Size and Shape Change of the Human Rib Cage
To fully understand the effects of aging on the integrity of the normal skeleton, detailed geometric models are needed to complement material property data. The purpose of this research is to develop a predictive model for age-related changes in rib-cage geometry using the generalized Procrustes approach. This predictive model is coupled with the finite element method to isolate the effects age-related size and shape change have on the structural response of the rib cage.
The normal aging process is associated with a number of well-documented skeletal changes that can negatively impact quality of life, and increase susceptibility to disease and trauma. Of particular interest is how age-related size and shape change of the human thorax relates to clinical outcomes following trauma. The increase in the size of the elderly population has raised questions on the safety of elderly motor vehicle occupants. The chest is the most commonly injured body region in fatal frontal impacts of drivers over the age of 64, and rib fractures were the most serious injury sustained by 40% of patients over 60 who died of chest injuries following an automobile crash. This shift in populations demographics, coupled with a higher susceptibility to thoracic trauma with age motivates a better understanding of age-related changes in thoracic biomechanics.
We developed a predictive model for age-related changes in rib-cage geometry using an advanced method of shape analysis known as the Procrustes method. This method is based on direct analysis of landmark coordinates and has been used extensively in anthropology to study size and shape differences between populations of people. The Procrustes method can be used to create a function from landmark coordinates which describes where in space a landmark is located based on an extrinsic variable, such as age.
If two landmark data sets are organized in two matrices X1 and X2, their geometric relationship can described mathematically in Equation 1.
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Here, t is a translation vector, H is a rotation matrix, r is an isometric scaling factor and 1 is a vector of ones. Each of these variables represents an operation performed on the landmark datasets to isolate real shape differences, E. The translation moves the average coordinate location of the landmarks in a set to a common origin, the rotation matrix rotates each point set rigidly around the origin and the scaling is a dilatation or compression of the set. What remains is E, which is the real shape difference between X1 and X2.
Finite element model construction employed the landmark sets generated from the multivariate regression analysis. We employed data representing three males ages 20, 50, and 80 years-old. A 23.4kg impactor was placed 0.3 mm away from the midline node between the 4th and 5th rib, and rotated parallel to the sternum. Impacts were simulated at 3.4m/s. The total amount of energy absorbed during the impact was calculated from force versus displacement data. The data resulting from the GPA was used to determine if significant geometric changes with age could be discerned. Separately regressing size onto age for individuals under fifty and those over fifty (omitting the fifty year old) results in a mildly statistically significant regression for the younger group (p=0.09, R2=0.68) and a significant regression for the older group (p=0.03, R2=0.72). The results of the finite element analysis are summarized below in the figure showing force versus normalized displacement of the sternum.
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Above, T1-T7 height versus age showing separate regressions of size onto age for younger (age < 50) and older (age > 50) | Above, Max force registered during impact (right axes) and total energy absorbed (left axes) during the impact simulations for all three age groups. |
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Above, Progression of finite element impact simulation, 20 year old rib cage. (A) time = 0, (B) 20% chest compression, (C) 40% chest compression. |
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