Mortality model Aging

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{html} <table border="1" cellpadding="6" cellspacing="0"> <thead> <tr> <th>Model Name</th> <th>Formula (Simplified)</th> <th>Description</th> </tr> </thead> <tbody> <tr> <td><strong>Integrated Damage Model (proposed)</strong></td> <td><code>ba(t) = P(t) · (1/N<sub>r</sub>) · ∫[f<sub>resp</sub>(u) / f(m,e)] du</code></td> <td>Refines Escala’s theory by integrating respiration cycles over time, adjusted for species-specific maintenance (f) and life-phase acceleration (P). Can explain aging inflections and outliers like bats. Mechanistic and time-continuous.</td> </tr> <tr> <td><strong>Escala’s Respiration-Cycle Law</strong></td> <td><code>t<sub>life</sub> ≈ N<sub>r</sub> / f<sub>resp</sub></code></td> <td>Proposes organisms undergo a nearly fixed number (~10⁸) of respiration cycles per lifetime. Supported across ~300 species from microbes to mammals. Unifies metabolism and lifespan.</td> </tr> <tr> <td><strong>Entropy Generation Model (Silva & Annamalai)</strong></td> <td><code>∫σ(t) dt ≈ constant</code></td> <td>Connects aging to total entropy generated over lifetime. Predicts human lifespan from heat dissipation per kg. Conceptually links thermodynamics and aging.</td> </tr> <tr> <td><strong>Reliability Theory of Aging</strong></td> <td><code>Vitality(t) = V<sub>0</sub> - k·t + noise</code></td> <td>Models aging as loss of systemic redundancy. Predicts rising mortality even when components have fixed failure rates. Supports late-life mortality plateaus.</td> </tr> <tr> <td><strong>Kleiber’s Law</strong></td> <td><code>B ∝ M<sup>3/4</sup></code></td> <td>Basal metabolic rate scales as body mass to the 3/4 power. Foundational to metabolic and lifespan scaling laws across all taxa.</td> </tr> <tr> <td><strong>Lifespan–Mass Allometry</strong></td> <td><code>t<sub>life</sub> ∝ M<sup>1/4</sup></code></td> <td>Empirical observation that lifespan increases with body mass. Follows from Kleiber’s law and constant energy-per-mass assumptions.</td> </tr> <tr> <td><strong>Rate-of-Living Hypothesis (Rubner)</strong></td> <td><code>E<sub>life</sub>/M ≈ constant</code></td> <td>Suggests that organisms expend the same amount of energy per gram over a lifetime. Holds across mammals but breaks down across classes (e.g. birds).</td> </tr> <tr> <td><strong>Gompertz–Makeham Law</strong></td> <td><code>μ(t) = α·e<sup>β·t</sup> + λ</code></td> <td>Classical model of mortality where death risk grows exponentially with age and includes a constant background risk. Very good empirical fit but not mechanistic.</td> </tr> <tr> <td><strong>Gompertz Law</strong></td> <td><code>μ(t) = R<sub>0</sub>·e<sup>b·t</sup></code></td> <td>Simpler form of Gompertz–Makeham. Predicts exponential rise in mortality with age. Used widely in demography and aging studies.</td> </tr> <tr> <td><strong>Weibull Mortality Law</strong></td> <td><code>μ(t) = k·λ·t<sup>k-1</sup></code></td> <td>Predicts mortality using a power law. Used in reliability theory and some species. Less common for biological aging.</td> </tr> <tr> <td><strong>DNA Methylation Clock (Horvath)</strong></td> <td><code>DNAmAge = β₀ + Σ(β<sub>i</sub>·CpG<sub>i</sub>)</code></td> <td>Uses weighted DNA methylation levels at CpG sites to predict biological age. Highly accurate.</td> </tr> <tr> <td><strong>Phenotypic Age (Levine)</strong></td> <td><code>PhenoAge = f(albumin, WBC, etc.)</code></td> <td>Combines standard blood biomarkers to predict mortality risk and biological age.</td> </tr> </tbody> </table> {/html}
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