LINEAR SKIN RHEOMETER 325 GøoclYer Figure 4. The linear skin rheometer. force and displacement data. Both force and displacement are monitored continuously at a rate of 1 KHz using a 12-bit ADC plug-in card (National Instruments MIO16). The motor is controlled with an analogue output signal also generated by the PC. The desired force/time cycle, which is normally a single sinusoid, is calculated initially and then stored in memory as a table of values. The actual force applied to the probe is compared with the desired value in the table 1000 times a second. A feedback loop is used to control the motor that moves the load cell in such a way as to minimize any discrepancy. The force applied thus follows the desired force/time cycle extremely closely. The control loop uses an algorithm with proportional and integral terms, whose relative weighting can be varied. The PC logs all the force and displacement values over a complete measurement cycle, which is usually set at 0.33 Hz, thus generating 3000 pairs of points over a three-second cycle. Two waveform plots are then obtained (Figure 5). Three parameters may be obtained from these curves: Fmax: the peak force that is applied to the skin surface Pmax: the peak displacement occuring as a result of that force T: the phase shift between the two signals The dynamic spring rate (DSR) of the stratum corneum is given simply by the formula Fm,,x/Pma x. Derivatives are calculated and expressed as g/mm, mm/N, and lam/g.

326 JOURNAL OF COSMETIC SCIENCE Force F max t=O Time Position P max Ph ' t=O Figure 5. Waveform plots demonstrating a complete LSR measurement cycle. The viscous component of the stratum corneum is often inferred by calculating the area of the ellipse shown in Figure 2. A more rigorous approach is to perform a regression on the original sinusoidal data in order to solve the equations: F = Fm•,• Sin(t) (1) P = Pm•,• Sin(t + T) (2) where F = instantaneous force, Fm•,• = peak force, t -- time for one complete cycle in seconds, P = instantaneous displacement, Pm•x = peak displacement, and T = phase shift in radians. Having solved for these equations, it is then a straightforward problem to solve the integral over one cycle that represents the area of the ellipse: o:=Fm•,•Sin(t)Pm•,•Cos(t + T) (3) The LSR software solves the above equations for both elastic and viscous components of the data. These are subsequently displayed, directly after measurement. Note: units of pm/g (1/DSR, a measure of stretching or compression of the stratum corneum in response to a given applied force) will be used as a convenient expression of skin elasticity/softness in the rest of this paper.