Proposed research model · Version 2.0

PRĀṆA–PD

Prāṇa-Regulated Adaptive Network Architecture for Parkinson's Disease. An integrative mathematical model, inspired by the Praśna Upaniṣad and Ayurvedic principles, for studying multisystem dysfunction and functional recovery in Parkinson's disease (PD).

1. One fundamental correction: Prāṇa does not "approach zero"

The original proposal states

This is philosophically interesting, but it cannot be established as a biological description of Parkinson's disease. Praśna Upaniṣad III.4–III.7 describes the principal Prāṇa as assigning functions to the other Prāṇas, like a king appointing officials. We keep that coordination principle as the philosophical foundation and replace the untestable limit with a measurable quantity: the Prāṇa-inspired physiological coordination reserve

• \(\rho=1\): reference level of coordinated physiological functioning.
• \(0<\rho<1\): reduced coordination relative to the reference.
• \(\rho=0\): theoretical loss of the measured coordination under study. It is not the disappearance of Prāṇa and not the death of the patient.

PD does not necessarily degrade all systems together. Some people have prominent motor difficulty, others prominent gastrointestinal, autonomic, sleep or speech problems. So the model describes selective disruption of individual systems and of their connections, rather than assuming one global factor decays to zero.

2. The five-Prāṇa physiological architecture

The five-dimensional state vector is retained, but each component is an estimated functional state with its own measurable indicators, never the literal quantity of a subtle energy.

3. The five-system mathematical model

Let \(\mathbf x(t)\in[0,1]^5\) be normalised functional capacity: 1 is a selected healthy reference, 0 is the lower endpoint of the defined assessment scale. These are research scores, not physiological quantities of Prāṇa.

3.1 The central equation

The original \(\dot{\mathbf\Psi}=\mathcal P\mathbf A\mathbf\Psi+\mathbf E(t)\) is expanded to:

Three distinct phenomena are modelled: (1) individual system function, (2) coordination between systems, (3) response to therapeutic and environmental influences.

3.2 The 5 × 5 coupling matrix

Instead of assuming independent Prāṇas, we investigate their relationships. The off-diagonal entries are hypothesised and must be identified from longitudinal data, never assigned arbitrarily.

\(\mathbf C(t)\) is a dynamic coupling matrix and \(\odot\) is element-wise multiplication, so one connection can deteriorate while another stays preserved.

4. The central nervous system as a regulatory network

A sixth concept is added so that the five-Prāṇa framework connects to modern neurology without claiming Prāṇa is a neurological structure.

Central research question: can measurable changes in neurological network function help explain differences in coordination between the five physiological domains? This can be investigated with neurological examination, autonomic testing, gait analysis, physiological recordings and, in suitable research settings, neuroimaging.

5. The disease-disruption model

\(d_1\ldots d_5\) are the Prāṇa, Apāna, Samāna, Vyāna and Udāna domain impairments, each estimated from clinical measurement. Example: a patient with marked constipation and urinary urgency, preserved mobility and no swallowing difficulty may show \(d_2>d_4\) and \(d_5\approx 0\). That means the Apāna-related domain has greater measured impairment than the Udāna-related domain. It does not mean one Prāṇa is biologically depleted.

5.1 Individualised patient profiles (illustrative, invented to demonstrate the method)

Higher score = greater impairment. These are not clinical assessments. They are the same profiles preloaded in the Sākṣī clinician view and the simulator.

A single treatment plan or intervention score would not represent these differences, which is why a personalised functional model is worth investigating.

6. The recovery model: from disease management to functional restoration

Three goals must be kept separate: (1) improving symptoms; (2) restoring functional ability and independence; (3) preventing or reversing the underlying neurodegeneration. The first two can be pursued through established treatment and rehabilitation. The third remains an unsolved research problem, and there is currently no established cure for PD. We therefore define recovery as:

Regaining, maintaining or improving physiological function and quality of life, even when the underlying disease remains present.

6.1 Target vector and intervention vector

Each component is a clinician-approved intervention category, not a dose or prescription.

6.2 Adaptive intervention equation

\(\mathbf K\): intervention-response relationship. \(\hat{\mathbf x}\): estimated state. \(\operatorname{sat}\): safety constraint on intensity. In practice: measure, identify the key difficulties, build a multidisciplinary plan, measure the response, adjust with the treating professionals. This is a research control-system design. It must not independently change PD medication, exercise intensity or herbal treatments. In the executable model the medical channel is fixed by the clinician and the controller is never allowed to move it.

6.3 Recovery objective

\(\mathbf Q\) prioritises patient-important outcomes, \(\mathbf R\) penalises intervention burden, \(S\) is safety risk, \(\lambda\) is the weight on safety. In plain language: maximise meaningful functional improvement while minimising treatment burden and safety risk. The weights must be elicited from clinicians and patients, not chosen arbitrarily.

7. Interventions for each Prāṇa domain

Established PD care is kept separate from traditional practices that still need evaluation.

8. Ayurvedic variables: a second layer

These are traditional assessment constructs that need standardised definitions and reliability testing before they can enter a model. Two levels result: the five Prāṇas (functional systems and their coordination) and the seven Ayurvedic constructs (individualised traditional assessment and therapeutic context). Vata and the Apāna functional score may be associated, but they remain independently measured variables. The scientific test is whether Ayurvedic assessment improves prediction beyond conventional neurological and functional measures.

9. The PRĀṆA–PD measurement dashboard

Analysis: correlation and multivariate regression; longitudinal mixed-effects models; dynamic network analysis; state-space modelling; Bayesian inference; machine learning with independent validation. The same patient should be assessed under consistent medication timing and testing conditions so that normal fluctuations are not mistaken for improvement or deterioration. The Sākṣī app is the prototype capture instrument: it pairs measured and reported scores for each domain and surfaces discordance without labelling it "poor awareness".

10. How to prove whether the model works

Indicative study-planning timeline, not a completed or approved clinical trial.

1. Months 1–3 · Textual and scientific foundations. Review the Praśna Upaniṣad, Ayurvedic concepts and the current PD literature. Define each mapping and its limits.
2. Months 4–6 · Measurement development. Build the five-domain instrument. Review by Ayurvedic experts, neurologists, physiotherapists and measurement scientists.
3. Months 7–9 · Pilot observational study. Repeated clinical measurements in people with PD. Inter-domain associations and reliability.
4. Months 10–12 · Mathematical validation. Estimate the coupling matrix, coordination reserve and impairment parameters. Test reproducibility and prediction.
5. Months 13–15 · Intervention feasibility. Feasibility, adherence and safety of adding standardised complementary practices to usual care.
6. Months 16–18 · Independent review and trial design. Prepare a larger randomised controlled study if justified.

Eighteen months can support model and feasibility development. It cannot prove disease reversal or long-term neuroprotection.

11. Five scientific contributions the model could pursue

12. Final scientific architecture: three layers

The final master equation

subject to \(0\le\rho(t)\le1\), \(\mathbf x(t)\in\mathcal X_{\text{safe}}\), and the individualised objective

13. What has been built, and what the numbers do and do not show

14. The three deliverables, built

The aim is to help people living with Parkinson's regain and preserve as much physical, cognitive, social and functional independence as possible. The five-Prāṇa framework is offered as a research hypothesis for studying that aim. Any claim that it cures PD, restores lost neurons or reverses disease progression must wait for convincing clinical evidence.