Longevity Formulas- Immortality Knowledge Base

Longevity Formulas

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Model Name	Formula (Simplified)	Year Introduced	Description
Integrated Damage Model (proposed)	`ba(t) = P(t) · (1/N_r) · ∫[f_resp(u) / f(m,e)] du`	Proposed in this work (not yet published)	Refines Escala’s theory by mathematically integrating respiration cycles over continuous time, adjusted for species-specific maintenance factors (f) and life-phase acceleration (P). It provides a mechanistic, time-continuous framework to account for aging inflections, shifts, and outliers like bats that live exceptionally long relative to their size.
Escala’s Respiration-Cycle Law	`t_life ≈ N_r / f_resp`	c. 2019–2022 (Escala; verify exact publication)	Proposes that organisms undergo a nearly fixed number (~10⁸ to 10⁹) of respiration cycles per lifetime, supported across ~300 species from microbes to mammals. This unifies metabolism, physiological pacing, and maximum biological lifespan.
Bejan’s Constructal Law Model	`Flow access optimization → M^3/4 & M^1/4`	1996 (constructal law); applied to allometry c. 2006	Derived from thermodynamic first principles, it explains that flow systems (like vascular and respiratory networks) must evolve configuration to minimize flow resistance. This successfully derives why metabolic rates scale to the 3/4 power and frequencies/lifespans to the 1/4 power.
West, Brown, & Enquist (WBE) Model	`dm/dt = (B₀/E_c)m^3/4 - (B_c/E_c)m`	1997 (network model, Science); 2001 (growth model, Nature)	A foundational mathematical framework treating biological transport systems as space-filling, energy-minimizing fractal networks. It derives Kleiber's Law and ontogenetic growth curves from cellular-level constraints and hydrodynamics.
Entropy Generation Model (Silva & Annamalai)	`∫σ(t) dt ≈ constant`	2008–2009	Connects organismal aging directly to the total thermodynamic entropy generated over a lifetime. It evaluates heat dissipation per kilogram to predict longevity (including human lifespan), bridging classical thermodynamics with biophysical aging.
Reliability Theory of Aging	`Vitality(t) = V₀ - k·t + noise`	1991 (Gavrilov & Gavrilov); 2001 (formal paper). Linear vitality form dates to Strehler–Mildvan, 1960	Models biological aging as the progressive loss of systemic redundancy and component failure in complex networks. It explains why mortality rates rise even when individual components have fixed failure rates, and accounts for late-life mortality plateaus.
Kleiber’s Law	`B ∝ M^3/4`	1932	The empirical cornerstone of metabolic scaling: basal metabolic rate scales non-linearly with body mass to the three-quarters power, so larger organisms are more energetically efficient per gram of tissue. Foundational to metabolic and lifespan scaling laws across all taxa.
Lifespan–Mass Allometry	`t_life ∝ M^1/4`	c. 1959–1981 (Sacher 1959; Lindstedt & Calder 1976/1981)	The empirical observation that maximum lifespan increases with body mass, scaling with mass to the one-quarter power. It follows from Kleiber’s law and constant energy-per-mass assumptions, and matches the inverse scaling of metabolic and heart rates.
Rate-of-Living Hypothesis (Rubner)	`E_life/M ≈ constant`	1908 (Rubner); popularized by Pearl, 1928	Suggests that animals expend a roughly fixed amount of energy per gram of tissue over their entire lifetime. Holds across many mammals but breaks down across broader taxa (e.g. birds).
Gompertz–Makeham Law	`μ(t) = α·e^β·t + λ`	1860 (Makeham)	A classical demographic model where death risk grows exponentially with age, plus a constant background risk representing environment-driven hazard. A very good empirical fit, but not mechanistic.
Gompertz Law	`μ(t) = R₀·e^b·t`	1825 (Gompertz)	A simpler form omitting the external environmental term, predicting an exponential rise in baseline mortality with age. A cornerstone of biogerontology, demography, and actuarial science.
Weibull Mortality Law	`μ(t) = k·λ·t^k-1`	1939 (Weibull; popularized 1951)	Uses a power-law formulation to model failure rates and mortality over time. Heavily used in reliability engineering and for some species; less common for biological aging.
DNA Methylation Clock (Horvath)	`DNAmAge = β₀ + Σ(β_i·CpG_i)`	2013	A molecular epigenetic tool using weighted methylation levels at specific CpG sites to predict biological age and healthspan, with high cross-tissue accuracy.
Phenotypic Age (Levine)	`PhenoAge = f(albumin, WBC, etc.)`	2018	Combines standard clinical blood biomarkers (albumin, white blood cell count, metabolic markers) to quantify biological age and mortality risk.

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