabilitation in Table 2 is built into the placeholder \(\mathbf B\); it demonstrates that the controller allocates effort sensibly given an assumed response, not that any intervention works. Evidence for exercise and multidisciplinary rehabilitation in PD comes from clinical trials and guidelines [3,5,6], not from this model.

Ayurvedic constructs. Vata, Pitta, Kapha, Agni, Āma, Dhātu and Ojas are proposed as a second layer, entered only if standardised definitions with acceptable inter-rater reliability are achieved, and only to test whether they improve prediction beyond conventional measures, with each variable measured independently of the domain scores. Evidence regarding specific preparations is limited: a 2025 systematic review identified five clinical trials of Mucuna pruriens in PD (108 participants) with methodological limitations [8], and the plant is a source of levodopa, so it interacts with prescribed medication. Some Ayurvedic products have contained harmful quantities of lead, mercury or arsenic [13]. For these reasons the proposed protocol limits complementary practices to non-ingestible, supervised mind–body and movement approaches during feasibility testing and excludes L-DOPA-containing and unbatched-tested products.

5.1 Limitations

• All parameters are placeholders; none has been estimated from patient data.
• The five-domain structure, the pair list and the state-space form are hypotheses. Alternatives (more domains, nonlinear couplings, hidden states, medication-cycle effects such as ON/OFF fluctuations) are not modelled.
• Normalised domain scores require validation, including how different instruments are combined into one \(x_i\).
• Identifiability was assessed only under the model's own assumptions with weekly sampling; real clinic data are sparser and noisier.
• Safety is represented by a smooth penalty; it does not replace clinical judgement or stopping rules.
• Simulated treatment effects are not predictions.

5.2 Proposed validation programme

An 18-month programme is proposed (details in the clinical protocol): conceptual and measurement development; a pilot observational study to test reliability and inter-domain associations; mathematical validation including estimation of \(\rho\), \(\mathbf A_C\) and \(\mathbf D\) with simulation-based calibration; a feasibility phase for standardised complementary practices added to usual care; and independent review before any randomised study. Six hypotheses (H1–H6) are pre-specified: reliable operationalisation (H1); domain–symptom associations (H2); incremental value of coordination measures (H3); benefit of individualised rehabilitation (H4); incremental benefit of standardised adjuncts (H5); and superior prediction of individual outcomes versus a conventional baseline (H6). Eighteen months cannot establish disease modification or long-term neuroprotection.

6. Conclusion

PRĀṆA–PD offers a falsifiable, individualisable formulation of multisystem function in PD that respects the distinction between symptom relief, functional restoration and disease modification. It is a hypothesis-generating framework. Its value will be determined by whether its domains can be measured reliably, whether its couplings can be estimated honestly, and whether coordinated rehabilitation guided by it improves outcomes that matter to people living with PD.

Data and code availability

All simulation code (TypeScript model, Python reference implementation, Monte-Carlo and identifiability scripts, and result files) is available on the Code page. No patient data were used.

Conflict of interest and ethics

To be completed. No human participants were involved in the work reported here. The proposed studies require approval from an institutional ethics committee and prospective registration (e.g. CTRI in India or ClinicalTrials.gov).

References

Verify every citation against the source before submission. They were compiled from the model document, published guidance and the authors' knowledge of the literature.

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