Modeling costal cartilage using local material …people.virginia.edu/~rwk3c/papers/Forman2011-Modeling costal... · Modeling costal cartilage using local material properties with

Journal of Biomechanics ] (]]]]) ]]]–]]]

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Journal of Biomechanics

0021-92

doi:10.1

n Corr

Navarra

Navarra

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Pleasgross

www.JBiomech.com

Modeling costal cartilage using local material properties with considerationfor gross heterogeneities

Jason L. Forman a,b,n, Richard W. Kent a

a University of Virginia, Center for Applied Biomechanics, USAb European Center for Injury Prevention, University of Navarra, School of Medicine, Irunlarrea 1 (ed. Los Castanos s230), 31008 Pamplona, Navarra, Spain

a r t i c l e i n f o

Article history:

Accepted 29 November 2010Contemporary computer models of the thorax designed to predict injury in automobile collisions model

the costal cartilage as a homogeneous material using properties derived from local material character-

Keywords:

Costal cartilage

Computer model

Indentation

Impact

Biomechanics

90/$ - see front matter & 2010 Elsevier Ltd. A

016/j.jbiomech.2010.11.034

esponding author at: European Center for Inj

, School of Medicine, Irunlarrea 1 (ed. Los Cast

, Spain. Tel.: +34 948 425 600x6469; fax: +3

ail address: [email protected] (J.L. Forman).

e cite this article as: Forman, J.L., Kheterogeneities. Journal of Biomech

a b s t r a c t

ization tests. No studies have validated the accuracy of these models in predicting the structural

mechanics of costal cartilage. Two heterogeneities – the perichondrium and calcified regions – may affect

the behavior of costal cartilage in a manner not accounted for by current models. This study sought to

investigate the predictive ability of subject-specific models of whole costal cartilage segments, with the

calcified regions modeled distinctly and with the perichondrium removed (from the physical specimens

as well as from the simulations). Finite element models were developed in the case of five cadaveric costal

cartilage segments. The properties of the cartilage were derived from indentation testing of each

specimen, where the characteristic average instantaneous elastic moduli ranged from 8.7 to 12.6 MPa.

Matched simulations and experiments were then performed, subjecting each specimen to cantilever-like

loading with a dynamic posterior displacement of the sternal boundary (all other boundary degrees-of-

freedom fixed). The models predicted the resulting peak anterior–posterior forces generated on the costal

boundary with a minimum error of 1% and a maximum error of 36%. These results provide support to the

previous implicit assumption that insight can be gained into the structural behavior of costal cartilage by

observing the local material properties (when calcified regions are included and the perichondrium is

removed). Future work includes the addition of the perichondrium, so as to model the whole costal

cartilage composite structure.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Prediction of automobile collision injuries with a finite elementmodel requires an accurate reproduction of not only the individualtissues, but also of their interactions. In the study of thoracic injuryprediction, considerable research has been focused on the studyof mechanics of osseous components of the ribs and the sternum(e.g., Charpail et al., 2005; Li et al., 2010). Very little is known,however, of the cartilaginous components that connect them.

The costal cartilage consists of irregular cylinders of hyalinecartilage that connect the anterior ends of ribs 1–4 to the sternumand that connect ribs 5–10 to each other. In situations whereloading is applied over a limited area of the anterior chest, thecostal cartilage dictates the coupling of the ribcage components,affecting the propagation of stress and strain to the ribs. Thisdictates the overall stiffness and deformation of the ribcage and the

ll rights reserved.

ury Prevention, University of

anos s230), 31008 Pamplona,

4 948 425 649.

ent, R.W., Modeling costalanics (2010), doi:10.1016/j

probability of injury to each of the ribcage components (Murakamiet al., 2006; Oyen et al., 2005).

Many current thorax models include homogeneous representa-tions of costal cartilage, with material property definitions derivedfrom local material characterizations (Lee and Yang, 2001;Iwamoto et al., 2002; Kimpara et al., 2006; Wang, 1995). Thereare, however, at least two types of heterogeneities in costalcartilage that may cause models developed with local materialproperties to erroneously predict its overall structural behavior.First, what is commonly termed the ‘‘costal cartilage’’ is actually acomposite structure composed of an inner cylinder of hyalinecartilage surrounded by a thick layer of fibrous perichondrium. In aseries of structural tests with the perichondrium intact and withthe perichondrium removed, Forman et al. (2010) demonstratedthat the perichondrium contributes an average of 50% of the struc-tural stiffness of the costal cartilage in certain loading modes.

Second, costal cartilage’s mid-substance often undergoes a pro-gressive calcification with age (Fig. 1; Teale et al., 1989; Rejtarovaet al., 2004; Bahrami et al., 2001; McCormick, 1980; Linn and Sokoloff,1965; Dearden et al., 1974; McCormick, 1980). Calcification has thepotential to drastically change the local material properties of costalcartilage’s mid-substance, from a modulus in the order of 1–10 MPa in

cartilage using local material properties with consideration for.jbiomech.2010.11.034

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dx.doi.org/10.1016/j.jbiomech.2010.11.034

mailto:[email protected]



Fig. 1. Micro-CT scans illustrating different types and severity of costal cartilage calcification. The cartilage is shown in shaded opaque regions.

Table 1Specimen information, test matrix, and characteristic average moduli.

Specimen

ID#

Location

(rib#)Age Gender #Sa #Ta E0 (MPa)b

403 4L 47 M 4 20 11.0

322 4L 49 M 4 19 10.5

400 4L 53 M 3 14 12.6

187 4R 54 M 4 16 9.5

197 4R 57 F 3 14 8.7

a #S is the total number of cross-sectional slices tested in indentation with that

specimen and #T is the total number of indentation tests of that specimen.b Characteristic average instantaneous elastic modulus derived from the linear

visco-elastic models of the indentation tests with each specimen. E0 used as the

pseudo-elastic modulus in the subsequent finite element models.

Fig. 2. A typical cartilage segment finite element model illustrating the surface and

cross-sectional mesh. Left: superior view and right: cross-sectional view.

J.L. Forman, R.W. Kent / Journal of Biomechanics ] (]]]]) ]]]–]]]2

healthy hyaline cartilage to a potential modulus in the order of1–10 GPa (Lau et al., 2008). Dependent on the magnitude as well as onthe pattern, calcification has the potential to affect the structuralbehavior of costal cartilage in a manner that cannot be predicted bythe modeling of costal cartilage homogeneously with the materialproperties of healthy hyaline cartilage.

This study sought to take the first step towards the investigationof the relationship between the local material properties and theoverall structural behavior of whole costal cartilage segments.Specifically, the aim of this study was to determine if the structuralbehavior of individual costal cartilage segments (with the peri-chondrium removed) could be predicted with subject-specificfinite-element models that incorporated both cartilage and calci-fied regions.

2. Methods

2.1. Specimens

Costal cartilage segments were harvested from the 4th ribs of human cadavers

(Table 1). The 4th rib cartilage was chosen because it was relatively long (unlike the

2nd and 3rd rib cartilages); but it still consisted of a single cylinder of cartilage

(unlike the cartilages of ribs 6–10). The specimens consisted of a portion of the

sternum, the entire length of the cartilage, and approximately 3 cm of attached rib.

The perichondrium was removed, taking care to not damage the underlying

cartilage. Prior to the collection of these specimens, the source cadavers were

Please cite this article as: Forman, J.L., Kent, R.W., Modeling costalgross heterogeneities. Journal of Biomechanics (2010), doi:10.1016/j

screened for HIV and hepatitis A, B, and C. All cadaver handling and test procedures

were approved by the University of Virginia institutional review board.

2.2. Modeling

Finite element models were developed from CT scans of each costal cartilage

specimen. The resolution of the CT scans was 0.625 mm/pixel in-plane, with slices at

0.6 mm intervals. Contours describing the axial-circumference geometry of the

specimens were digitized from the CT scans using WinSurf (SURFdriver Software,

Kailua, Hawaii) 3-D digitization software. These contours were converted into a 3-D

mesh of eight-node solid elements using custom software developed in MatLab

(Version 7.1, The Mathworks, Inc.). For each specimen, the mesh was segmented into

rib, cartilage, sternum, and calcification sections (Fig. 2). All simulations were

performed with the dynamic finite element solver of LS-DYNA (version 970,

Livermore Software Technology Corporation, Livermore, CA).

Fully integrated solid elements were used to eliminate hourglassing. A preli-

minary mesh sensitivity study was performed, where two models with different

mesh densities (1.5 and 1 mm nominal element sizes) were constructed for each

of the two specimens (187-4R and 403-4L). The 1 mm models each contained

approximately 2.8 times the number of elements of their 1.5 mm counterparts. This

increase in mesh density did not appreciably change the force–deflection responses

targeted in this study (less than 4% change in peak anterior–posterior,

x-axis force; 10% or less change in peak lateral, y-axis force). Because these models

were observed to be insensitive to mesh density within this range, the 1.5 mm

element size was deemed to be sufficient and was used to model the remainder of

the specimens.

The cartilage substance was modeled as an isotropic, homogeneous, linear

pseudo-elastic material, where the term pseudo-elastic is used here to indicate that

the material models were developed with regard to a specific range of loading rates

(Fung et al., 1979). In the finite element code, the cartilage was represented as a

simple homogeneous, linear elastic material. The pseudo-elastic moduli of the

cartilage of each specimen were determined from the indentation tests described

below. All osseous regions (bone and calcified regions) were also modeled as

homogeneous, isotropic, and linear elastic materials. An elastic modulus of 1 GPa



J.L. Forman, R.W. Kent / Journal of Biomechanics ] (]]]]) ]]]–]]] 3

was used with the bone and calcified regions of all of the models. This was chosen as

a hybrid of the typical modulus of cortical bone (8–30 GPa; Kemper et al., 2005) and

trabecular bone (0.04–0.7 GPa; Li et al., 2010; Kent et al., 2005).

All these regions (bone, cartilage, and calcification) were assumed to be nearly

incompressible, with a Poisson’s Ratio (n) equal to 0.49. A Poisson’s Ratio sensitivity

study was performed with two specimens (187-4R and 403-4L), with n values of

0.495 and 0.499. Changing n in that manner resulted in a less than 2% change in the

peak forces (x and y) generated.

2.3. Indentation testing

Pseudo-elastic moduli were determined for the cartilage of each specimen using

spherical indentation material characterization tests (Lau et al., 2008). The cartilage

specimens were separated into 3–4 cross-sectional test specimens each (each

approximately 6 mm thick) by sectioning with a low-speed, diamond blade saw.

Each of these specimens was potted in a plastic dish with Fast Casts, with the cross-

sectional surface to be indented facing upwards (Fig. 3). Prior to testing, each of the

specimens was soaked in a bath of physiologic saline at body temperature for

approximately 30 min. Each specimen was then placed on the testing stage of a

custom-built indentation machine. At initiation of testing, the indentor tip (2 mm

diameter sphere) moved at approximately 0.5 mm/s (attaining this velocity prior to

contact with specimen, so as to reduce inertial effects) till penetration into the

cartilage to a depth of approximately 0.25 mm (approximately 4% of the 6 mm

sample thickness). At this small relative depth of penetration, the tests can be

regarded (and analyzed) to be an indentation into an infinite half-space (Oliver and

Pharr, 1992). Previous studies have also demonstrated that costal cartilage visco-

elastic material behavior is approximately linear under indentation deformations of

this magnitude (Mattice et al., 2006).

The force generated by the indentation was measured by a 22.2 N uniaxial load cell

(Honeywell Sensotec) mounted between the actuator of the indenter and the indenter

tip; displacement was measured by means of the control instruments located within

the indenter actuator. Data were sampled at 100 Hz. Each cross-section was indented at

Fig. 3. Pictures of indentation testing. (a) A cross-sectional costal cartilage speci-

men prepared and potted in fast-cast. (b) A specimen being subjected to an

indentation test.

Fig. 4. Illustration of the structural costal cartilage experiments. The pic


up to five locations. Indentation locations were chosen to avoid engaging calcified

regions visible on the surface of the cross-sections.

The force–displacement results of the indentation tests were then used to

calculate an instantaneous (short-time) elastic modulus for each specimen. First,

obvious, presumed outliers were identified in the force–response datasets of each

specimen and were removed from the analysis. Then a ‘‘characteristic average’’

force–response was calculated for each specimen using the method developed by

Lessley et al. (2004). Using this characteristic average response, instantaneous

elastic moduli were then determined using the analytical technique described by

Lau et al. (2008). This analytical solution (Oyen, 2005; Mattice et al., 2006) assumes

material linearity, isotropy, and homogeneity to determine a time-dependent

(visco-elastic) description of the shear modulus of the material using a Hertzian

contact solution. Assuming incompressibility, this approach yields an instantaneous

(short-time) elastic modulus combined with a relaxation function. The pseudo-

elastic cartilage moduli were then defined as the instantaneous elastic moduli

derived from the characteristic average visco-elastic models of each specimen. The

full analytical method is described by Lau et al. (2008) and Oyen et al. (2005).

2.4. Structural tests

Structural tests were performed on each costal cartilage specimen to evaluate

the ability of the finite element models to predict their overall structural behavior.

These were all performed prior to indentation testing (due to the destructive nature

of those tests).

The goal of these tests was to study the structural behavior of the specimens

under a simplified loading scenario that may occur as a result of chest loading in an

automobile collision. The boundary conditions chosen for this study were the same

as those used by Forman et al. (2010), and the impetus for these boundary condi-

tions is described in detail therein. The whole cartilage segments were tested by

displacing the sternal boundary posteriorly (in the x-direction), holding all other

boundary degrees of freedom fixed (Fig. 4). Following the approximation of Forman

et al. (2010), posterior displacement of the sternum was applied in the form of a

400 mm/s ramp. The maximum displacement was set to 15 mm, although sub-

sequent analyses were conducted only up to the time of the first observance of

failure in the specimen (as noted by examination of high-speed video).

The specimens were first collected from the ribcages of human cadavers and

were cleaned of all superficial tissue (including the perichondrium). The capsular

ligaments of the sterno-costal joints were left intact to preserve the integrity of the

joint. The sternum and rib ends of the segments were potted in blocks of Fast Casts

(Goldenwest Manufacturing, Inc.) casting resin. These potting blocks were mounted

in a test rig powered by an Instron (model 8874) material test machine. Forces in the

anterior–posterior (x) direction those in the lateral (y) directions were measured

using a custom, low-range load cell (Model 7931, Robert A. Denton, Inc., Rochester

Hills, Michigan) attached to the costal end of the specimens (Fig. 4). All data were

digitally sampled at a rate of 10 kHz with a dynamic data acquisition system (DEWE-

2010 Series, Dewetron, Graz). All force signals were filtered using the Channel

Frequency Class (CFC) 30 described in the Society of Automotive Engineers Standard

J211 (1995); all displacement signals were filtered to CFC 1000. All specimens were

soaked in body-temperature saline prior to testing.

These boundary conditions were then applied to the finite element models of

the cartilage segments (Fig. 5). The model displacements were defined on the basis

tures (left) and the schematic illustrations show the superior view.




of the displacement time-histories measured in the physical tests. The forces on all

the constrained nodes on the costal boundary were summed to determine the total

reaction force. The resulting force–displacement behaviors of the models were

then compared to the observed force–displacement behaviors of their physical

counterparts.

Fig. 5. An example of a cartilage segment finite element model subjected to a

structural test (superior view).

Fig. 6. Superior views of the meshes of the cartilage segment specimens. The images on

within the cartilage. (images not to scale).


3. Results

3.1. Indentation tests

A total of 83 indentation tests were performed on 18 cross-sectional slices of costal cartilage specimens. The peak forcesresulting from the applied 0.25 mm indentations varied fromapproximately 0.25 to 4 N. The resulting characteristic averageinstantaneous elastic moduli parameters are shown in Table 1.

3.2. Models and structural experiments

Subject-specific finite element models were developed usingthe characteristic average instantaneous elastic moduli shown inTable 1. The meshes of these models are shown in Fig. 6. Theresulting force–displacement responses of these models are com-pared to their corresponding experiments in Figs. 7 and 8.

4. Discussion

4.1. Model prediction fit

In three of the five cases, the models predicted the peak x-axisforces within 30% of those observed in the experiments. In all cases,

the right show models with the cartilage removed so as to display calcified regions



Fig. 7. Plots of the force–displacement responses of the models developed with their perichondrium removed compared to their respective structural tests. The data are

shown until the time of the first signs of failure of the physical specimens (as determined from high-speed video).


the peak x-axis model forces were within 36% of the forces observedin the experiments. While an error range of 36% is not ideal, theseresults are nonetheless encouraging given the simplicity of thefinite element and material models used. This error is smallcompared to the effect of the perichondrium (which increasesthe stiffness of the total structure by an average of 100%; Formanet al., 2010). This error is also small when compared to the spreadof costal cartilage modulus values in current whole-body finitemodels, which range from 9 (Ruan et al., 2003) to 49 MPa (Kimparaet al., 2006).

Most of the specimens exhibited softening non-linearities intheir force–deflection responses, the types of which are usuallyassociated with either sub-critical failure or plastic deformation(specimens 403-4L, 322-4L, 400-4L, and 197-4R). The models wereable, however, to reproduce the general characteristics of theseresponse curves, despite the fact that they were built with linearelastic material models. This indicates that those response featuresare at least partially the result of the geometry (and the geometry ofdeformation) of the specimens.


The errors observed with the models consistently took the formof an over-prediction of the peak forces generated. This suggeststhat the average local indentation material properties erredtowards being too stiff. This could occur for several reasons. First,although the indentation sites were chosen to avoid visible areas ofcalcification, it is possible that calcified regions were presentundetected below the surface of some indentation sites. Second,it is possible that the cartilage undergoes a nonlinear softening atstrains greater than those produced in the indentation tests. Thiscould be caused by a material plasticity, or it may be the result ofmicro-structural damage (for example, damage to the collagenfibril matrix in the cartilage). It may be possible to improve theprediction accuracy using a plastic or micro-structural damagemodel for the cartilage (e.g., Wren and Carter, 1998); however, careshould be taken to ensure that such models reflect the actualmaterial behavior and not some other unknown phenomenon.

The models predicted the y-axis force–displacement responses ofthe specimens less consistently than the x-axis responses. The y-axisresponses appeared to match the experimental data very well for two



Fig. 8. Plots (continued) of the force–displacement responses of the models developed with their perichondrium removed compared to their respective structural tests. The

data are shown until the time of the first signs of failure of the physical specimens (as determined from high-speed video).


of the specimens (197-4R and 403-4L), but not very well for the otherspecimens. This may be indicative of material anisotropy or com-pressive instability in some of the specimens and may represent thelimitation of representing the cartilage as a linearly elastic material.

4.2. Practical implications

Many investigations have studied the local material propertiesof costal cartilage (Feng et al., 2001; Guo et al., 2007; Roy et al.,2004; Abrahams and Duggan, 1964; Mattice et al., 2006; Lau et al.,2008). Up till now, there have been no validating data to indicatehow these local material properties affect the structural function ofcostal cartilage. By showing that local material properties can beused to predict structural function, this study provides support tothe previous implicit assumption that by studying local materialproperties we can gain an insight into the overall mechanicalbehavior of costal cartilage. In the future, the effects of changes incartilage properties or those in calcification geometries could bestudied using relatively simple finite element models such as thosedeveloped here.

4.3. Future work

The perichondrium contributes a substantial portion of thestiffness of the whole costal cartilage structure (Forman et al.,2010). Any effort to model the complete costal cartilage structure(e.g., in a whole-body model) must account for the effects of theperichondrium in some manner. Future work could include addi-tion of the perichondrium to detailed models such as thosedeveloped here to study the mechanics of the complete compositestructure of costal cartilage. Future work could also include study ofthe specific effects that calcified regions have on the structural


behavior of the cartilage, including the effects of calcificationgrowth with age.

Finally, future work also should include investigation into howthe material behavior of costal cartilage, and the structuralbehavior of individual cartilage segments, affects the in situ orin vivo mechanical behavior of the ribcage as a whole. Previouscomputational studies have indicated that costal cartilage may playa significant role in the distribution of stress and strain throughoutthe ribcage when an external load is applied (Murakami et al., 2006;Oyen et al., 2005) due to its role as a mechanical coupler. Thecurrent study represents the first step towards the understandingof a link between the material properties of costal cartilage and thestructural behavior of costal cartilage segments. The next step is toinvestigate how the behavior of costal cartilage (combined with theperichondrium) affects the structural behavior of the chest as awhole, possibly through in situ biomechanics experiments withcadaveric tissue.

5. Conclusion

Five subject-specific costal cartilage models (with the perichon-drium removed) were developed and studied in cantilever-likeloading with a dynamic posterior displacement of the sternum. Thematerial properties of the cartilage in the models were derivedfrom local indentation tests—the characteristic average instanta-neous elastic moduli of these specimens ranged from 8.7 to12.6 MPa. The resulting models predicted the peak x-axis forcesgenerated on the costal border during cantilever-like loading with aminimum error of approximately 1% and a maximum error of 36%.The models also predicted x-axis force-versus-displacementresponse curves similar in shape to their experimental counter-parts. These results suggest that when calcified regions areincluded in the models (and the perichondrium is removed from




the tests), models of costal cartilage developed with subject-specific material properties can reproduce the x-axis structuralbehavior of costal cartilage reasonably well (under the type ofloading studied here). Topics for future study include the investi-gation of methods to model the effect of the perichondrium and theinvestigation of different loading modes and rates.

Conflict of interest statement

None of the authors have any conflicts of interest to report.

Acknowledgements

All experiments and computer modeling were performed at theUniversity of Virginia Center for Applied Biomechanics. This manu-script was prepared with support from a Whitaker InternationalScholars Grant. All analyses and opinions expressed here are solelythose of the authors.

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