Cortical Bone Mechanics Technology™ (CBMT)

CBMT performs a non-invasive, dynamic 3-point bending test on the ulna bone in the forearms of living people. The ulna bone is chosen for its superficial location and for its unique, almost ideal biomechanics in bending. The technology comprises two steps: data collection and data analysis.

Data Collection

For data collection, the subject lies supine with the arm to be tested resting in the “tomahawk” position.  The proximal end of the ulna is supported by the articulating humerus while the distal end is supported via the radius on a rigid platform.  A lateral support on the elbow allows the arm to completely relax in this position.

Static and oscillatory forces are then applied via a blunt probe to the skin overlying the ulna bone.  The static force feels like the force on one’s fingertip when pressing an elevator button, while the oscillatory force (spanning a frequency range of 40-1200 Hz) is similar to the force one feels when holding an electric toothbrush or electric razor.

It is impossible for a CBMT operator to recognize by sight or touch where to put the force probe on the forearm, because:

1. The ulna is covered by soft tissue,

2. Ulnas differ greatly in shape from one person to another, and

3. The pattern of intra-cortical destruction of the ulna also differs greatly from person to person.

So, the operator positions the probe mid-way along the length of the ulna and starts the data collection process. An algorithm in the system’s computer then automatically positions and repositions the probe at many sites, while it collects and analyzes data at each site, until it recognizes distinctive features of data from the correct place.

At each data collection site, the applied oscillatory force and the resulting vibratory acceleration of the probe are measured, and transformed into a complex accelerance (i.e., acceleration/force) frequency response function (FRF, Figure 1).

Figure 1. Typical complex accelerance FRF data.

This FRF contains two resonances.  The higher frequency resonance (~600 Hz in Figure 1) is determined primarily by the mechanical properties of the skin, while the lower frequency resonance (~200 Hz in Figure 1) is determined primarily by the mechanical properties of the underlying ulna bone.

Figure 2. Mechanical Model.

Modeling of Forearm Dynamics.


Data Analysis
01 Modeling of Forearm Dynamics
The forearm is modeled as a 7-parameter mechanical skin-bone system (Figure 2, above) that accounts for the mass M, stiffness K and damping D of the skin S and of the underlying bone B, as well as damping by peripheral soft tissue DP.
02 Solving the differential equations
of motion for this mechanical model yields the analytical transfer function (TF) for the Real and Imaginary parts of the stiffness of the skin-bone system in the form of a 4th order rational polynomial, in which w = frequency in radians/s:
03 The TF for the complex compliance
of the forearm is the inverse of the complex stiffness TF.  In both, the coefficients are algebraic functions of the 7 parameters in the mechanical model:
04 Parameter Estimation
Estimation of the values of the 7 parameters proceeds in four steps.

1. The compliance and stiffness FRFs are computed by

1.1. Integrating the accelerance FRF twice to obtain the complex compliance FRF (Figure 3).

1.2. Inverting the complex compliance FRF to obtain the complex compliance FRF (Figure 4).

Figure 3. Typical complex compliance FRF
Figure 4. Typical complex stiffness FRF
2. The TF coefficients (Ai, Ci) are then determined by curve fitting

2.1. The compliance TF to the complex compliance FRF; and

2.2. The complex stiffness TF to the complex stiffness FRF

3. The values of the 7 model parameters are then calculated from the simultaneous solution of the algebraic equations using coefficients from:

3.1. The compliance FRF, and

3.2. The stiffness FRF.

4. Invariably, the parameter values derived from the fits to the complex compliance and complex stiffness FRFs do not agree. The system software then:

4.1. Applies proprietary, non-arbitrary, objective, quantitative criteria to determine whether the FRF came from the correct site, and if so

4.2. Reports the values of the 7 parameters, including MB, KB and DB.

Advantages of CBMT

CBMT provides direct, functional measurements of cortical bone damping D and mass M, as well as stiffness K – in living human subjects. Thus, CBMT opens unique opportunities to investigate the mechanical behavior of cortical bone under more realistic dynamic conditions.

Having measured ulna bending stiffness K, CBMT calculates ulna flexural rigidity (EI = KL3/48).  EI is the product of the elastic modulus (E) and cross-sectional moment of inertia (I) of the ulna bone.  Ulna EI is what predicts quasistatic bending strength so accurately, and what EI enables ulnas of different length (i.e., of different people) to be compared to one another.

As indicated above, CBMT measurement of ulna damping and mass opens the opportunity to investigate the dynamic strength of cortical bone.  It also enables CBMT to calculate and report the mechanical quality factor () of ulna cortical bone.  Q quantifies the relative amounts of mechanical energy dissipated and absorbed by ulnar cortical bone under dynamic loading conditions.