 Nail-plate material age from growth marks

Nail-plate material age from growth marks estimates how long a marked part of the nail plate has travelled since crossing a specified reference. It is a transport clock, not a direct observation of the instant when the material first formed in the nail matrix. The anatomical reference and any hidden travel before reaching it must be specified.

In a primary growth experiment, 22 young adults made file marks near the proximal fold, recorded their positions and repeated the measurements one to three months later.^[ref] This measures average displacement during the observation interval; it does not by itself recover every earlier growth rate.

For an original one-dimensional advection model, let a material element cross the reference at time $t_0$. If plate advance is spatially uniform with speed $v(t)>0$, its later position isA known growth history permits inversion for $t_0$. A current speed alone need not. For example, 30 days at $0.08$ mm/day followed by 30 days at $0.12$ mm/day gives displacement 6 mm and age 60 days. Dividing by the final speed gives only 50 days, because it substitutes today's speed for the earlier history.

If only bounds $0<v_{\min }\le v(s)\le v_{\max }$ are justified throughout the travel, thenFor 6 mm and stipulated speeds between 0.08 and 0.12 mm/day, the reference-crossing age lies between 50 and 75 days. These bounds describe an original model, not published population limits.

A clipping also spans material positions. Even at a perfectly known constant speed of 0.10 mm/day, a 3 mm longitudinal segment spans 30 days of reference-crossing times. Temporal averaging in nail clippings therefore remains after instrument precision improves. External contamination or chemical exchange can further separate a measured chemical signal from the time of matrix production. Record mark position, reference fold, clipping extent and observation dates before treating a nail plate sample as a dated exposure record.