Sri Amit Ray’s 36 Hours Ekadashi Fasting Protocol: A Mathematical Model

Ekadashi fasting, a biweekly practice rooted in ancient Vedic traditions and aligned with lunar cycles, has been reinterpreted through modern scientific lenses by Sri Amit Ray. This review examines Ray’s mathematical model, which employs impulsive differential equations to quantify the impacts of periodic 36-hour fasts on key aging biomarkers, including autophagy flux, mitochondrial quality, reactive oxygen species (ROS) levels, and NAD⁺/NADH ratios.

The model highlights an optimal fasting window of 120°–132° lunar elongation for the waxing phase (Shukla Paksha) and 300°–312° for the waning phase (Krishna Paksha), with an extended practical range of ±12° (108°–144° and 288°–324°, respectively) to accommodate preparation, core fasting, and gentle breaking phases. Simulations over 365 days demonstrate that biweekly fasting induces autophagy spikes, enhances mitochondrial integrity by approximately 22%, reduces ROS by 18%, and elevates NAD⁺/NADH ratios by 1.4-fold, promoting metabolic resilience and healthy aging.

Abstract | 1. Introduction | 2. Background on Ekadashi Fasting | 3. Scientific Basis of Lunar Alignment in Fasting | 4. The Mathematical Model | 5. Autophagy Dynamics and Timeline | 6. Benefits of the 36-Hour Fasting Protocol | 7. Discussion | 8. Conclusion | References

The 36-hour protocol aligns with autophagy activation timelines, peaking in mitophagy between 24–36 hours, and offers benefits such as improved insulin sensitivity, lipid metabolism, and neuroprotection, as supported by empirical studies. Integrating chronobiology, gerontology, and Vedic spirituality—particularly the activation of Vaikuntha chakras in Ray’s 114-chakra system—this model bridges traditional practices with quantitative biology. Limitations include assumptions of biological uniformity and the need for longitudinal human trials. Future directions involve stochastic extensions and AI-driven personalization for precision chrononutrition.

1. Introduction

Healthy aging, defined as the preservation of physiological function and minimization of age-related diseases, represents a paramount challenge in contemporary biomedicine. Intermittent fasting (IF), a dietary regimen involving periodic caloric restriction, has garnered substantial attention for its potential to extend lifespan and mitigate degenerative processes across species. Rooted in evolutionary biology, IF mimics ancestral feast-famine cycles, triggering adaptive cellular responses such as autophagy—the lysosome-mediated degradation of damaged organelles and proteins—which counters cellular senescence and oxidative stress.

Among IF variants, Ekadashi fasting stands out as a culturally embedded practice from Vedic traditions, observed biweekly on the 11th lunar day (tithi) following new and full moons. Sri Amit Ray, a proponent of integrating ancient wisdom with modern science, has advanced a “scientific Ekadashi fasting” framework that aligns fasting with lunar gravitational influences on human physiology.

In his model, detailed in “Ekadashi Fasting and Healthy Aging: A Mathematical Model” (2025), Ray employs impulsive differential equations to simulate the discrete metabolic perturbations induced by 36-hour fasts, quantifying their cumulative effects on longevity markers.

This review synthesizes Ray’s contributions, elucidating the logical underpinnings of the optimal lunar windows (core: 120°–132° waxing/300°–312° waning; extended: 108°–144°/288°–324°), the mathematical formalism, autophagy dynamics, and the physiological benefits of the 36-hour protocol.

Drawing from verified empirical studies, we explore how this model bridges chronobiology, autophagy research, and spiritual dimensions, such as the activation of higher-dimensional chakras in Ray’s system. By providing a rigorous, quantitative lens, Ray’s work offers a foundation for empirical validation and personalized interventions in gerontology.

2. Background on Ekadashi Fasting

Ekadashi, derived from Sanskrit “ekadasi” (eleventh), refers to the 11th tithi in both Shukla Paksha (waxing moon) and Krishna Paksha (waning moon) of the Hindu lunar calendar, occurring approximately 24 times annually. Traditionally dedicated to Lord Vishnu, the fast aims at spiritual purification, sin expiation, and moksha (liberation). Practitioners abstain from grains, legumes, and often water (Nirjala variant), focusing on meditation, mantra chanting, and charity.

Sri Amit Ray reframes Ekadashi as “scientific fasting,” emphasizing its synchronization with lunar cycles for physiological optimization. In his tradition, it activates Vaikuntha chakras—higher-dimensional energy centers in a 114-chakra system—facilitating transcendence beyond the seven conventional chakras. Ray posits that fasting during specific lunar elongations minimizes gravitational stress influence on body fluids (comprising 60–70% water), enhancing detoxification and mental clarity.

Empirically, IF protocols like Ekadashi correlate with reduced inflammation, improved metabolic flexibility, and longevity. Studies on caloric restriction (CR) and IF demonstrate mTOR inhibition, AMPK activation, and sirtuin upregulation, mechanisms central to Ray’s model. For instance, periodic fasting extends lifespan in model organisms by 20–30% through autophagy enhancement. Ray’s innovation lies in incorporating lunar periodicity as an infradian rhythm modulator, hypothesizing evolutionary adaptations to tidal forces. This background sets the stage for the model’s lunar logic and mathematical structure. 

3. Scientific Basis of Lunar Alignment in Fasting

The lunar cycle, spanning 360° synodic elongation (Sun-Moon angular separation from Earth), influences terrestrial biology through gravitational tides. Each tithi approximates 12°; Ekadashi aligns with ~120° post-new moon (waxing) or ~300° post-full moon (waning), positions of balanced low lunar pull. Ray’s core optimal window—120°–132° (waxing) and 300°–312° (waning)—coincides with minimal atmospheric pressure, reducing digestive strain and cortisol spikes while optimizing serotonin-melatonin balance for introspection.

The extended ±12° range (108°–144° waxing; 288°–324° waning) accommodates a 36-hour protocol: preparation in late Dashami (~108°–120°/288°–300° evening), core Ekadashi (~120°–132°/300°–312°), and gentle break in early Dwadashi (~132°–144°/312°–324° morning). Logically, this symmetry maintains a 5-tithi offset from new/full moon peaks, where gravitational extremes could exacerbate metabolic stress.

Mathematically, efficacy peaks at midpoint (126°/306°): \( E(\theta) = k \cdot \sin(\theta / 2) \cdot e^{-\alpha (\theta – 126^\circ)^2} \), with Gaussian decay extending benefits to ±12° for practical alignment.

Studies support lunar effects: altered sleep/melatonin during full moons, menstrual synchronization, and mood fluctuations. In fasting, this window amplifies autophagy by 18–22% via reduced inflammation, as low-pressure phases redirect energy from digestion to repair. For waning, the 360° minus waxing offset ensures equivalence, aligning with chronobiology’s infradian rhythms. This logic integrates astrophysics with physiology, validating Ray’s model for enhanced fasting outcomes. 

4. The Mathematical Model

Ray’s model uses impulsive differential equations to capture periodic fasting “impulses” within continuous biological dynamics. Six state variables are modeled: autophagy activity \(A(t)\), mitochondrial quality \(M(t)\), ROS \(R(t)\), SIRT1 activity \(S(t)\), insulin sensitivity \(I(t)\), and NAD⁺/NADH ratio \(N(t)\). Impulses occur at \(t_k = 14.8k\) days (biweekly lunar half-cycle).

The governing equations are:

$$ \frac{dA}{dt} = -\beta_1 A(t) + \sum_{k=0}^N F_k \delta(t – t_k) $$ $$ \frac{dM}{dt} = \alpha_2 A(t) – \gamma_2 R(t) – \beta_2 M(t) $$ $$ \frac{dR}{dt} = \rho_1 M(t) – \rho_2 A(t) – \beta_3 R(t) $$ $$ \frac{dS}{dt} = \theta_1 N(t) – \beta_4 S(t) $$ $$ \frac{dI}{dt} = \xi_1 – \xi_2 R(t) – \beta_5 I(t) $$ $$ \frac{dN}{dt} = -\lambda_1 N(t) + \lambda_2 F(t) – \lambda_3 S(t) $$

Where \(F(t) = \sum F_k \delta(t – t_k)\) and \(F_k = F_0 = 0.5\). At impulses: \(A(t_k^+) = A(t_k^-) + F_0\).

Parameters (e.g., \(\beta_1 = 0.1\), \(\alpha_2 = 0.05\)) are biologically derived. Solved via 4th-order Runge-Kutta (\(\Delta t = 0.1\)) over 365 days, simulations show autophagy spikes decaying with half-life ~6.9 days, leading to cumulative improvements. This formalism quantifies how lunar-aligned impulses enhance resilience, distinguishing Ray’s model from steady-state approaches. (Approximately 650 words)

5. Autophagy Dynamics and Timeline

Autophagy, modeled as \(A(t) \propto \frac{1}{1 + mTOR(t)}\), activates progressively during fasting. Ray’s timeline:

• 0–12 hours: Minimal; glycogen depletion, \(AMPK(t) = k_1 \log(t+1)\) initiates.
• 12–24 hours: Early flux; mTOR decline, \(LC3-II(t) = k_2 (1 – e^{-t/\tau})\).
• 24–36 hours: Peak mitophagy; \(\beta-HB(t) = k_3 (t – T_{th})^n\) enhances sirtuins.
• 36–48 hours: Plateau; \(p53(t) = k_4 t e^{-t/T_c}\) adapts survival.
• Beyond 48 hours: Shift to conservation, risking excess.

In Ekadashi’s 36-hour window, core fasting hits peak flux, clearing misfolded proteins and boosting immunity. Crosstalk with gene expression (e.g., *ulk1*, *lc3b*) modeled via integrals in related studies supports non-linear accumulation. Ray ties this to spiritual bliss via anandamide modulation.

6. Benefits of the 36-Hour Fasting Protocol

The 36-hour protocol, spanning extended lunar windows, maximizes autophagy without excess. Studies show fourfold BHB rise (0.14 to 0.66 mM/L), enhancing epigenetics, mitochondrial biogenesis, and anti-inflammation. Weight loss (12.1% over 82 weeks), improved insulin sensitivity (-2% glucose, -3.4% HbA1c), and lipid profiles (-47% LDL) occur without RMR decline.

Scientific studies observed that fasting vastly remodels the plasma lipidome and markedly alters the concentrations of several lipid species. These changes in lipid metabolism for 36 hours fasting have important implications for the management of cardiometabolic health and healthy aging [25]

7. Discussion

Ray’s model innovatively quantifies lunar-fasting synergy but assumes uniform responses; stochastic elements could address variability. Empirical validation needed via RCTs tracking biomarkers in lunar aligned vs. non-aligned IF. Integration with gut microbiota or immune models enhances scope. Spiritually, Vaikuntha chakra activation offers holistic appeal, bridging science and tradition.

Limitations:

Simplified interactions overlook sex/age differences; adverse effects like hunger in prolonged fasts warrant caution. Future AI-personalization could optimize windows for precision health. We performed a simulation study with a single fasting episode and very limited data.  Hence, future studies over a more extended period of time are required to detail the entire spectrum of potentially beneficial effects of the Ray 36 hours Ekadashi biweekly fasting.

8. Conclusion

Sri Amit Ray’s model elucidates Ekadashi fasting’s potential in healthy aging, merging impulsive equations with lunar chronobiology. The 108°–144°/288°–324° windows optimize 36-hour protocols for autophagy peaks and metabolic benefits, supported by simulations and studies. This review underscores its promise for longevity, urging further research to validate and refine for global application.