Note: For the moment "better" means that the technique requires the least load to cause a given skin deflection (also causing the least stress in the muscle and periosteum for a given skin deflection).

The sketch shown here models a cross-sectional view of the subperiosteal dissection with a load applied. At the left of the sketch, a free-body diagram is shown which represents the load applied to the skin flap, F and the corresponding loads generated in the skin, muscle and periosteum.

Note: skin, muscle and periosteum are structural layers but the connective tissue layers do not support significant loads.

F - total load applied to flap

L - flap length

W - flap width

t_s - skin thickness

t_m - muscle thickness

t_p - periosteum thickness

P_s - load supported by skin

P_m - load supported by muscle

P_p - load supported by periosteum
 
 

From the free-body diagram, note that the forces must balance if the flap is at equilibrium (not moving). In that case the total force is

F = P_s + P_m + P_p (eq 1)

From principles of mechanics of materials we can relate skin deflection (how much the skin will move, to the load applied.

P_s = A_sE_s/L (eq 2)

where

- skin deflection

A_s - skin cross sectional area (W * t_s)

E_s - skin modulus of elasticity ( a material property - stiffness)

It is also true that the deflection must be the same in all three layers so that the loads in each layer are dependent on the cross-sectional area of each layer and the material stiffness.

P_m = A_mE_m/L (eq3) and P_p = A_pE_p/L (eq4)

Substituting equations 2,3, and 4 into 1 we can see the total load required for a given deflection:

F = /L (A_sE_s+A_mE_m+A_pE_p) (eq5)

Now compare the subgaleal dissection. Comparable sketches and free-body diagram are shown. Not that the periosteum does not support any of the load in this case. From the free body diagram, we can see that the total force F is now a combination of only the skin and muscle load. (Mimi - I see there is a minor error in the free-body diagram. P_p should be P_m - lrw)

F = P_s + P_m (eq6)

F = /L (A_sE_s+A_mE_m) (eq7)

Therefore, the load, F, required to give skin deflection, , is smaller in the case of the subgaleal dissection.