3.1 Overview
In-vivo measurement of the elastic and viscous properties of skin is an essential requirement when
assessing the effectiveness of moisturisers and other cosmetic skin treatments. By their very nature such
measurements are difficult to perform, not just because they are in-vivo, but also because the forces and
displacements that are required to be measured are extremely small - typically a peak lateral force of
around 3 gf will produce displacements of less than 1 mm.
It is now possible to manufacture such an instrument which employs micromechanical moving
components, and computer feedback control with full graphical display and analysis of the data in real
time. Such an Instrument is the Linear Skin Rheometer, which is detailed in this paper.
3.2 The Measurement Principle
When measuring the elastic and viscous properties of a material we are seeking to determine how far the
material moves when a lateral force is applied to it. If we apply a sinusoidal force, then we expect to see a
resultant displacement that also changes sinusoidally. The phase shift between the force and
displacement curves is also of great interest.
To carry out this measurement a probe is attached to the surface of the skin, and a sinusoidal force is
then applied along its' axis and thereby onto the skin. Typically the peak force applied will be in the region
of 3g. If we simultaneously measure the displacement of the skin caused by the force then we will obtain
a pair of readings as shown in figure 1. These are ideal readings, shown for the purpose of this
discussion only, some real readings are shown in figure 3, and it can be seen that they do correspond
reasonably well with the predicted behaviour.
Three parameters can be obtained from the curves F Max which is the peak force that is applied to the skin surface
P Max which is the peak displacement that occurs as a result of that force
T which is the phase shift between the two signals
The elastic component of the skin is given simply by the formulae F max / P max, and is usually
expressed in units of grams force per millimetre.
The more usual way of presenting this data is to plot force directly against displacement. In which case an
ellipse will be formed, as the component parts are two sine waves with an identical period, but shifted in
time. Such a picture, as taken from the LSR, is shown in figure 2 below.
The phase shift is due to the viscous properties of the skin, and is represented in figure 2 by the area of
the enclosed ellipse in units of gram force metres. In effect the area of the ellipse represents the energy
that is lost in moving the probe over one complete cycle. Had the force and displacement sine waves
been in phase then the resultant plot (a straight line) would have represented a perfectly elastic material.
Figure 3 below shows the real force and displacement traces that generated the ellipse in figure 2.
The area of the ellipse can be obtained in one of two ways. The easiest method is to perform an analysis
of the ellipse directly, and to attempt to fit an ellipse to the real data by analytical techniques (e.g. such as
finding the true centre, and determining the major and minor axes).
The LSR uses a rigorous approach by performing a regression on the original sinusoidal data in order to
solve for the equations F = FmaxSin(t)
P = PmaxSin(t+T)
Where
F = instantaneous force
Fmax = the maximum force
t = time over one cycle in radians
P = instantaneous displacement
Pmax = the maximum displacement
T = the phase shift in radians
Having solved for these equations it is then a straightforward problem to solve the integral over one cycle
the represents the area of the ellipse
To summarise, what we are trying to do is to measure the elastic and viscous properties of skin. This is
achieved by applying a sinusoidally varying force to the skin, and measuring the displacement that
results. The resultant signals are a sine wave of force with respect to time, and a resultant displacement
with respect to time. The ratio of peak force to peak displacement is a measure of the elastic properties of
skin, and the phase lag between the two sine waves is a measure of the viscous properties of skin. It is
usual to plot the two signals against eachother, as shown in figure 2, where it can be seen that the slope
of the ellipse along its' major axis is the elastic parameter, and the area of the ellipse is the viscous
parameter.
3.3 How It Is Done
The key to the design of the LSR was the means to apply a continuously varying, but controlled, force to
the surface of the skin. Figure 4 shows a schematic of probe head design.
From the measuring head a light stiff probe protrudes. The far end of which is bent through a right angle
and has at its' tip a small round disc, which is attached to the skin under study by means of double-sided
adhesive tape. Inside the measuring head, the probe is attached to a load cell, which is moved along the
probe axis by a motor-driven lead screw. An LVDT is used to monitor the position of the load cell and
probe.
An IBM (or compatible) PC is used to control the movement of the sensing head. Both force and position
are continuously monitored at a rate of 1 kHz using a 12-bit ADC plug in card. 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 initially calculated from an equation, 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 per
second. A feedback loop is used to control the motor, which moves the load cell in such a way as to
minimise the discrepancy. The force applied thus follows closely the desired force/time cycle. 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 readings over the complete measurement cycle, which is
usually set to be 3 seconds thus generating 3000 pairs of points. This data is then used to generate the
graphs that are shown above, and are analysed to determine the elastic and viscous parameters.
The load cell used in the LSR is supplied by Maywood and has a full scale reading of 10g, with an overall
accuracy of better then 0.02g. The LVDT is supplied by Solartron, type DF2.5, which has an accuracy of
better than 4 microns. The motor is
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