**Volume 1 Issue 1 Third-Party
Research & Development April 1997**38 Trolley Road RD1 / Cortlandt Manor, New York 10567
Phone/Fax:914-528-9111 Internet:johnrpotts@ Compuserve.com

**Inside This Issue**

**PRINCIPLES OF BALLISTOMETRY
IDRA® BALLISTOMETERS
ADVANTAGES of HALLPOT® SENSORS**

MATHEMATICAL MODELING

**IDRA® Transducer Mounting Plate With Ballistic Hammer,
Holding Magnet, Calibration Clinometer, and Rigid Stand.**

The biomechanical technique involves a light-weight hammer, hinged at one end to a rotary transducer, free-fall of the hammer onto a test surface, and the analysis of the resulting oscillatory displacement-time data to determine characteristic physical parameters for a material. The indentation of the material is a result of forces developed on hammer impact. For a complex material such as human skin, one can observe plastic, elastic, and viscose behavior. Several intrinsic parameters are used to characterize skin:COR, CAC, and STIFFNESS. The COR, or Coefficient of Restitution is a measure of elasticity and is defined as the ratio of hammer rebound speed to its speed just before impact.The CAC, or Cutaneous Absorption Coefficient is also a measure of elasticity defined as a dynamic time constant and presumes that hammer impact energy is lost exponentially with time. STIFFNESS provides stress-strain information and is defined as the ratio of the hammer impact force to the skin deformation.

**Basic Response Curve(Angular Displacement vs Time)**The
basic IDRA® response curve is the output of the rotary sensor vs time. The
baseline on a response curve is a line parallel to the time axis, which
corresponds to the position of the hammer when resting on the skin. Generally,
the data above the baseline is used to determine COR and CAC, whereas, STIFFNESS
is determined from the data below the baseline.

Contact John Potts at the address above for more product information.

IDRA® is a new, commercial ballistometer offered by Third-Party
Research & Development. The name stands for ** I**ntegrated
**D**ynamic **R**ebound **A**nalyzer. Currently, both ac RVDT and dc
brushless potentiometers are employed as rotary sensors in an IDRA® system, a
pc-based instrument.

Both RVDT (Rotary Variable Differential Transformers) and HallpotÒ transducers give highly reproducible DC analogs, with excellent linearity, over a wide range of angular displacement. The HallpotÒ used in an IDRA® system is custom-made for Third-Party Research & Development by Elweco Inc. and incorporates several superior design features which permit precision Ballistometric measurements on human skin, in vivo. Critical design features of the HallpotÒ sensors include, miniature ultra-low friction bearings with non-viscous lubricant, very wide sensor bandwidth and excellent reproducibility and linearity for up to 60 degrees angular displacement Although the HallpotÒ angular measurement range is somewhat less than for an RVDT, it is generally quite adequate for Ballistometry. A HallpotÒ sensor does not require an expensive energizing amplifier (an RVDT sensor does) which reduces the selling cost of an IDRA® system significantly.

The accuracy, reproducibility, and relevancy of characteristic parameters, determined by Ballistometry, depend markedly on the skin elasticity, design of the ballistic hammer, testing and data processing techniques, dynamic measurement range, and the test quadrant selected. Significant surface movement during a measurement cannot be tolerated. A 95% measurement success rate is easily achieved with proper technique. Unacceptable surface movement is automatically detected in IDRA® software.

The COR and CAC place less demand on instrumentation, since they are generally determined from peak values of angular displacement. COR’s can be determined with a precision of 1% and CAC’s to within 1-2%. In contrast, STIFFNESS, which is defined as the force of impact of the ballistic hammer divided by the associated uniaxial surface deformation, requires instrumentation with wide-bandwidth and high angular resolution. The data used to determine STIFFNESS is below the baseline with displacements ranging only a few degrees over a time period of milliseconds. STIFFNESS can be determined with a precision of 5-6%, for skin, given an instrument calibration technique that is optimal for the simultaneous measurement of all three parameters. With more optimal calibration conditions set for the determination of just STIFFNESS, measurement precision can be significantly improved for this parameter.

For accurate, simultaneous determination of COR, CAC, STIFFNESS, and other parameters, an IDRA® system employs interrupt-driven, 12 bit A/D data collection, at rates of up to 8000 data points per second, coupled with optimal parameter calculation techniques. The instrument bandwidth is adequate to permit accurate free-fall, contact, and rebound angular displacement measurements to +/- 0.05 degrees with non-linearity of 0.5 degrees over a range of 60 degrees.

The IDRA® system is well designed and has potential application for theoretical studies of the dynamic behavior of skin and other materials, as well as for routine analysis.

The hammer is a rigid body which rotates about a noncentroidal axis and the basic scalar equation needed to represent the motion is:

å M_{o}=I_{o}·
a

where, å M_{o} is the
algebraic sum of the moments of the external forces about the axis of rotation
(o), I_{o} is the moment of inertia of the hammer about the axis of
rotation, and a is the angular acceleration of the
hammer. This is a 2nd order non-linear differential equation and has no
closed-form solution. It is convenient and instructive to solve the equation
numerically using a pc software program, such as Mathcad (made by MathSoft
Inc.), although least squares fitting is cumbersome. Readers may contact John
Potts for more details.

Fitting Maxwell Model For Skin and Latex Rubber

A numerical model was developed, to more fully understand ballistometer behavior, which used simple analogs to account for hammer design factors, frictional, gravitational, elastic, and viscose forces. The curves on the right are for Latex rubber (squiggle line) and the fitted model (smooth line). The agreement suggests that a Maxwell model of spring (elastic analog) and dashpot (viscose analog) describe the dynamic behavior of Latex well. The curves on the left is the skin response (noisy line) very near the end of the transient (oscillatory) hammer response and the fitted model (smooth line). The disagreement shows that a simple Maxwell model for skin, although useful for understanding the Ballistometric experiment, does not describe skin’s behavior very well. This observation was expected, based on similar kinds of modeling studies reported in the literature. However, these results clearly show that a well designed ballistometer has potential application for theoretical studies on skin as well as for routine clinical analysis.