Digital Design of Kurtosis-Controlled Ti-6Al-4V Lattices for Patient-Specific Orthopedic Implants: A Computational Framework

Porous Ti-6Al-4V lattice implants combine high specific strength, osseointegrative porosity, and compatibility with additive manufacturing, but conventional stiffness tuning through porosity, pore size, or unit-cell topology compromises biological pore requirements. This study presents a computational design framework in which structural kurtosis, the normalized interlayer offset between neighboring layers of a periodic cubic lattice, regulates elastic response at fixed global porosity. Closed-form expressions for the effective modulus are derived from first principles: the aligned configuration from the axial load-bearing area fraction, and the interlayer-shifted configuration from Euler–Bernoulli beam theory for guided-end connecting members. The derivations reproduce the Gibson–Ashby exponents n = 1 and n = 2, replacing the previously asserted power law, and a calibrated one-parameter interpolation bridges intermediate offsets. At 65% porosity, the effective modulus falls from 16.5 GPa in the aligned lattice to 2.64 GPa in the shifted lattice. A local-yield analysis based on peak bending curvature gives recoverable elastic strains of 1.37% at 89% porosity and 0.68% at 65%; the compliance-based values of 20.5% and 5.12% are kinematic upper bounds that neglect plastic hinging. A prefactor-free benchmark shows that obtaining the same 6.25-fold reduction by increased porosity alone would require 85.9–94.4% porosity and 0.17–0.28 mm struts, outside the osseointegration window and the resolution of selective laser melting. A GAN-CAD-FEA workflow reproduced the analytical moduli to within 7% across six design cases. All results are analytical and numerical; no specimens were fabricated or tested, and experimental validation remains required.