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Research Papers

Pelvic Construct Prediction of Trabecular and Cortical Bone Structural Architecture

[+] Author and Article Information
Dan T. Zaharie

The Royal British Legion Centre for
Blast Injury Studies,
Imperial College London,
London SW7 2AZ, UK;
Structural Biomechanics,
Department of Civil and
Environmental Engineering,
Imperial College London,
Skempton Building, South Kensington Campus,
London SW7 2AZ, UK
e-mail: dan.zaharie10@imperial.ac.uk

Andrew T. M. Phillips

The Royal British Legion Centre for
Blast Injury Studies,
Imperial College London,
London SW7 2AZ, UK;
Structural Biomechanics,
Department of Civil and
Environmental Engineering,
Imperial College London,
Skempton Building, South Kensington Campus,
London SW7 2AZ, UK
e-mail: andrew.phillips@imperial.ac.uk

1Corresponding author.

Manuscript received December 5, 2016; final manuscript received November 10, 2017; published online May 24, 2018. Assoc. Editor: Steven D. Abramowitch.

J Biomech Eng 140(9), 091001 (May 24, 2018) (11 pages) Paper No: BIO-16-1497; doi: 10.1115/1.4039894 History: Received December 05, 2016; Revised November 10, 2017

The pelvic construct is an important part of the body as it facilitates the transfer of upper body weight to the lower limbs and protects a number of organs and vessels in the lower abdomen. In addition, the importance of the pelvis is highlighted by the high mortality rates associated with pelvic trauma. This study presents a mesoscale structural model of the pelvic construct and the joints and ligaments associated with it. Shell elements were used to model cortical bone, while truss elements were used to model trabecular bone and the ligaments and joints. The finite element (FE) model was subjected to an iterative optimization process based on a strain-driven bone adaptation algorithm. The bone model was adapted to a number of common daily living activities (walking, stair ascent, stair descent, sit-to-stand, and stand-to-sit) by applying onto it joint and muscle loads derived using a musculoskeletal modeling framework. The cortical thickness distribution and the trabecular architecture of the adapted model were compared qualitatively with computed tomography (CT) scans and models developed in previous studies, showing good agreement. The sensitivity of the model to changes in material properties of the ligaments and joint cartilage and changes in parameters related to the adaptation algorithm was assessed. Changes to the target strain had the largest effect on predicted total bone volumes. The model showed low sensitivity to changes in all other parameters. The minimum and maximum principal strains predicted by the structural model compared to a continuum CT-derived model in response to a common test loading scenario showed good agreement with correlation coefficients of 0.813 and 0.809, respectively. The developed structural model enables a number of applications such as fracture modeling, design, and additive manufacturing of frangible surrogates.

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Figures

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Fig. 1

Lower limb musculoskeletal model in (a) standing and (b) seated positions

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Fig. 2

Transverse 2.5 mm slice of the pelvic for the base FE model. Shell elements representing cortical bone are shown in gray in the border areas; truss elements representing trabecular bone are shown in the interior in red (see color figure online).

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Fig. 3

Pelvis model with ligaments included: Sacroiliac ligaments in blue (center top), pubic ligament in red (center bottom), sacrospinous ligaments in yellow (middle), sacrotuberous ligaments in purple (outer edge of sacrospinous ligaments) and inguinal ligaments in green (diagonal front) (see color figure online)

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Fig. 7

Contours of position-dependent cortical thickness ranging from 0.1 mm to 5 mm are shown in the top row: (a) frontal view of pelvis, (b) anterior and (c) medial views of the right innominate. Trabecular elements' radii distribution ranging from 0.1 mm to 2 mm is shown in the bottom row: (d) frontal view, (e) anterior, and (f) medial views of the right innominate. Trabecular elements with a radius < 0.1 mm were excluded for clarity.

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Fig. 4

(a) Load applicator at the hip and (b) fixator at the top of the sacrum. The elements representing the bone are shown in light gray, with the two layers of soft elements (from left to right in (a) and top to bottom in (b)) in red and the two layers of stiffer elements in blue (dark blue represents the stiffest layer of elements in the hip applicator). In addition, the black arrow illustrates the peak load applied on the hip joint during walking (see color figure online)

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Fig. 5

Hip JCFs derived from musculoskeletal model for cycles of (a) walking, (b) stair ascent, (c) stair descent, and (d) sit-to-stand and stand-to-sit are shown in green lines for the right leg and blue lines for the left leg. The frames selected for each activity to be used in the FE simulations are highlighted using solid circles. Hip JCFs recorded and reported by Bergmann et al. [3] for the right leg are shown in dashed lines for each activity (see color figure online)

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Fig. 6

Modeling framework

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Fig. 8

Selected 5 mm slices of the converged pelvic model illustrating the trabecular structure and cortical thickness. Truss elements with a radius >0.1 mm are shown in red (largest clusters), with elements with a radius of 0.1 mm shown in blue. Elements with a radius of 1 μm are not shown for clarity.

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Fig. 9

Trabecular trajectories formed in the ilium adapted from (a) walking and (b) all activities. The trajectories highlighted correspond to regions in the ilium with a higher trabecular density caused by walking observed by Machiarelli et al. [64]: superior bundle (sb), anterior bundle (ab), sacropubic bundle (spb), iliocotyloid bundle (icb), ilioischial bundle (iib), and trabecular chiasma (tc). Truss elements with a radius >0.1 mm are shown in red (clusters with thick elements). Truss elements with a radius of 0.1 mm appear in blue (see color figure online).

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Fig. 10

Figure illustrating transverse slices from the CT scans (a, c, e, g) shown along with corresponding slices of the pelvic model (b, d, f, h) generated using an in-house code developed in matlab. Shell elements and truss elements with a radius > 0.1 mm are shown in light gray. Truss elements with a radius of 0.1 mm appear in dark gray. Elements with a radius of 1 μm are not shown for clarity.

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Fig. 11

Influence of activities on cortical (a, b, c) and trabecular (d, e, f) structure of converged pelvic model. The elements are color mapped based on the activity which has been most influential in determining their thickness. Further information on the influence of activities on the cortical and trabecular architecture can be found in the supplemental Fig. S1 which is available under the “Supplemental Data” tab for this paper on the ASME digital collection.

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Fig. 12

Comparison between the minimum (a) and the maximum (b) principal strains across the surface of the structural model (x axis) and CT-derived model (y axis). Lines of best fit are shown in solid lines for each case and do not differ greatly from the y = x line shown in dash line.

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