Table 1 Parameters considered for compacting \(P_{C}\) and thread flank area \(P_{F}\), with Vd—displaced bone volume, Do—outer diameter, Dc—core diameter, L—screw length, Vc—bone compacting, p—screw pitch, d—thread depth.

From: Influence of thread design on anchorage of pedicle screws in cancellous bone: an experimental and analytical analysis

Compacting parameters \(P_{C}\)

Thread flank area parameters \(P_{F}\)

Compacting between thread flanks

\(P_{C\_1} = \frac{{V_{d} }}{{\frac{\pi }{4} \left( {D_{o}^{2} - D_{c}^{2} } \right) L}}\)

Relative flank area over thread length

\(P_{F\_1} = \frac{{D_{o}^{2} - D_{c}^{2} }}{{D_{o}^{2} }} \cdot \frac{L}{p}\)

Compacting

\(P_{C\_2} = V_{c} = \frac{{V_{d} }}{{\frac{\pi }{4} D_{o}^{2} L}}\)

Relative flank area per thread turn

\(P_{F\_2} = \frac{{D_{o}^{2} - D_{c}^{2} }}{{D_{o}^{2} }}\)

Displaced diameter

\(P_{C\_3} = 2 \cdot \sqrt {\frac{{V_{d} }}{\pi L}} \cdot \frac{1}{\left[ m \right]}\)

Ratio of thread depth to thread pitch

\(P_{F\_3} = \frac{d}{p}\)

Outer diameter times compacting

\(P_{C\_4} = D_{o} \cdot V_{c} \cdot \frac{1}{\left[ m \right]}\)

Number of thread turns per thread length

\(P_{F\_4} = \frac{L}{p}\)