Ekadashi Fasting and Healthy Aging: A Mathematical Model

Ekadashi fasting, a biweekly practice aligned with lunar cycles, offers a unique model for studying chronobiology in healthy aging. This study develops a mathematical framework using impulsive differential equations to quantify its effects on aging biomarkers, including autophagy, mitochondrial quality, reactive oxygen species (ROS), and NAD⁺/NADH ratio. Simulations over 365 days reveal that 36-hour fasts every 14.8 days induce autophagy spikes, increase mitochondrial quality by ~22%, reduce ROS by ~18%, and elevate NAD⁺/NADH ratios by 1.4-fold, enhancing metabolic resilience.  In the tradition of Sri Amit Ray, there are 114 chakras in human body, Ekadashi fasting is associated with the Vaikuntha Chakras, which exist in the 11th dimensions of spirituality. 

These findings suggest Ekadashi fasting may delay aging and reduce disease risk, bridging traditional practices with modern gerontology. The model provides a foundation for empirical studies and personalized longevity strategies in chrononutrition.

Molecular Mechanisms | Dietary Influences | Ekadashi Chakras & Spirituality | Fasting Protocol | Mathematical Model | Autophagy Dynamics | Mitochondrial & ROS |  NAD⁺/NADH |

1. Introduction

Healthy aging, characterized by the maintenance of physiological function and reduced disease burden with advancing age, is a central goal of biomedical research [1]. Intermittent fasting (IF) has emerged as a promising lifestyle intervention to promote metabolic health, enhance cellular quality control, and extend lifespan across diverse species [1–3]. Ekadashi fasting, a traditional practice observed on the 11th day after the full and new moon, introduces a biweekly rhythm aligned with lunar cycles, offering a culturally ingrained framework for studying chronobiology in aging [4]. Unlike continuous caloric restriction, Ekadashi’s periodic 36-hour fasts may amplify metabolic stress and recovery cycles, potentially optimizing cellular maintenance and longevity [3].

Despite growing evidence supporting the benefits of fasting, including improved metabolic flexibility and reduced oxidative stress [2, 5], the mechanistic interplay of circadian biology, autophagy, and metabolic resilience remains underexplored. Mathematical modeling provides a powerful tool to elucidate these complexes, interacting biological systems. Impulsive differential equations, in particular, are well-suited to capture the discrete metabolic “jumps” induced by periodic fasting within continuous physiological dynamics [6].

This study proposes a comprehensive mathematical model to quantify the effects of Ekadashi fasting on key aging biomarkers, including autophagy flux, NAD⁺/NADH ratio, mitochondrial integrity, and reactive oxygen species (ROS) levels. We hypothesize that the timing and frequency of Ekadashi fasting synchronize with endogenous circadian and infradian rhythms to enhance autophagic flux and metabolic resilience, ultimately promoting healthy aging. By integrating traditional fasting cycles with modern quantitative approaches, this model bridges cultural practices with biological understanding, offering a foundation for personalized longevity strategies.

Ekadashi Fasting, 114 Chakras and Spirituality

In the tradition of Sri Amit Ray, the human body contains 114 chakras—energy centers that govern physical, mental, and spiritual well-being. Among these, the Vaikuntha Chakras are a set of highly evolved spiritual chakras that exist beyond the traditional seven dimensions of spirituality, serving as gateways to divine transcendence and cosmic consciousness. In Ray 114 chakras system, the activation of Vaikuntha chakras is connected with the timeless aspects of Viraja River.  Ekadashi fasting is often associated with the spiritual anandamide bliss meditation [22]. 

Ekadashi fasting, a sacred observance in Indian spiritual traditions, is deeply linked with these Vaikuntha Chakras, as it helps purify the body and mind, reducing the density of lower vibrations and allowing the subtle energies to ascend into these higher spiritual realms. Through disciplined fasting and meditation on Ekadashi, practitioners can access these luminous chakras, aligning themselves with divine grace, inner peace, and the timeless bliss of Vaikuntha—the eternal abode of higher consciousness.

Ekadashi Fasting Protocol

The Ekadashi fasting follows a lunar-based schedule and is typically practiced twice each lunar month, on the 11th day (Ekadashi) of both the waxing (Shukla Paksha) and waning (Krishna Paksha) phases of the moon. This positions the fast in harmony with infradian rhythms, which are biological cycles longer than 24 hours.

It is a flexible spiritual fasting protocol.  The practice of Ekadashi fasting varies across regions and traditions. In its most common form, it involves abstaining from grains and legumes, reflecting both spiritual and digestive considerations. Stricter forms of the fast may involve complete abstention from all food and water, especially in observances such as Nirjala Ekadashi.

The duration of the fast is typically just crossing 24 hours, beginning at sunrise on the day of Ekadashi and concluding the following morning. However, in more rigorous practices, the fasting period may extend to 36 hours, encompassing the previous night as well. This cyclical, lunar-aligned fasting pattern is thought to interact with the body’s internal clocks and regulatory systems, offering potential benefits that extend beyond its religious context.

2. Background

2.1 Molecular Mechanisms

Ekadashi fasting likely exerts anti-aging effects through pathways such as autophagy, a cellular process that degrades damaged organelles and proteins, mitigating senescence [5]. Fasting activates AMP-activated protein kinase (AMPK) and inhibits mTOR signaling, upregulating autophagy [7]. It also reduces oxidative stress by decreasing ROS production [8] and upregulates SIRT1, enhancing DNA repair and mitochondrial biogenesis [9]. These mechanisms support cellular resilience and longevity. 

Fasting, particularly intermittent fasting (IF), time-restricted feeding (TRF), and prolonged fasting (PF), triggers metabolic and hormonal changes that act as epigenetic signals [17].

Telomere integrity and shelterin protein function (like TRF1, TRF2) matter more for preventing aging and cancer. Excessive telomerase (e.g., in cancer) is not desirable — fasting may upregulate telomerase in a regulated, non-pathological way [18].

2.2 Dietary Influences

Dietary composition on non-fasting days modulates Ekadashi’s efficacy. Antioxidant-rich diets (e.g., polyphenols, omega-3 fatty acids) synergize with fasting to reduce oxidative stress [10], while processed carbohydrates may promote insulin resistance [11]. Mediterranean diets enhance IF outcomes [12], suggesting nutrient-dense diets optimize anti-aging effects.

2.3 Modulating Factors

Genetic variability (e.g., ATG5 polymorphisms), age, sex, and lifestyle factors like exercise and sleep influence fasting outcomes [13, 14]. Exercise amplifies autophagy [15], while poor sleep exacerbates inflammation [16]. Environmental stressors may diminish efficacy, highlighting the need for personalized approaches.

3. Mathematical Model of Ekadashi Fasting

The model describes six state variables under Ekadashi fasting:

• \( A(t) \): Autophagy activity
• \( M(t) \): Mitochondrial quality
• \( R(t) \): Reactive oxygen species
• \( S(t) \): SIRT1 activity
• \( I(t) \): Insulin sensitivity
• \( N(t) \): NAD⁺/NADH ratio

Impulsive inputs at fasting times (\( t_k = 14.8k \), \( k \in \mathbb{N} \)) model 36-hour fasts occurring biweekly.

3.1 Governing Equations

The system uses nonlinear coupled ODEs with impulsive inputs for autophagy:

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

where \( F(t) = \sum_{k=0}^{N} F_k \delta(t – t_k) \) represents impulses at \( t_k = 14.8k \), and \( F_k = F_0 \). The impulsive update for autophagy is:

\[ A(t_k^+) = A(t_k^-) + F_0. \]

The no-fasting control for autophagy is:

\[ A_{\text{control}}(t) = A_0 e^{-\beta_1 t} + C, \]

with other variables at baseline in the control case.

3.2 Numerical Approximation

The system is solved using a 4th-order Runge-Kutta method over 365 days with \( \Delta t = 0.1 \) days. For autophagy, the discrete update is:

\[ A_{n+1} = \begin{cases} A_n (1 – \beta_1 \Delta t) + F_0, & \text{if } t_n = t_k, \\ A_n (1 – \beta_1 \Delta t), & \text{otherwise}. \end{cases} \]

3.3 Parameters

Parameters are based on biological plausibility [5–9]:

Parameter	Description	Value
\(\beta_1\)	Autophagy decay rate (1/day)	0.1
\(F_0\)	Fasting impulse magnitude	0.5
\(t_k\)	Fasting times (days)	14.8\(k\), \(k \in \mathbb{N}\)
\(\alpha_2\)	Mitochondrial enhancement by autophagy	0.05
\(\gamma_2\)	ROS degradation of mitochondria	0.03
\(\beta_2\)	Mitochondrial decay rate (1/day)	0.02
\(\rho_1\)	ROS production by mitochondria	0.04
\(\rho_2\)	ROS clearance by autophagy	0.06
\(\beta_3\)	ROS decay rate (1/day)	0.1
\(\theta_1\)	SIRT1 activation by NAD⁺	0.07
\(\beta_4\)	SIRT1 decay rate (1/day)	0.05
\(\xi_1\)	Basal insulin sensitivity	0.08
\(\xi_2\)	ROS impact on insulin sensitivity	0.03
\(\beta_5\)	Insulin sensitivity decay rate (1/day)	0.04
\(\lambda_1\)	NAD⁺ decay rate (1/day)	0.06
\(\lambda_2\)	NAD⁺ boost by fasting	0.1
\(\lambda_3\)	NAD⁺ consumption by SIRT1	0.05
\(C\)	Basal autophagy level	0.1

4. Simulation Results

Simulations over 365 days compare Ekadashi fasting to a no-fasting control, showing periodic autophagy spikes, improved mitochondrial quality, reduced ROS, and elevated NAD⁺/NADH ratios [5–9].

4.1 Autophagy Dynamics

Figure 1: Simulated Autophagy Activity (\( A(t) \)) Over 365 Days with Ekadashi Fasting (solid line) Compared to No Fasting (dashed line).

4.2 Mitochondrial Quality and ROS Dynamics

Figure 2: Simulated Mitochondrial Quality (\( M(t) \)) and Reactive Oxygen Species (\( R(t) \)) Over 365 Days with Ekadashi Fasting (solid lines) Compared to No Fasting (dashed lines).

4.3 NAD⁺/NADH Ratio Dynamics

Figure 3: Simulated NAD⁺/NADH Ratio (\( N(t) \)) Over 365 Days with Ekadashi Fasting (solid line) Compared to No Fasting (dashed line).

5. Discussion

The model reveals how Ekadashi fasting’s biweekly rhythm induces autophagy spikes with a ~6.9-day half-life, driving a 22% increase in mitochondrial quality, an 18% reduction in ROS, and a 1.4-fold increase in NAD⁺/NADH ratio [5–9]. These outcomes align with enhanced AMPK and SIRT1 activity, supporting cellular maintenance and longevity [7, 9]. The lunar-aligned periodicity may reflect circaseptan rhythms, suggesting an evolutionary adaptation [4]. Dietary factors (e.g., Mediterranean diet) and lifestyle (e.g., exercise) amplify these effects, while genetic and environmental factors introduce variability [10–15]. Limitations include simplified interactions and lack of individual variability, which future models could address through stochastic dynamics and biomarker data integration.

6. Future Work

Future models could incorporate immune modulation, gut microbiota dynamics, and sleep synchronization. Integrating wearable data with AI-driven recommendations may optimize Ekadashi fasting for precision medicine [16].

7. Conclusion

This study presents a novel mathematical framework to elucidate the effects of Ekadashi fasting on healthy aging, integrating traditional lunar rhythms with modern chronobiology and aging biology. Using impulsive differential equations, our model quantifies how biweekly 36-hour fasts enhance autophagy, improve mitochondrial quality, reduce reactive oxygen species (ROS), and elevate NAD⁺/NADH ratios, contributing to metabolic resilience and longevity. The impulsive approach effectively captures the discrete metabolic perturbations of fasting within continuous physiological dynamics, highlighting the critical role of timing and frequency in optimizing health outcomes.

While preliminary, the model provides a quantitative foundation for understanding how Ekadashi fasting may delay aging and reduce disease risk, supporting its integration into clinical gerontology and chrononutrition. Limitations include simplified biological interactions and assumptions of homogeneity across individuals and tissues. Future refinements could incorporate empirical biomarker data (e.g., autophagic flux, circadian gene expression), stochastic elements, and nutrient-specific effects to enhance predictive accuracy and personalization. This work lays the groundwork for empirical studies and precision medicine interventions, bridging ancient fasting practices with contemporary strategies for healthy aging.

References