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 skin, 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. Note that the weight of each layer due to gravity is shown simplified as a load acting at the center of gravity of each element. Since the weight of the flap is very small compared to F, this is a reasonable simplification. Also note that the weight of the connective tissue is not shown. 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.

In this sketch, L is the distance from the incision site to an anchor point below the brow. Note:  It is necessary to deflect (raise) all five layers in order to achieve skin deflection.

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

H - horizontal flap distance

t_s - skin thickness

t_m - muscle thickness

tp - 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 = dA_sE_s/L (eq 2)

where

d - skin deflection

A_s - skin cross sectional area (H * 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 = dA_mE_m/L (eq3) and P_p = dA_pE_p/L (eq4)

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

F = d /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.

F = P_s + P_m (eq6)

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

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

In the case of the brow lift, the objective is to deflect (raise) the skin at the brow level. By applying the load directly to the muscle and skin layer, through sutures, directly at or just above brow level, the applied load raises the brow without stretching the skin or periosteum between the brow and the hairline. This reduces the skin tension to approximately zero between the brow and the hairline. In the figure shown, the total applied load, F_i, is shown applied to the skin and muscle at the brow level. Note that the load required is

F_i =d _i/L_i (A_sE_s+A_mE_m)

where F_i represents the total load required. L_i represents the flap length from anchor point to the level of load application. In this simplified model, the total load to achieve a give deflection will be the same if d _i/L_i = d /L, which is a very close approximation. In other words the strain, d /L, is the same everywhere along the flap.

Therefore, applying the load directly at the brow does not reduce the magnitude of the required load, but it does reduce the tension in the skin and muscle between the brow and hairline. In addition, it significantly decreases skin deflection at the hairline.