Twente spine model: A complete and coherent dataset for musculo-skeletal modeling of the lumbar region of the human spine

Author’s Accepted Manuscript Twente Spine Model: A Complete and Coherent Dataset for Musculo-Skeletal Modeling of the Lumbar Region of the Human Spine Riza Bayoglu, Leo Geeraedts, Karlijn H.J. Groenen, Nico Verdonschot, Bart Koopman, Jasper Homminga www.elsevier.com/locate/jbiomech

PII: DOI: Reference:

S0021-9290(17)30010-6 http://dx.doi.org/10.1016/j.jbiomech.2017.01.009 BM8081

To appear in: Journal of Biomechanics Accepted date: 5 January 2017 Cite this article as: Riza Bayoglu, Leo Geeraedts, Karlijn H.J. Groenen, Nico Verdonschot, Bart Koopman and Jasper Homminga, Twente Spine Model: A Complete and Coherent Dataset for Musculo-Skeletal Modeling of the Lumbar Region of the Human Spine, Journal of Biomechanics, http://dx.doi.org/10.1016/j.jbiomech.2017.01.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Twente Spine Model: A Complete and Coherent Dataset for Musculo-Skeletal Modeling of the Lumbar Region of the Human Spine Riza Bayoglua,∗, Leo Geeraedtsb , Karlijn H. J. Groenenc , Nico Verdonschota,c , Bart Koopmana , Jasper Hommingaa a Department

of Biomechanical Engineering, University of Twente, Enschede, the Netherlands university medical center, Department of Anatomy, Nijmegen, the Netherlands c Radboud university medical center, Radboud Institute for Health Sciences, Orthopaedic Research Laboratory, Nijmegen, The Netherlands b Radboud

Abstract

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Musculo-skeletal modeling can greatly help in understanding normal and pathological func-

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tioning of the spine. For such models to produce reliable muscle and joint force estimations, an

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adequate set of musculo-skeletal data is necessary. In this study, we present a complete and co-

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herent dataset for the lumbar spine, based on medical images and dissection measurements from

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one embalmed human cadaver. We divided muscles into muscle-tendon elements, digitized their at-

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tachments at the bones and measured morphological parameters. In total, we measured 11 muscles

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from one body side, using 96 elements. For every muscle element, we measured three-dimensional

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coordinates of its attachments, fiber length, tendon length, sarcomere length, optimal fiber length,

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pennation angle, mass, and physiological cross-sectional area together with the geometry of the

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lumbar spine. Results were consistent with other anatomical studies and included new data for

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the serratus posterior inferior muscle. The dataset presented in this paper enables a complete and

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coherent musculo-skeletal model for the lumbar spine and will improve the current state-of-the art

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in predicting spinal loading.

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Keywords: lumbar spine, cadaver, musculo-skeletal model, muscles, sarcomere length

∗ Corresponding author at: Department of Biomechanical Engineering, Horstring W213, University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands. Tel.: +31 053 4896477, Fax: +31 53 489 2287, E-mail address: [email protected] (Riza Bayoglu).

Preprint submitted to Journal of Biomechanics

January 10, 2017

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1. Introduction

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The combination of flexibility and rigidity that characterizes the spine makes it vulnerable to a

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range of mechanical and medical problems, and it is therefore an important area for biomechanical

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research. Most spine research has focused on the lumbar spine with a special focus on low back

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pain (McGill, 1992; Alireza et al., 2011; Zander et al., 2015; Putzer et al., 2016) and disc herni-

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ation (Wilke et al., 2016). Despite high quality research on the lumbar spine, our understanding

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of its in-vivo mechanical function remains limited due to its complex structure. Musculo-skeletal

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models of the lumbar spine would enable clinical insights into its functioning, and allow answering

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what if questions (Blemker et al., 2007).

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The capability of a muscle to produce torques at the joints is directly related to its moment arms,

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and thus to its origin and insertion, and to its strength (Vasavada et al., 1998). Therefore, repre-

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sentation of muscles in musculo-skeletal models demands special care to simulate true anatomy and

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realistic in-vivo muscle function. In the lower extremity, Carbone et al. (2012) demonstrated that

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small differences in muscle attachments may markedly affect muscle moment arms, and, thus af-

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fect muscle force predictions considerably. Furthermore, morphological parameters such as optimal

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fiber length, tendon length and physiological cross-sectional area, are critical inputs into musculo-

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skeletal models (Kamibayashi and Richmond, 1998). In short, accuracy of modeling lines-of-action

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and morphological parameters determine muscle activation levels and have significant effects on the

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output of a musculo-skeletal model.

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Currently there is no musculo-skeletal dataset which enables the development of a complete

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and coherent model for the lumbar spine. None of the previous studies quantified muscle attach-

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ments at the bones and measured complete morphological parameters for all muscles of the lumbar

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spine (Bogduk et al., 1992a,b, 1998; Macintosh and Bogduk, 1991; Macintosh et al., 1986; Delp

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et al., 2001; Phillips et al., 2008). Instead, they typically focused on a smaller part of the lumbar

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spine and presented anatomical drawings to illustrate muscle attachments. Subsequently, current

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musculo-skeletal models require piecing together data from these studies and making assumptions

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when data does not exist. Consequently, such models will require complex scaling between the

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geometries and the muscle architectures of the cadaveric specimens (de Zee et al., 2007; Arjmand

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et al., 2009; Christophy et al., 2012; Ignasiak et al., 2016). This approach may then result in a 2

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musculo-skeletal system that never really existed (Borst et al., 2011). Therefore, a musculo-skeletal

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model based on one complete and coherent dataset–obtained from one body–would further improve

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our understanding of the human spine and is, thus, a better approach for clinical use (Klein Hors-

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man et al., 2007). The aim of our work is to obtain a complete and coherent anatomical dataset

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for the entire human spine, but in this paper we focus on the lumbar spine alone. This dataset

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includes segmented bone surfaces, three-dimensional coordinates of muscle attachment sites, bony

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wrapping surfaces and morphological muscle parameters from a single human cadaver.

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2. Materials and Methods

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2.1. Cadaveric specimen

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An embalmed human cadaver body (79 years-old, male, height: 154 cm, mass: 51 kg) was ob-

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tained with institutional approval from Radboud university medical center. The cause of death was

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Alzheimer. We noticed that the fifth lumbar vertebra was fused to the sacrum. In the cadaver, we

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distinguished 33 bones: twelve thoracic and four lumbar vertebrae, twelve ribs, sternum, humerus,

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femur, sacrum and pelvis.

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2.2. Medical imaging

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Prior to dissection, we acquired full body supine computed tomography (CT) images (Siemens

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SOMATOM Sensation 64, Siemens AG, Munich, Germany, voxel size 0.977 mm x 0.977 mm x

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1 mm).

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2.3. Cadaveric measurements

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We measured muscles of the lumbar spine from the right side of the trunk, therefore we removed

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complete skin and subcutaneous fat on this side. Subsequently, we inserted reference tube-screw

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connectors (see Fig. 1a) in the bones under the guidance of a C-arm device (Phillips BV 29).

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These connectors were used to construct temporary local reference frames in the bones enabling

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the consistent alignment of the optical reference tool between position measurement sessions. To

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strengthen the fixation between the bones and the connectors, Polymethylmethacrylate (PMMA)

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was poured through the screw guide holes. The positions of muscle attachments in three-dimensions

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with respect to the corresponding reference frames of the bones were measured using the NDI Hybrid

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Polaris Spectra tracking system. Because it was not possible to insert the connectors in the ribs,

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muscles that had attachments to the ribs were measured with respect to other bones nearby (for

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example, an attachment site at the twelfth rib was measured with respect to the reference frame of

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the twelfth vertebra). A graphical user interface was developed in Matlab R2014b to communicate

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with the tracking system and was utilized to properly record the measurements. Prior to the

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experiment, we assessed the accuracy of using these connectors. We found a position error of

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0.331 ± 0.391 mm for measuring a single attachment point.

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2.3.1. Muscle attachment sites

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After identification of a target muscle, fat at the intramuscular connections was removed, and

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the muscle was divided into several muscle-tendon elements to represent its function more accu-

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rately in the musculo-skeletal model. The number of elements (functionally different parts of a

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muscle) was decided by using a previously described method (Breteler et al., 1999). The dissections

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were performed by an experienced anatomist. After locating the tendons at origin and insertion of

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the muscle elements, colored beads were used to mark the attachments of the elements (see Fig.

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1b). Subsequently, we resected muscle elements and measured positions of their attachments at

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origin and insertion. We also measured the positions of via points (locations where a muscle is

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constrained to move) for elements with a curved lines-of-action. Depending on the size and shape

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of the muscles, we measured the attachments in one of the three geometrical forms, point, line or

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surface (see Fig. 2). Finally, we labeled the muscle elements and stored them in 2 % formaldehyde

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solution until the measurement of morphological parameters.

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The resection procedure differed slightly for iliocostalis, longissimus, and multifidus muscles.

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Dividing these muscles into elements in-situ was not possible due to superficial and deep layers of

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muscle fibers. First, positions of attachments (where possible) at the bones were measured, and

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the entire muscle was resected afterwards. Later, they were micro-dissected and were divided into

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elements as done in previous anatomical studies (Macintosh et al., 1986; Macintosh and Bogduk,

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1987). In addition, measuring the attachments of the psoas major muscle was impossible, as this

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muscle has its origins inside the abdominal cavity on the anterior side, which prevented the optical

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tools from being seen by the camera. We identified and noted its origins at the bones and later

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modeled their lines-of-action based on the study by Bogduk et al. (1992b).

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2.3.2. Muscle morphological parameters

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For every element, we measured the following morphological muscle parameters: fiber length,

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tendon length, sarcomere length, optimal fiber length, pennation angle, mass, and physiological

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cross-sectional area. Prior to measuring these parameters, remaining fat and connective tissue on

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the surface of the muscle elements were carefully removed.

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Pennation angle was measured by using a protractor (we neglected to measure the angles below

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10°). Subsequently, the muscle element was placed on a flat table, and its musculo-tendon length 5

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(tendon-muscle-tendon length) between most proximal and distal ends was measured by using a

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ruler with a resolution of 0.5 mm. Depending on the size of an element, we measured the lengths of

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up to six representative fibers to calculate an average fiber length for that element. Next, tendons

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were cut at both ends, and an average tendon length was calculated by subtracting average fiber

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length, multiplied by the cosine of the pennation angle, from measured musculo-tendon length.

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Then, we weighed the muscle elements (muscle fibers) by using a scale which had a resolution of

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0.01 g. Elements were wiped with tissue to remove excess fluid before weighing. Due to the complex

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tendinous connections of the abdomen muscles, obliquus externus abdominis and obliquus internus

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abdominis, we measured their tendon lengths while the muscles were still intact.

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Average sarcomere length for every muscle was calculated by using the laser diffraction method (Cross

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et al., 1981). For this, a vertical laser set-up which employed a Helium-Neon laser with a beam

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diameter of 2 mm and a wavelength of 632.8 nm was used (see Fig. 1c). A constant distance (D

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= 55 mm) was kept between the samples and reading screen throughout the measurements. We

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measured the distance between the first diffraction bands (2T in Fig. 1c) with a digital caliper

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(with a resolution of 0.01 mm) and calculated sarcomere length (SL, in µm) from this distance by

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using equation 1:

SL =

632.8 × 10

r −3

×D× T

(

T 2 ) +1 D

(1)

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Six to ten samples–consisting of one to five muscle fibers–were peeled from the representative

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element under an operation microscope and were used for the measurements. Samples were pre-

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pared from proximal end, distal end, and middle of the element. If the standard deviation of six

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samples exceeded 0.25 µm, we included up to four more samples taken between the proximal end

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and middle, and distal end and middle of the element. For each sample, we performed three sar-

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comere length measurements (at either ends and middle of the sample) and calculated the mean of

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three measurements. Subsequently, the average sarcomere length of a muscle was calculated from

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all the samples.

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The optimal fiber length of an element (in mm) was calculated by using equation 2, `fo =

`f × 2.7 `s

(2)

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where `f is the average fiber length and `s is the average sarcomere length of the muscle. We

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assumed an optimal sarcomere length of 2.7 µm for skeletal muscles (Breteler et al., 1999).

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The volume of muscle elements was calculated by assuming a density of 1.0576 g/cm3 for muscle

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tissue (Breteler et al., 1999). Moreover, physiological cross-sectional area (PCSA, in cm2 ) was

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calculated according to equation 3, P CSA =

mass × cos(α) ρ × `fo

(3)

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where α is the pennation angle, ρ is the muscle density, mass is the mass of the element, and `fo

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is the optimal fiber length. In line with Brown et al. (2011), for the rectus abdominis PCSA was

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calculated as the largest measured regional PCSA and was distributed among its elements with

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respect to their masses. Fiber lengths were summed for all regions.

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2.4. Processing of muscle attachments

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We manually segmented CT images into stereolithography (STL) geometry files (Mimics 18.0

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Materialise N. V., Leuven, Belgium). The iterative closest point algorithm was used to register

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point clouds (scanned over the bone surfaces) with the STL files (Besl and McKay, 1992). See

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Appendix A.1 for more details. After registration, muscle attachments (measured with respect to

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the temporary local reference frames of the bones) were transformed to the global reference frame

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defined by the CT scanner. In the global reference frame, x, y, and z axes point cranially, posteri-

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orly, and laterally (to the left), respectively.

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For line-shaped attachments, a polynomial of third degree was fit through the measured points.

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Subsequently, n equidistant points (n is the number of elements that share an attachment site

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together) were calculated on the fitted polynomial curve as to represent the attachments of the

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elements (Pellikaan et al., 2014). The point-shaped attachments did not require further process-

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ing. For surface-shaped attachments, first a plane was fitted through the measured points. The

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measured points were projected onto the fitted plane, and a surface area was interpolated through 7

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the projected points. Later, the centroids of the n equi-areal parts of the surface were calculated

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to represent the attachments for the elements (Pellikaan et al., 2014), referring to (der Helm et al.,

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1992). Finally, all the calculated attachments were either projected on the surface of the STL files

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or left intact, depending on whether an element attached to only one bone or spanned between

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multiple bones, respectively.

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Furthermore, we graphically estimated wrapping surfaces–from the geometry of the spine and

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measured point clouds over the structures that muscles wrap–in the AnyBody Modeling SystemT M

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version. 6.0.4 (AnyBody Technology A/S, Aalborg, Denmark). Depending on the shape of a surface,

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either a cylinder or an ellipsoid was estimated. See Appendix A.2 for details.

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3. Results

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The complete list of measured muscle elements is given in Table 1. In total, we measured 11

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muscles from one side of the body using 96 muscle elements. For every element, we obtained the

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coordinates of its attachments at origin and insertion together with the morphological parameters:

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fiber length, sarcomere length, optimal fiber length, tendon length, pennation angle, mass, and

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physiological cross-sectional area (PCSA). Individual PCSAs were relatively small, the largest be-

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ing 2.74 cm2 for an element of the psoas major. Total muscle PCSAs ranged from 2.07 cm2 for the

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serratus posterior inferior to 18.50 cm2 for the longissimus thoracis. Mean sarcomere lengths ranged

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from 2.14 µm for the internal oblique to 3.57 µm for the longissimus thoracis. Fiber length ranged

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from 2.0 cm for an element of the transversus abdominis to 26.3 cm for an element of the rectus

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abdominis. Mean optimal fiber lengths ranged from 4.0 cm for multifidus to 25.1 cm for the rectus

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abdominis. Tendon lengths for the thoracic component of the longissimus thoracis were very long,

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ranging from 7.4 cm to 26.6 cm, while its lumbar component had relatively short tendon lengths.

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The definitions of wrapping surfaces can be found in Appendix A.2, and the coordinates of via

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points can be found in Appendix A.3 both as digital appendices. All the bones with re-constructed

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muscle lines-of-action were visualized in the AnyBody Modeling SystemT M ver. 6.0.4 (AnyBody

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Technology A/S, Aalborg, Denmark) and are depicted in Fig. 3.

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Table 1: Per muscle element: element number (#), fiber length (`f ), sarcomere length (`s ), optimal fiber length (`fo ), tendon length (`t ), pennation angle (α), physiological cross-sectional area (PCSA), and coordinates of attachments at origin and insertion with respect to the global reference frame defined by the CT scanner. muscle

#

obliquus externus abdominis obliquus externus abdominis obliquus externus abdominis obliquus externus abdominis obliquus externus abdominis obliquus externus abdominis obliquus externus abdominis iliocostalis lumborum iliocostalis lumborum iliocostalis lumborum iliocostalis lumborum iliocostalis lumborum iliocostalis lumborum obliquus internus abdominis obliquus internus abdominis obliquus internus abdominis obliquus internus abdominis obliquus internus abdominis obliquus internus abdominis latissimus dorsi latissimus dorsi latissimus dorsi latissimus dorsi latissimus dorsi longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis longissimus thoracis multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus multifidus psoas major psoas major psoas major psoas major psoas major psoas major psoas major psoas major psoas major psoas major quadratus lumborum quadratus lumborum quadratus lumborum quadratus lumborum quadratus lumborum quadratus lumborum Continued on next page

1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6

`f

`s

f `o

`t

α

[mm]

[µm]

[mm]

[mm]

71.1 103.8 125.6 131.7 96.7 58.5 56.2 81.5 100.4 106.7 98.0 114.7 114.7 36.8 55.5 88.5 57.9 51.5 56.5 229.7 228.8 209.7 190.5 171.3 93.0 80.7 85.0 105.3 87.0 77.0 27.0 42.0 64.0 91.7 109.3 135.3 87.7 102.8 63.5 68.3 57.8 82.3 76.3 67.0 119.8 126.0 87.0 55.0 47.0 51.7 42.7 42.0 38.6 34.1 27.5 59.9 57.7 44.5 83.4 72.7 57.3 30.0 112.6 112.8 138.0 97.5 115.8 126.6 128.4 108.0 131.3 136.3 21.0 26.2 37.4 60.7 51.4 26.3

2.82 2.82 2.82 2.82 2.82 2.82 2.82 2.81 2.81 2.81 2.81 2.81 2.81 2.14 2.14 2.14 2.14 2.14 2.14 2.26 2.26 2.26 2.26 2.26 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.84 2.84 2.84 2.84 2.84 2.84

68.2 99.6 120.4 126.2 92.7 56.1 53.9 78.3 96.4 102.4 94.1 110.1 110.1 46.4 70.1 111.8 73.1 65.0 71.4 274.6 273.5 250.7 227.7 204.8 70.3 61.0 64.3 79.6 65.8 58.2 20.4 31.8 48.4 69.3 82.7 102.4 66.3 77.7 48.0 51.6 43.7 62.3 57.7 50.7 90.6 95.3 65.8 44.4 37.9 41.7 34.5 33.9 31.1 27.5 22.2 48.3 46.6 35.9 67.3 58.6 46.3 24.2 117.1 117.2 143.4 101.3 120.4 131.6 133.4 112.2 136.5 141.7 20.0 24.9 35.6 57.8 48.9 25.1

35.9 95.2 172.4 153.4 120.7 137.7 83.7 23.5 59.6 108.3 172.0 202.3 235.3 19.8 29.5 135.0 117.1 87.7 64.5 123.8 196.6 120.3 112.0 103.7 225.3 215.8 203.7 217.7 204.5 240.4 12.0 18.0 20.0 33.3 55.7 73.8 150.2 168.6 216.3 210.4 241.2 224.7 237.6 266.3 223.3 223.6 265.5 12.0 21.0 55.7 41.7 27.0 72.8 28.3 19.5 40.5 30.7 7.0 28.0 33.8 4.7 11.5 157.4 223.8 201.0 200.5 223.2 226.9 206.6 191.5 206.7 211.7 31.0 29.8 33.6 35.3 32.1 29.7

mass

pcsa

[deg]

[g]

[cm2 ]

bone

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8.18 19.04 20.29 16.59 12.76 9.51 1.53 15.54 18.99 7.87 5.95 5.84 5.84 8.08 13.23 27.09 8.92 5.41 4.83 70.14 37.88 37.62 19.27 9.74 6.49 0.77 2.31 2.51 1.94 1.05 4.86 5.69 7.90 12.57 22.89 15.52 11.41 4.08 1.43 1.80 1.18 2.43 2.54 1.40 3.83 6.06 0.91 0.33 0.33 2.83 1.95 0.61 4.37 1.93 0.71 4.36 4.17 0.97 5.27 4.74 2.37 0.86 14.44 21.13 11.84 4.68 14.63 38.08 31.76 13.56 11.75 12.09 2.48 0.89 4.00 3.06 4.85 1.99

1.13 1.81 1.59 1.24 1.30 1.60 0.27 1.88 1.86 0.73 0.60 0.50 0.50 1.65 1.78 2.29 1.15 0.79 0.64 2.42 1.07 1.42 0.80 0.45 0.87 0.12 0.34 0.30 0.28 0.17 2.25 1.69 1.54 1.71 2.62 1.43 1.63 0.50 0.28 0.33 0.26 0.37 0.42 0.26 0.40 0.60 0.13 0.07 0.08 0.64 0.54 0.17 1.33 0.66 0.30 0.85 0.85 0.26 0.74 0.76 0.48 0.34 1.17 1.70 0.78 0.44 1.15 2.74 2.25 1.14 0.81 0.81 1.17 0.34 1.06 0.50 0.94 0.75

Pelvis Pelvis Pelvis Linea alba Linea alba Linea alba Linea alba Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis Pelvis L2 T11 T9 T7 L4 Sacrum Sacrum L5 Sacrum Sacrum Sacrum Pelvis Pelvis Pelvis Pelvis Sacrum Sacrum Sacrum Sacrum Sacrum Sacrum L5 L4 L4 L3 L2 L1 Sacrum Sacrum Sacrum Sacrum Sacrum Sacrum L5 L5 Pelvis Sacrum L4 Pelvis L5 L4 L3 Sacrum L3L4IVD L3 L4 L2 L1 L1 L3 L2L3IVD L2 Pelvis Pelvis Pelvis Pelvis L3 Pelvis

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origin

form

line line line line line line line surface surface surface surface surface surface line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line line surface surface surface surface surface surface surface point surface surface point surface surface point point surface surface surface surface surface surface surface surface surface surface surface surface line line point line

position [m]

insertion

x

y

z

bone

-0.1262 -0.1365 -0.1233 0.0000 0.0000 0.0000 0.0000 -0.0601 -0.0551 -0.0503 -0.0466 -0.0440 -0.0420 -0.0923 -0.1194 -0.1345 -0.1275 -0.1135 -0.0973 -0.0775 -0.0034 -0.0046 -0.0055 -0.0077 -0.0070 -0.0073 -0.0073 -0.0081 -0.0040 -0.0073 -0.0391 -0.0406 -0.0412 -0.0412 -0.0412 -0.0445 -0.0398 -0.0253 -0.0040 -0.0073 -0.0073 -0.0081 -0.0070 -0.0076 -0.0086 -0.0072 -0.0063 -0.0121 -0.0348 -0.0368 -0.0241 -0.0334 -0.0440 -0.0279 -0.0350 -0.0407 -0.0237 -0.0341 -0.0417 -0.0245 -0.0321 -0.0242 -0.0356 -0.0280 -0.0336 -0.0329 -0.0260 -0.0192 -0.0231 -0.0248 -0.0270 -0.0257 -0.0791 -0.0755 -0.0859 -0.0785 -0.0513 -0.0798

-0.1046 -0.1401 -0.1700 -0.2142 -0.2240 -0.2316 -0.2407 -0.0522 -0.0475 -0.0437 -0.0406 -0.0387 -0.0370 -0.0777 -0.0997 -0.1294 -0.1628 -0.1783 -0.1797 -0.0647 -0.0461 -0.0373 -0.0347 -0.0364 -0.0475 -0.0370 -0.0370 -0.0445 -0.0270 -0.0398 -0.0559 -0.0422 -0.0406 -0.0406 -0.0406 -0.0426 -0.0397 -0.0349 -0.0270 -0.0370 -0.0398 -0.0445 -0.0475 -0.0476 -0.0491 -0.0481 -0.0463 -0.0279 -0.0331 -0.0387 -0.0365 -0.0391 -0.0416 -0.0533 -0.0652 -0.0526 -0.0518 -0.0799 -0.0554 -0.0546 -0.0748 -0.0838 -0.0939 -0.1080 -0.0922 -0.0960 -0.0909 -0.0897 -0.0984 -0.1085 -0.1150 -0.1140 -0.0783 -0.0713 -0.0756 -0.0697 -0.0816 -0.0810

0.7301 0.7092 0.6836 0.6541 0.7226 0.7841 0.8538 0.7270 0.7198 0.7122 0.7057 0.6989 0.6941 0.7381 0.7329 0.7208 0.6931 0.6720 0.6399 0.7360 0.7770 0.8546 0.9029 0.9558 0.7327 0.6866 0.6866 0.7140 0.6551 0.6919 0.7002 0.6979 0.6962 0.6962 0.6962 0.6467 0.6417 0.6400 0.6551 0.6866 0.6919 0.7140 0.7327 0.7410 0.7572 0.7772 0.8014 0.6555 0.6513 0.6333 0.6528 0.6747 0.6489 0.6990 0.7250 0.6850 0.6920 0.7411 0.6988 0.6990 0.7456 0.7742 0.6951 0.7360 0.7600 0.7301 0.7890 0.8199 0.8289 0.7462 0.7700 0.7784 0.7431 0.7428 0.7434 0.7427 0.7607 0.7410

R11 R10 R9 R8 R7 R6 R5 R11 R10 R9 R8 R7 R6 R11 R10 Linea alba Linea alba Linea alba Linea alba Humerus Humerus Humerus Humerus Humerus R5 R8 R8 R6 R9 R7 L5 L4 L3 L2 L1 T12 T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 L5 L5 L4 L4 L4 L3 L3 L3 L2 L2 L2 L1 L1 L1 L1 Femur Femur Femur Femur Femur Femur Femur Femur Femur Femur L3 L2 L2 L1 R12 L3

form

line surface surface surface line line line point point point point point point line line line line line line line line line line line point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point point line line line line line line line line line line line line line point line point

position [m] x

y

-0.1167 -0.1253 -0.1312 -0.1368 -0.1324 -0.1208 -0.1109 -0.0776 -0.0766 -0.0741 -0.0800 -0.0798 -0.0709 -0.1170 -0.1216 0.0000 0.0000 0.0000 0.0000 -0.1382 -0.1362 -0.1365 -0.1375 -0.1385 -0.0425 -0.0403 -0.0454 -0.0492 -0.0456 -0.0513 -0.0367 -0.0338 -0.0263 -0.0247 -0.0240 -0.0220 -0.0268 -0.0295 -0.0299 -0.0314 -0.0316 -0.0320 -0.0336 -0.0279 -0.0239 -0.0209 -0.0222 -0.0082 -0.0100 -0.0065 -0.0061 -0.0083 -0.0091 -0.0099 -0.0092 -0.0068 -0.0068 -0.0089 -0.0051 -0.0051 -0.0036 -0.0064 -0.0818 -0.0818 -0.0818 -0.0818 -0.0818 -0.0818 -0.0818 -0.0818 -0.0818 -0.0818 -0.0488 -0.0493 -0.0491 -0.0433 -0.0425 -0.0513

-0.0965 -0.1010 -0.1159 -0.1413 -0.1707 -0.1893 -0.1952 -0.0601 -0.0504 -0.0495 -0.0513 -0.0556 -0.0610 -0.1012 -0.1643 -0.2365 -0.2320 -0.2237 -0.2146 -0.1698 -0.1652 -0.1616 -0.1588 -0.1566 -0.0749 -0.0558 -0.0496 -0.0653 -0.0473 -0.0552 -0.0690 -0.0784 -0.0796 -0.0786 -0.0703 -0.0603 -0.0529 -0.0476 -0.0444 -0.0481 -0.0531 -0.0618 -0.0752 -0.0896 -0.1049 -0.1211 -0.1453 -0.0457 -0.0506 -0.0485 -0.0541 -0.0612 -0.0511 -0.0580 -0.0662 -0.0496 -0.0496 -0.0700 -0.0496 -0.0486 -0.0553 -0.0635 -0.1022 -0.1022 -0.1022 -0.1022 -0.1022 -0.1022 -0.1022 -0.1022 -0.1022 -0.1022 -0.0827 -0.0791 -0.0799 -0.0757 -0.0700 -0.0825

z

0.78 0.81 0.84 0.86 0.87 0.89 0.92 0.84 0.88 0.92 0.96 0.97 1.01 0.77 0.77 0.83 0.77 0.71 0.65 1.05 1.05 1.04 1.04 1.04 1.04 0.97 0.96 1.02 0.93 0.99 0.72 0.73 0.76 0.78 0.81 0.84 0.87 0.90 0.92 0.96 0.98 1.01 1.03 1.05 1.07 1.09 1.11 0.70 0.70 0.73 0.72 0.73 0.74 0.75 0.75 0.77 0.77 0.77 0.79 0.79 0.79 0.80 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.75 0.78 0.78 0.82 0.83 0.75

Table 1: Continued from previous page muscle

#

`f

`s

f `o

`t

α

mass

pcsa

origin

form

quadratus lumborum quadratus lumborum rectus abdominis rectus abdominis rectus abdominis serratus posterior inferior serratus posterior inferior serratus posterior inferior transversus abdominus transversus abdominus transversus abdominus transversus abdominus transversus abdominus transversus abdominus transversus abdominus transversus abdominus transversus abdominus transversus abdominus .

7 8 1 2 3 1 2 3 1 2 3 4 5 6 7 8 9 10

[mm] 33.0 52.0 262.7 253.3 244.3 27.1 43.2 53.3 47.5 56.5 112.0 115.0 115.0 105.0 50.0 49.0 35.0 20.0

[µm] 2.84 2.84 2.72 2.72 2.72 2.74 2.74 2.74 2.83 2.83 2.83 2.83 2.83 2.83 2.83 2.83 2.83 2.83

[mm] 31.4 49.5 260.3 251.0 242.1 26.7 42.5 52.4 45.2 53.8 106.7 109.5 109.5 100.0 47.6 46.7 33.3 19.0

[mm] 25.5 64.0 50.3 54.2 66.7 98.4 89.8 98.3 69.0 89.5 159.8 157.3 161.1 168.7 65.8 43.6 24.7 27.1

[deg] 0 0 0 0 0 0 0 0 0 0 10 10 10 10 10 10 10 10

[g] 3.07 7.81 28.23 56.19 31.53 1.80 3.39 3.79 1.36 1.36 2.91 2.91 2.91 2.91 1.96 1.96 1.96 1.96

[cm2 ] 0.92 1.49 1.13 2.24 1.26 0.64 0.75 0.68 0.28 0.24 0.25 0.25 0.25 0.27 0.38 0.39 0.55 0.96

bone Pelvis Pelvis Pelvis Pelvis Pelvis L1 T12 T10 Pelvis Pelvis L4 L3 L2 L1 R11 R10 R9 R7

line line surface surface surface line line line line line line line line line line line line line

1 Musculo-tendon

position [m] x -0.0932 -0.1052 -0.0094 -0.0094 -0.0094 -0.0047 -0.0064 -0.0071 -0.1146 -0.1157 -0.0484 -0.0454 -0.0463 -0.0396 -0.1195 -0.1216 -0.0839 -0.0464

y -0.0875 -0.0925 -0.1766 -0.1766 -0.1766 -0.0447 -0.0397 -0.0360 -0.1588 -0.1100 -0.0828 -0.0808 -0.0787 -0.0745 -0.1054 -0.1643 -0.2217 -0.2393

z 0.7439 0.7430 0.6040 0.6040 0.6040 0.7996 0.8387 0.8774 0.6950 0.7359 0.7386 0.7590 0.7900 0.8240 0.7761 0.7738 0.8121 0.8595

insertion

form

bone L2 R12 Sternum R7 R5 R11 R10 R9 Linea alba Linea alba Linea alba Linea alba Linea alba Linea alba Linea alba Linea alba Linea alba Linea alba

line line line line line line line line line line line line line line line line line line

lengths of longissimus thoracis elements were estimated based on their modeled lines-of-action. we accidentally removed the superficial fibers of multifidus around the pelvis. The presented morphological parameters for these elements were estimated based on their modeled lines-of-action. 3 The mathematical definitions of wrapping surfaces for the psoas major, latissimus dorsi, serratus posterior inferior, obliquus externus abdominis, obliquus internus abdominis, rectus abdominis, and transversus abdominis muscles are presented in Appendix A.2, and the via points for the psoas major, longissimus thoracis, iliocostalis lumborum, and the transversus abdominis muscles are given in Appendix A.3 2 Unfortunately,

11

position [m] x -0.0491 -0.0466 0.0005 -0.0249 -0.0602 -0.1026 -0.1119 -0.1187 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

y -0.0799 -0.0702 -0.2333 -0.2437 -0.2448 -0.0774 -0.0818 -0.0907 -0.2005 -0.2086 -0.2147 -0.2192 -0.2225 -0.2251 -0.2276 -0.2303 -0.2338 -0.2385

z 0.78 0.83 0.90 0.89 0.89 0.80 0.83 0.87 0.61 0.63 0.66 0.69 0.73 0.76 0.79 0.82 0.84 0.86

12

present

other

other BR1

14.6 ± 1.0 8.8 ± 3.0 9.9 ± 1.2 14.2 ± 2.1D1 7.8 ± 0.4BR1 7.3 ± 2.1 26.4 ± 1.0G1 24.6 ± 3.0 6.4 ± 1.9 11.7 ± 2.1D1 5.7 ± 0.7W3 4.0 ± 1.2 12.5 ± 1.4 12.69 ± 2.0R1 , 11.69 ± 1.66W2 3.7 ± 1.4 7.1D1 BR1 25.1 ± 0.9 26.7 ± 1.6 , 28.0 ± 4.2D1 4.1 ± 1.3 N/A 9.7 ± 0.4BR1 6.7 ± 3.5

present

`fo [cm]

2.82 2.81 2.14 2.26 3.57 3.35 2.60 2.84 2.72 2.74 2.83

present

a References: [B1]: (Bogduk et al., 1992a), eight adult human cadavers embalmed in a supine position. PCSA was calculated by dividing the volume of each fascicle by its length. Only PCSA of iliocostalis lumborum pars thoracis was shown in the table. PCSA of iliocostalis lumborum pars lumborum was reported as 6.33 cm2 . b [B2]: (Bogduk et al., 1992b), three embalmed human adult male cadavers aged in excess of 60 years. PCSA was calculated by dividing the volume of each fascicle by its length. For comparison, PCSA of each fascicle was summed. c [BR1]: (Brown et al., 2011), five male (mean ± standard deviation age = 71.8 ± 17.9 years, height = 174.8 ± 6.6 cm, mass = 67.8 ± 9.4 kg) and six female (82.7 ± 14.5 years, height = 165.6 ± 3.7 cm, mass = 63.1 ± 11.8 kg) embalmed human cadavers. d [D1]: (Delp et al., 2001), four unembalmed and one embalmed human cadavers (two males and three females, mean ± standard deviation age = 67.0 ± 9.1 years, height = 170.6 ± 4.2 cm, mass = 76.2 ± 13.3 kg). For comparison purposes, PCSAs of the proximal and distal parts were summed, and sarcomere and optimal fiber lengths were averaged between the parts. optimal fiber length was assumed to be 2.8 µm. e [G1]: (Gerling and Brown, 2013), twelve embalmed human cadavers (nine male, three female, mean ± standard deviation age = 63.0 ± 11.0 years). f [N/A]: Not available. g [R1]: (Regev et al., 2011), thirteen human cadavers (mean ± standard deviation age = 50.0 ± 6.0 years) h [V1]: (Veeger et al., 1991), five males and two females embalmed human cadavers (mean ± standard deviation age = 80.0 ± 7.0 years, height = 171.1 ± 6.9 cm, mass = 76.1 ± 16.4 kg). i [W1]: (Ward et al., 2009b). Muscle specimens were obtained from patients, iliocostalis lumborum (n=7), longissimus (n=7), and multifidus (n=23). j [W2]: (Ward et al., 2009c), 19 embalmed human male and female specimens. k [W3]: (Ward et al., 2009a), eight human cadaveric specimens of both genders, (mean ± standard deviation age = 84.0 ± 3.0 years, height = 170.5 ± 11.1 cm, mass = 81.1 ± 15.3 kg).

BR1

5.8 ± 0.7 obliquus externus abdominis 8.95 iliocostalis lumborum 6.07 5.47B1 , 4.1 ± 1.9D1 obliquus internus abdominis 8.30 8.6 ± 0.8BR1 latissimus dorsi 6.16 5.6 ± 0.5G1 , 8.64 ± 3.05V1 longissimus thoracis 18.50 16.08B1 , 5.9 ± 2.5D1 multifidus 8.08 8.42B1 , 23.9 ± 3.0W3 B2 psoas major 12.99 14.63 , 18.45 ± 4.7R1 , 7.7 ± 2.3W2 quadratus lumborum 7.18 2.8D1 BR1 rectus abdominis 4.63 3.3 ± 0.5 , 2.6 ± 0.9D1 serratus posterior inferior 2.07 N/A transversus abdominus 3.83 5.2 ± 0.7BR1 .

muscle

PCSA [cm2 ]

Table 2: Comparison of the muscle morphological parameters measured in the present study with other anatomical studies

3.18 ± 0.1 2.37 ± 0.17D1 , 2. 2.61 ± 0.0 2.69 ± 0.0 2.31 ± 0.17D1 , 2. 2.06 ± 0.03W1 , 2. 3.03 ± 0.3R1 , 3.1 2.38D1 BR1 3.29 ± 0.07 , 2. N/A 2.58 ± 0.0

other

`s [µm]

200

4. Discussion

201

In this study we measured a musculo-skeletal dataset for the lumbar region of the trunk, consist-

202

ing of the coordinates of muscle attachments, three-dimensional geometry of the bones (in the form

203

of STL files), and morphological parameters of muscles. We noticed that most muscles had curved

204

lines-of-action. Therefore, the coordinates of via points and the definitions of wrapping surfaces

205

were provided in addition to their origins and insertions. For every muscle element, we provided

206

morphological parameters: fiber length, tendon length, sarcomere length, optimal fiber length, pen-

207

nation angle, mass, and PCSA. These parameters facilitate better simulation of muscle mechanics

208

and hence will improve these types of models (Zajac, 1989). As the dataset was obtained from a

209

single cadaver, it is complete and coherent and omits the uncertainties associated with combining

210

musculo-skeletal data from different specimens and measurement methods (Dao and Tho, 2015;

211

Carbone et al., 2015). Additionally, it includes new data for the serratus posterior inferior muscle.

212

As such, the dataset enables construction of a complete and coherent musculo-skeletal model for

213

the lumbar spine. With this dataset we aim to contribute to an improvement of the state-of-the art

214

in predicting lumbar spinal loading. This dataset is freely available to be used for non-commercial

215

purposes through http://www.utwente.nl/ctw/bw/research/projects/TwenteSpineModel, upon the

216

acceptance of our research license agreement.

217

218

During measurements we observed some interesting differences compared to previous studies.

219

Firstly, we did not encounter the lumbar fascicles of iliocostalis lumborum as seen by Macintosh

220

and Bogduk (1987), but encountered the lumbar fascicles of longissimus thoracis. Our findings were

221

thus more in line with those of (Bustami, 1986) who did not find any attachment of the iliocostalis

222

to the lumbar transverse processes. Secondly, the thoracic component of the longissimus thoracis

223

only had attachments at ribs 5 to 9, whereas (Macintosh and Bogduk, 1987) found connections at

224

ribs 6 to 12. Thirdly, we did not find any bundles of psoas major originating from the L1L2 disc

225

nor from the L4L5 disc, but we observed bundles originating from the L2 and L3 vertebrae. Small

226

variations were also found for other muscles. These disparities are most likely explained by the

227

variations in the anatomy of the specimens and the differences in the techniques.

228

229

This research had several limitations. Firstly, we noticed a slight scoliosis around the cadaver’s

230

neck, and after dissection of the muscles we discovered that L5 vertebra was fused to the sacrum (Ma13

231

hato, 2013). One would not expect an effect on the muscle architecture in the lumbar region due

232

to the scoliosis, however the same may not be true due to the sacralization. The muscles between

233

the L5 and sacrum are thus most likely different in this cadaver. Secondly, we dissected only on

234

the right side of the specimen. When a model is built upon this dataset, this requires assump-

235

tions about the skeletal geometry and the muscle architecture on the left side. Although it is

236

simply convenient to build a left-right symmetrical model, no one ever has a perfectly symmetrical

237

musculo-skeletal system. Thirdly, measured morphological parameters may not represent in-vivo

238

function accurately. Cutts (1988) reported no significant decrease in muscle fiber lengths when the

239

muscles were fixed on the skeleton, but a mean shrinkage of 2 % when the muscles were fixed in

240

isolation. This implies that sarcomere and fiber lengths measured in-vitro may be slightly lower

241

than in-vivo. Similarly, measured optimal fiber lengths and physiological cross-sectional areas may

242

change slightly. Fourthly, this dataset was obtained from an elderly male and thus represents a sub-

243

ject specific model, not a generic one. Therefore, certain care should be allocated if a personalized

244

model is aimed to be built upon this dataset. Fifthly, we represented the mechanical function of

245

large muscles by dividing them into a number of muscle-tendon elements. This method simplified

246

the complex function of skeletal muscles and made it suitable to implement in musculo-skeletal

247

models. It is important to emphasize that this approach was a modelling procedure in itself and

248

required some assumptions. The details and underlying assumptions of this method were previously

249

described (van der Helm and Veenbaas, 1991).

250

251

Laser diffraction is an accurate method for measuring sarcomere length in skeletal muscle

252

fibers (Cross et al., 1981). We used this method to calculate an average sarcomere length for every

253

muscle and hence to estimate optimal fiber lengths, and PCSAs of its elements. Measured mean

254

sarcomere lengths varied from 2.14 µm to 3.57 µm, which is consistent with the data from Walker

255

and Schrodt (1974). Overall mean and standard deviation on the mean sarcomere lengths were

256

2.79 ± 0.41 µm, implying that muscles measured in this study were close to their optimal lengths

257

(∼2.7 µm). There exists evidence that the distribution of sarcomere lengths within a muscle fiber

258

is not uniform (Infantolino et al., 2010). Previous studies elaborated on the needed sample size to

259

effectively calculate a mean sarcomere length for a muscle and the effect of sample size on optimal

260

fiber length variation. Langenderfer et al. (2004) showed for the shoulder and elbow muscles that

261

the standard deviation of mean optimal muscle length was about 1.25 mm for 120 samples and 14

262

increased to nearly 4 mm for 10 samples. Our measurements also confirmed the non-uniform na-

263

ture of sarcomere length distributions within the muscle fibers. We performed 18 sarcomere length

264

measurements (6 samples × 3 measurements). Therefore, the optimal fiber lengths and PCSAs

265

presented in this paper should be regarded with similar variation. Furthermore, we compared mor-

266

phological parameters such as PCSAs, optimal fiber lengths, and sarcomere lengths, measured in

267

this study with similar anatomical studies in Table 2. The data reported in literature indicates some

268

variations for these parameters, especially for PCSAs of the longissimus thoracis, latissimus dorsi,

269

multifidus, and psoas major muscles. Although, in general, we found similar sarcomere lengths

270

with the other studies, we systematically calculated relatively shorter optimal fiber lengths in the

271

present study. The comparison of the fiber lengths revealed lower fiber lengths compared to the

272

other studies. This was attributed to the differences between the heights of the cadavers measured

273

(154 cm in this study and around 170 cm in others). Other reasons which led to such differences

274

may be due to differences in the measurement techniques and the number of samples used for sar-

275

comere length measurements. Moreover, our PCSAs fit with the range of data reported in literature.

276

277

In the last decade, the demand in individualized musculoskeletal models has considerably in-

278

creased aiming to improve the quality of patient specific treatment options. The state-of-the-art

279

approach to obtain personalized models is to morph the medical images of a person to a previously

280

built atlas containing muscle tendon attachment sites and lines-of-action (Pellikaan et al., 2014;

281

Carbone et al., 2015). However, employing such an approach to create personalized models of the

282

spine may only be reasonable up to some degree due to the high variability of muscle attachments

283

with the bones. In this sense, imaging modalities should be improved to help more with creation of

284

such models enabling identification of muscle attachments and obtaining muscle architectural pa-

285

rameters from living subjects (Blemker et al., 2007; Bruno et al., 2015). This objective is definitely

286

one of the future challenges in musculo-skeletal modeling. Meanwhile, we hope that the dataset

287

reported hereby will be a great value to researchers in the field.

288

15

289

Conflict of interest statement

290

None of the authors have any financial or personal relationships with other people or organization

291

that could inappropriately influence their work.

292

293

Acknowledgment

294

We gratefully acknowledge the financial support by fonds NutsOhra. We also like to thank several

295

colleagues for their help on this research, Vincenzo Carbonne and Kenan Niu for great discussions on

296

musculo-skeletal modeling and working with motion capture systems, Frans Segerink for providing

297

a laser for sarcomere length measurements, Andre Sprengers for his help during CT and MRI scans,

298

and Radiology Department and the Anatomy Department of the Radboud university medical center

299

for their hospitality during the medical imaging and cadaveric measurement sessions. Furthermore,

300

we thank Huub Maas from VU University of Amsterdam for his advice on laser diffraction method.

16

301

302

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at this address

303

(to be provided by the journal).

304

Appendix A.1. Registration of the bones

305

Registration of the STL files of the bones with the point clouds (highlighted as red dots) is

306

illustrated in Fig. 4. A mean error of 0.78 mm was found for all the bones. STL geometry files

307

(defined in the same reference frame as for the muscle attachments) are available through

308

http://www.utwente.nl/ctw/bw/research/projects/TwenteSpineModel.

17

309

Appendix A.2. Mathematical descriptions of wrapping surfaces

310

Estimation of wrapping surfaces is illustrated in Fig. 5. In this figure, red dots represent the

311

point cloud measured over the bone surfaces of the femur and the pelvis. In this case, a cylinder

312

was estimated for the psoas major muscle.

313

314

18

315

Appendix A.3. Coordinates of via attachments for muscle elements with a curved line-of-action. Table A.4: Coordinates of via attachments with respect to the global reference frame. muscle

# via

iliocostalis lumborum 1 iliocostalis lumborum 1 iliocostalis lumborum 1 iliocostalis lumborum 1 iliocostalis lumborum 1 iliocostalis lumborum 2 iliocostalis lumborum 2 iliocostalis lumborum 2 iliocostalis lumborum 2 iliocostalis lumborum 2 iliocostalis lumborum 2 iliocostalis lumborum 2 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 3 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 4 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 5 iliocostalis lumborum 6 iliocostalis lumborum 6 iliocostalis lumborum 6 iliocostalis lumborum 6 Continued on next page

bone

1 2 3 4 5 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 1 2 3 4

L1 L2 L3 L4 L5 R11 T12 L1 L2 L3 L4 L5 R10 R11 T12 L1 L2 L3 L4 L5 R9 R10 R11 T12 L1 L2 L3 L4 L5 R8 R9 R10 R11 T12 L1 L2 L3 L4 L5 R7 R8 R9 R10

19

position [m] x

y

z

-0.0747 -0.0695 -0.0652 -0.0620 -0.0594 -0.0718 -0.0704 -0.0682 -0.0638 -0.0602 -0.0575 -0.0555 -0.0707 -0.0660 -0.0647 -0.0627 -0.0590 -0.0557 -0.0534 -0.0517 -0.0755 -0.0707 -0.0657 -0.0637 -0.0616 -0.0573 -0.0536 -0.0509 -0.0490 -0.0777 -0.0736 -0.0698 -0.0645 -0.0620 -0.0597 -0.0554 -0.0517 -0.0492 -0.0472 -0.0685 -0.0662 -0.0633 -0.0610

-0.0593 -0.0647 -0.0696 -0.0732 -0.0770 -0.0546 -0.0581 -0.0616 -0.0675 -0.0717 -0.0755 -0.0770 -0.0496 -0.0546 -0.0591 -0.0636 -0.0700 -0.0737 -0.0776 -0.0770 -0.0453 -0.0497 -0.0535 -0.0587 -0.0640 -0.0709 -0.0747 -0.0790 -0.0770 -0.0494 -0.0450 -0.0460 -0.0505 -0.0576 -0.0647 -0.0719 -0.0755 -0.0800 -0.0770 -0.0537 -0.0477 -0.0449 -0.0467

0.8211 0.7875 0.7589 0.7387 0.7235 0.8499 0.8383 0.8211 0.7875 0.7589 0.7387 0.7235 0.8911 0.8499 0.8383 0.8211 0.7875 0.7589 0.7387 0.7235 0.9286 0.8911 0.8530 0.8383 0.8211 0.7875 0.7589 0.7387 0.7235 0.9622 0.9300 0.9000 0.8587 0.8383 0.8211 0.7875 0.7589 0.7387 0.7235 0.9881 0.9626 0.9313 0.9050

Table A.4: Continued from previous page muscle

iliocostalis iliocostalis iliocostalis iliocostalis iliocostalis iliocostalis iliocostalis

# via

lumborum lumborum lumborum lumborum lumborum lumborum lumborum

bone

position [m] x

y

z

6 6 6 6 6 6 6

5 6 7 8 9 10 11

R11 T12 L1 L2 L3 L4 L5

-0.0579 -0.0550 -0.0535 -0.0505 -0.0479 -0.0461 -0.0447

-0.0513 -0.0592 -0.0672 -0.0743 -0.0771 -0.0815 -0.0768

0.8700 0.8383 0.8211 0.7875 0.7589 0.7387 0.7235

longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 1 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 2 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 3 longissimus thoracis 4 longissimus thoracis 4 Continued on next page

1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 1 2

T4 T5 T6 T7 T7 T8 T9 T10 T11 T12 L1 L2 L3 T7 T8 T9 T10 T11 T12 L1 L2 L3 L4 L5 T7 T8 T9 T10 T11 T12 L1 L2 L3 L4 L5 T5 T6

-0.0415 -0.0392 -0.0362 -0.0335 -0.0310 -0.0284 -0.0260 -0.0238 -0.0210 -0.0181 -0.0151 -0.0122 -0.0100 -0.0386 -0.0353 -0.0315 -0.0292 -0.0266 -0.0236 -0.0205 -0.0178 -0.0155 -0.0127 -0.0105 -0.0438 -0.0402 -0.0362 -0.0335 -0.0303 -0.0267 -0.0230 -0.0198 -0.0170 -0.0137 -0.0111 -0.0467 -0.0433

-0.0673 -0.0580 -0.0510 -0.0462 -0.0410 -0.0359 -0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.0491 -0.0450 -0.0450 -0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.0491 -0.0472 -0.0445 -0.0439 -0.0445 -0.0490 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.0491 -0.0472 -0.0445 -0.0545 -0.0485

1.0310 1.0110 0.9855 0.9620 0.9396 0.9172 0.8971 0.8773 0.8538 0.8282 0.8014 0.7772 0.7572 0.9590 0.9300 0.8971 0.8773 0.8538 0.8282 0.8014 0.7772 0.7572 0.7329 0.7140 0.9532 0.9262 0.8980 0.8773 0.8538 0.8282 0.8014 0.7772 0.7572 0.7329 0.7140 1.0047 0.9790

20

Table A.4: Continued from previous page muscle

# via

bone

position [m] x

longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 4 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 5 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 6 longissimus thoracis 12 longissimus thoracis 12 longissimus thoracis 12 longissimus thoracis 12 longissimus thoracis 12 longissimus thoracis 12 longissimus thoracis 12 longissimus thoracis 13 longissimus thoracis 13 longissimus thoracis 13 longissimus thoracis 13 longissimus thoracis 13 longissimus thoracis 13 Continued on next page

y

z

3 T7 -0.0405 -0.0455 0.9580 4 T8 -0.0365 -0.0442 0.9280 5 T9 -0.0319 -0.0493 0.8930 6 T10 -0.0298 -0.0365 0.8773 7 T11 -0.0267 -0.0395 0.8538 8 T12 -0.0234 -0.0425 0.8282 9 L1 -0.0198 -0.0463 0.8014 10 L2 -0.0165 -0.0481 0.7772 11 L3 -0.0140 -0.0491 0.7572 12 L4 -0.0108 -0.0472 0.7329 1 T9 -0.0439 -0.0438 0.9255 2 T10 -0.0389 -0.0495 0.8920 3 T11 -0.0333 -0.0395 0.8538 4 T12 -0.0295 -0.0425 0.8282 5 L1 -0.0255 -0.0463 0.8014 6 L2 -0.0220 -0.0481 0.7772 7 L3 -0.0190 -0.0491 0.7572 8 L4 -0.0155 -0.0472 0.7329 9 L5 -0.0127 -0.0445 0.7140 10 Sacrum -0.0087 -0.0370 0.6866 1 T6 -0.0482 -0.0470 0.9762 2 T7 -0.0440 -0.0430 0.9475 3 T8 -0.0402 -0.0450 0.9210 4 T9 -0.0367 -0.0490 0.8971 5 T10 -0.0340 -0.0365 0.8773 6 T11 -0.0305 -0.0395 0.8538 7 T12 -0.0270 -0.0425 0.8282 8 L1 -0.0230 -0.0463 0.8014 9 L2 -0.0195 -0.0481 0.7772 10 L3 -0.0167 -0.0491 0.7572 11 L4 -0.0132 -0.0472 0.7329 12 L5 -0.0105 -0.0445 0.7140 1 T12 -0.0240 -0.0425 0.8282 2 L1 -0.0270 -0.0463 0.8014 3 L2 -0.0297 -0.0481 0.7772 4 L3 -0.0320 -0.0491 0.7572 5 L4 -0.0347 -0.0472 0.7329 6 L5 -0.0369 -0.0445 0.7140 7 Sacrum -0.0400 -0.0370 0.6866 1 T11 -0.0280 -0.0395 0.8538 2 T12 -0.0296 -0.0425 0.8282 3 L1 -0.0310 -0.0463 0.8014 4 L2 -0.0323 -0.0481 0.7772 5 L3 -0.0334 -0.0491 0.7572 6 L4 -0.0348 -0.0472 0.7329

21

Table A.4: Continued from previous page muscle

# via

bone

position [m] x

longissimus thoracis 13 longissimus thoracis 13 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 14 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 15 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 16 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 17 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 Continued on next page

y

z

7 L5 -0.0358 -0.0445 0.7140 8 Sacrum -0.0373 -0.0370 0.6866 1 T10 -0.0292 -0.0365 0.8773 2 T11 -0.0288 -0.0395 0.8538 3 T12 -0.0284 -0.0425 0.8282 4 L1 -0.0278 -0.0463 0.8014 5 L2 -0.0276 -0.0481 0.7772 6 L3 -0.0272 -0.0491 0.7572 7 L4 -0.0268 -0.0472 0.7329 8 L5 -0.0265 -0.0445 0.7140 9 Sacrum -0.0261 -0.0370 0.6866 1 T9 -0.0270 -0.0365 0.8971 2 T10 -0.0252 -0.0365 0.8773 3 T11 -0.0229 -0.0395 0.8538 4 T12 -0.0204 -0.0425 0.8282 5 L1 -0.0179 -0.0463 0.8014 6 L2 -0.0155 -0.0481 0.7772 7 L3 -0.0137 -0.0491 0.7572 8 L4 -0.0113 -0.0472 0.7329 9 L5 -0.0096 -0.0445 0.7140 10 Sacrum -0.0070 -0.0370 0.6866 1 T8 -0.0278 -0.0359 0.9172 2 T9 -0.0260 -0.0365 0.8971 3 T10 -0.0242 -0.0365 0.8773 4 T11 -0.0222 -0.0395 0.8538 5 T12 -0.0198 -0.0425 0.8282 6 L1 -0.0175 -0.0463 0.8014 7 L2 -0.0153 -0.0481 0.7772 8 L3 -0.0136 -0.0491 0.7572 9 L4 -0.0115 -0.0472 0.7329 10 L5 -0.0098 -0.0445 0.7140 1 T7 -0.0280 -0.0365 0.9412 2 T8 -0.0261 -0.0359 0.9172 3 T9 -0.0244 -0.0365 0.8971 4 T10 -0.0227 -0.0365 0.8773 5 T11 -0.0208 -0.0395 0.8538 6 T12 -0.0187 -0.0425 0.8282 7 L1 -0.0165 -0.0463 0.8014 8 L2 -0.0145 -0.0481 0.7772 9 L3 -0.0128 -0.0491 0.7572 10 L4 -0.0108 -0.0472 0.7329 11 L5 -0.0092 -0.0445 0.7140 1 T6 -0.0290 -0.0405 0.9749 2 T7 -0.0263 -0.0365 0.9412 3 T8 -0.0244 -0.0359 0.9172

22

Table A.4: Continued from previous page muscle

# via

longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 18 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 19 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 20 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 21 longissimus thoracis 22 longissimus thoracis 22 longissimus thoracis 22 Continued on next page

bone

4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 1 2 3

T9 T10 T11 T12 L1 L2 L3 L4 T6 T7 T7 T8 T9 T10 T11 T12 L1 L2 L3 T4 T5 T6 T7 T8 T9 T10 T11 T12 L1 L2 L3 T4 T5 T6 T7 T8 T9 T10 T11 T12 L1 L2 T3 T4 T5

23

position [m] x

y

z

-0.0228 -0.0212 -0.0193 -0.0174 -0.0152 -0.0132 -0.0115 -0.0097 -0.0323 -0.0285 -0.0254 -0.0233 -0.0215 -0.0198 -0.0177 -0.0154 -0.0132 -0.0110 -0.0092 -0.0267 -0.0248 -0.0228 -0.0205 -0.0190 -0.0177 -0.0164 -0.0150 -0.0134 -0.0115 -0.0100 -0.0086 -0.0232 -0.0206 -0.0190 -0.0175 -0.0164 -0.0154 -0.0144 -0.0134 -0.0122 -0.0108 -0.0096 -0.0204 -0.0193 -0.0170

-0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.0491 -0.0472 -0.0630 -0.0405 -0.0365 -0.0359 -0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.0491 -0.0657 -0.0494 -0.0405 -0.0365 -0.0359 -0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.0491 -0.0787 -0.0494 -0.0405 -0.0365 -0.0359 -0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.0481 -0.1071 -0.0787 -0.0494

0.8971 0.8773 0.8538 0.8282 0.8014 0.7772 0.7572 0.7329 1.0200 0.9749 0.9412 0.9172 0.8971 0.8773 0.8538 0.8282 0.8014 0.7772 0.7572 1.0357 1.0057 0.9749 0.9412 0.9172 0.8971 0.8773 0.8538 0.8282 0.8014 0.7772 0.7572 1.0599 1.0057 0.9749 0.9412 0.9172 0.8971 0.8773 0.8538 0.8282 0.8014 0.7772 1.0832 1.0599 1.0057

Table A.4: Continued from previous page muscle

longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus longissimus

# via

thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis thoracis

bone

position [m] x

y

z

22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23

4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11

T6 T7 T8 T9 T10 T11 T12 L1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

-0.0158 -0.0143 -0.0132 -0.0124 -0.0117 -0.0106 -0.0095 -0.0083 -0.0216 -0.0208 -0.0197 -0.0169 -0.0153 -0.0135 -0.0123 -0.0113 -0.0103 -0.0090 -0.0078

-0.0405 -0.0365 -0.0359 -0.0365 -0.0365 -0.0395 -0.0425 -0.0463 -0.1209 -0.1071 -0.0787 -0.0494 -0.0405 -0.0365 -0.0359 -0.0365 -0.0365 -0.0395 -0.0425

0.9749 0.9412 0.9172 0.8971 0.8773 0.8538 0.8282 0.8014 1.0976 1.0832 1.0599 1.0057 0.9749 0.9412 0.9172 0.8971 0.8773 0.8538 0.8282

psoas major 1 psoas major 2 psoas major 2 psoas major 2 psoas major 3 psoas major 3 psoas major 3 psoas major 4 psoas major 4 psoas major 5 psoas major 5 psoas major 5 psoas major 5 psoas major 6 psoas major 6 psoas major 6 psoas major 6 psoas major 6 psoas major 7 psoas major 7 psoas major 7 psoas major 7 psoas major 7 psoas major 8 psoas major 8 Continued on next page

1 1 2 3 1 2 3 1 2 1 2 3 4 1 2 3 4 5 1 2 3 4 5 1 2

Pelvis Pelvis L5 L4 Pelvis L5 L4 Pelvis L5 Pelvis L5 L4 L3 Pelvis L5 L4 L3 L2 Pelvis L5 L4 L3 L2 Pelvis L5

-0.0738 -0.0738 -0.0510 -0.0366 -0.0738 -0.0573 -0.0469 -0.0738 -0.0523 -0.0738 -0.0577 -0.0475 -0.0359 -0.0738 -0.0585 -0.0485 -0.0372 -0.0283 -0.0738 -0.0600 -0.0513 -0.0414 -0.0334 -0.0738 -0.0513

-0.1499 -0.1499 -0.1290 -0.1158 -0.1499 -0.1262 -0.1113 -0.1499 -0.1215 -0.1499 -0.1300 -0.1174 -0.1030 -0.1499 -0.1328 -0.1220 -0.1097 -0.0998 -0.1499 -0.1360 -0.1272 -0.1170 -0.1088 -0.1499 -0.1310

0.6250 0.6250 0.6800 0.7150 0.6250 0.6800 0.7150 0.6250 0.6800 0.6250 0.6800 0.7150 0.7550 0.6250 0.6800 0.7150 0.7550 0.7870 0.6250 0.6800 0.7150 0.7550 0.7870 0.6250 0.6800

24

Table A.4: Continued from previous page muscle

psoas psoas psoas psoas psoas psoas psoas psoas psoas

# via

major major major major major major major major major

transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus transversus

abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis abdominis

bone

position [m] x

y

z

8 9 9 9 9 10 10 10 10

3 1 2 3 4 1 2 3 4

L4 Pelvis L5 L4 L3 Pelvis L5 L4 L3

-0.0374 -0.0738 -0.0560 -0.0445 -0.0318 -0.0738 -0.0565 -0.0455 -0.0330

-0.1190 -0.1499 -0.1365 -0.1280 -0.1185 -0.1499 -0.1370 -0.1287 -0.1195

0.7150 0.6250 0.6800 0.7150 0.7550 0.6250 0.6800 0.7150 0.7550

2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7

1 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

L4 L4 L4 L3 L4 L3 L3 L3 L4 L2 L3 L3 L3 L1 L2 L3 L3 L3

-0.1156 -0.0780 -0.1052 -0.1157 -0.1166 -0.0780 -0.1052 -0.1157 -0.1176 -0.0780 -0.1052 -0.1167 -0.1186 -0.0780 -0.1052 -0.1176 -0.1196 -0.1206

-0.1596 -0.0670 -0.0925 -0.1100 -0.1604 -0.0660 -0.0925 -0.1100 -0.1612 -0.0630 -0.0925 -0.1089 -0.1619 -0.0610 -0.0925 -0.1077 -0.1627 -0.1635

0.7063 0.7450 0.7447 0.7430 0.7175 0.7620 0.7560 0.7524 0.7288 0.7880 0.7700 0.7602 0.7400 0.8160 0.7850 0.7679 0.7513 0.7625

25

26

ellipsoid ellipsoid ellipsoid ellipsoid cylinder ellipsoid ellipsoid cylinder

form r

rx

ry

abdomen 0.132 0.09 abdomen 0.132 0.09 abdomen 0.132 0.09 abdomen 0.132 0.09 humerus 0.0124 thorax 0.124 0.091 thorax 0.124 0.091 pelvis 0.0375

region

0.22 0.22

0.26 0.26 0.26 0.26

rz ps y z

x

pe y

z

-0.0100 -0.1320 0.5850 -0.1003 -0.1085 0.6211

-0.1958 0.0805 0.8800 -0.1343 0.1827 1.0997

x

0 0

-0.007 -0.007 -0.007 -0.007

x

0.83 0.83 0.83 0.83

z

1 1 1 1

x

nx 0 0 0 0

y

-0.128 0.897 0.9511 -0.30 -0.128 0.897 0.9511 -0.30

-0.157 -0.157 -0.157 -0.157

pc y

1) r is the radius of the cylinder, rx, ry, and rz are the radii of the ellipsoid in x, y, and z directions, ps and pe are the start and end points of the cylinder, pc is the center of the ellipsoid, nx, ny and nz are the axes of the ellipsoid in x, y, and z directions. 2) All values are in meters.

obliquus externus abdominis obliquus internus abdominis rectus abdominis transversus abdominis latissimus dorsi latissimus dorsi serratus posterior inferior psoas major

muscle

Table A.3: Description of the geometrical forms for wrapping muscles

316

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323

324

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325

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337

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345

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Figure 1: (a) An instance during position measurements. (b) Locating attachments of Erector Spinae muscle group. (c) Laser diffraction set-up used for sarcomere length measurements.

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Figure 2: (a) Illustration of the geometrical forms used to classify line and surface-shaped muscle attachment sites. Rectus abdominis muscle is used for this illustration. (b) The insertions of this muscle was measured in line form. Black, green, and the blue dots represent the measured attachment points for the elements 1, 2, and 3, respectively. Three red dots indicate calculated attachment points for these elements. Note that n is equal to 1 in this case since the attachments of each element were measured separately. (c) Differently, the origin of the muscle was measured in surface form (black dots), and the red dot indicates the calculated attachment point (the centroid of the surface). Since this surface was considerably small, we opted to define one common origin for the all the elements (n = 1).

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34 Figure 3: Dissected muscles in the musculo-skeletal system. OEA: obliquus externus abdominis, OIA: obliquus internus abdominis, TA: transversus abdominis, RA: rectus abdominis, LT: longissimus thoracis, IL: iliocostalis lumborum, QL: quadratus lumborum, PM: psoas major, LD: latissimus dorsi, MF: multifidus, SPI: serratus posterior inferior.

Figure 4: Illustration of the registration of the bones with the point clouds. The geometry of L2 was plotted together with its point cloud.

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Figure 5: Illustration of the wrapping surface for the psoas major muscle.

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