The three times in human aging

In human aging we can distinguish three 'times'. Physical time, biological time and intrinsic, lived time (ontochronology).  The biological time can be written as a smooth function $b(t)$ of physical time. Ontochronology - which is in a sense the real age and time for a human being - is measured by the length of the graph $b(t)$ starting from the moment of birth $(t_0, b(t_0))$. Thus

$o(t) = \int_{t_0}^t\sqrt{1 + b'(t)^2} dt$

If we consider the total chronological time of a person's life as fixed, then corresponding to this constraint there are a great varieties of smooth graphs for $b(t)$ (subject to further biological constraints). For instance $b(t)$ may to a substantial extent lie beneath the diagonal $\Delta(t) = t$ and thus that person will have a longer youth and have a biological age less than their chronological age.