 Nail-plate storage balance

Nail-plate storage balance accounts for material accumulating in a chosen nail plate segment when production and removal are unequal. A measured advance speed is a boundary-transport observation; it does not alone specify how much material is stored or produced.

For an original fixed-segment mass conservation model, let $M(t)$ be stored structural mass, $F_{\mathrm{in}}$ and $F_{\mathrm{out}}$ its boundary fluxes, $P$ local production and $L$ other losses. ThenThis is the integrated continuity equation. If production is confined outside the selected segment, $P=0$ there even though the upstream nail matrix continues producing material. Moving the measurement boundary changes which processes appear as local production or inflow.

With constant density, an illustrative volume version has inflow $0.30\mathrm{m}{\mathrm{m}}^3/day$ and outflow $0.24\mathrm{m}{\mathrm{m}}^3/day$, giving storage gain $0.06\mathrm{m}{\mathrm{m}}^3/day$. After ten days the gain is $0.60\mathrm{m}{\mathrm{m}}^3$. Spread over a fixed $10\times 20\mathrm{m}{\mathrm{m}}^2$ footprint, that corresponds to an average thickness increase of 0.003 mm. These are geometric consequences of the chosen model, not measured nail-growth constants.

Clipping is a discrete loss. If a clipping of mass $m_c$ is removed at time $t_c$, the balance includes $M(t_c^{+})=M(t_c^{-})-m_c$. A smooth growth curve fitted across this jump could misinterpret removal as decreased production. Repeated position measurements should therefore be accompanied by clipping records.

Hydration versus production in nail mass balance separates structural material from water: $M_{\mathrm{wet}}=M_{\mathrm{structural}}+M_{\mathrm{water}}$. A rise in wet mass need not mean new structural material. A primary ellipsometry experiment measured changes in the complex refractive index of human fingernails during water uptake and loss, using a model with more weakly and more tightly associated water.^[ref] That establishes a conditioning-dependent material response, not matrix proliferation.

A useful experiment measures marked displacement, segment geometry and mass under matched conditioning while recording removals. The measurement model must identify whether it tracks wet material, structural material or an optical proxy; these are different storage quantities.