Development of a Canine Stifle Computer Model to Evaluate Cranial Cruciate Ligament Deficiency

Journal of Mechanics in Medicine and Biology Vol. 13, No. 2 (2013) 1350043 (29 pages) c World Scientific Publishing Company ° DOI: 10.1142/S0219519413500437

DEVELOPMENT OF A CANINE STIFLE COMPUTER MODEL TO EVALUATE CRANIAL CRUCIATE LIGAMENT DEFICIENCY

NATHAN P. BROWN Department of Mechanical Engineering, University of Louisville Louisville, KY 40202, USA [email protected] GINA E. BERTOCCI* Department of Bioengineering, University of Louisville Louisville, KY 40202, USA [email protected] DENIS J. MARCELLIN-LITTLE Department of Clinical Sciences, College of Veterinary Medicine North Carolina State University, Raleigh, NC 27606, USA [email protected]

Received 12 April 2012 Revised 24 October 2012 Accepted 15 January 2013 Published 14 March 2013 The objective of this study was to develop a three-dimensional (3D) quasi-static rigid body canine pelvic limb computer model simulating a cranial cruciate ligament (CrCL) intact and CrCL-deficient stifle during walking stance to describe stifle biomechanics. The model was based on a five-year-old neutered male Golden Retriever (33 kg) with no orthopedic or neurologic disease. Skeletal geometry and ligament anatomy determined from computed tomography (CT), optimized muscle forces, motion capture kinematics, and force platform ground reaction forces were used to develop the model. Ligament loads, tibial translation, tibial rotation, and femoromeniscal contact forces were compared across the intact and CrCLdeficient stifle. The CrCL was found to be the primary intact stifle load-bearing ligament, and the caudal cruciate ligament was the primary CrCL-deficient stifle load-bearing ligament. Normalized tibial translation and rotation were 0.61 mm/kg and 0.14 degrees/kg, respectively. Our model confirmed that the CrCL stabilizes the intact stifle and limits tibial translation and rotation. Model verification was confirmed through agreement with experimentally measured kinematics and previous in vivo, in vitro, and mathematical model studies. Parametric analysis indicated outcome measure sensitivity to ligament pre-strain. Computer modeling could be useful to further investigate stifle biomechanics associated with surgical stabilization techniques.

*Corresponding

author. 1350043-1

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little Keywords: Canine stifle (knee) computer model; cranial cruciate ligament deficiency; biomechanics.

1. Introduction Canine stifle joint stability can be compromised with cranial cruciate ligament (CrCL) degeneration.1
3 The CrCL limits stifle hyperextension and tibial internal rotation and cranial displacement relative to the femur.2 CrCL rupture may be the consequence of trauma, but more commonly results from CrCL degeneration over time until partial or complete rupture.4 Large dogs are more prone than small dogs to CrCL damage, possibly due to specific anatomical and biomechanical characteristics, and often require surgical intervention to stabilize the stifle.5,6 Intraarticular and extra-articular surgical procedures have been used to enhance stifle stability following CrCL deficiency,7,8 including proximal tibial osteotomy techniques designed to decrease cranial tibial translation.9,10 With the exception of a hypothesized increase in caudal cruciate ligament (CaCL) load after tibial plateau leveling osteotomy,3 the impact of various corrective osteotomies on other stifle joint ligament loads during the stance phase of walking gait are unknown.1,3,11
17 Computational models offer an in silico tool to investigate musculoskeletal injury types and underlying injury mechanisms. The main advantage of in silico models is that they can accurately include and represent measured kinematics, kinetics, joint articulation, tissue morphology, and tissue response dynamics while quantifying outcomes (such as ligament loads or contact forces) not directly measureable in vivo or in vitro. Additionally, computational models can incorporate muscle forces which are often simplified or neglected in in vitro studies. Medical imaging data allow for the detailed representation of biological morphology in models using noninvasive strategies. A high-resolution computed tomography scan is well suited for bony structure identification and is particularly useful for in silico models since threedimensional (3D) bone and joint conformation geometry can be easily reconstructed into subject-specific computerized solid models. A subject-specific computational model can therefore be developed noninvasively and used repeatedly to address a variety of biomechanical injuries. Furthermore, unlike in vivo and in vitro studies, model parameters can be nondestructively varied to investigate their influence on model outcomes, thereby reducing the need for and better informing in vitro and in vivo studies. This capability of conducting parametric sensitivity analyses alone illustrates the advantageous role of computational models in the investigation of CrCL deficiency, potential causative factors, treatment, and surgical management. Quasi-static canine pelvic limb (CPL) 3D mathematical models of the stance phase of gait have been used to investigate biomechanics of the intact stifle, the CrCLdeficient stifle, and the CrCL-deficient stifle following tibial plateau slope alteration.18
20 These models, however, did not report tibial kinematics and may have over-constrained the stifle by limiting tibial subluxation which is consistently present in in vivo and in vitro studies.3,9,21
25 Moreover, canine ligament biomechanical 1350043-2

Canine Stifle Computer Model to Evaluate CrCL Deficiency

properties were adapted from human ligament properties and menisci were neglected, likely influencing predicted stifle biomechanics. Therefore, there is a need to address these limitations in order to more accurately predict stifle biomechanics. The purpose of this study was to develop a quasi-static CPL 3D computer simulation model which will be used to evaluate stifle ligament loading patterns, cranial tibial translation, and internal tibial rotation in an intact and CrCL-deficient stifle. To our knowledge, this is the first anatomical, kinematic, and kinetic subject-specific CPL rigid body motion computer model capable of predicting ligament loads, tibial translation, tibial rotation, and femoromeniscal contact forces for both the intact and CrCL-deficient stifle for discrete stance phases. Additionally, these outcome measures will be compared following a sensitivity analysis to investigate ligament biomechanical properties, further demonstrating the capabilities of this in silico study. We hypothesized that (1) the CaCL will be the primary load-bearing ligament and tibial cranial translation and internal rotation will increase in the CrCL-deficient stifle and (2) ligament biomechanical properties will affect model outcome measures. 2. Materials and Methods 2.1. Model design A 3D quasi-static CPL computer model was developed to simulate the stance phase of walking gait. Model inputs included CPL anatomical structures, kinematics and kinetics, ligament material properties, contact properties, and muscle forces. The following sequence was used in our CPL model simulation approach at each stance phase: (1) inverse dynamics analysis was conducted to determine stifle joint reaction forces and moments, (2) muscle force optimization was conducted using the stifle joint reaction moments determined by the inverse dynamics analysis, and (3) gait was simulated using muscle forces determined by optimization to determine stifle biomechanics. Stifle ligament loads, tibial translation, tibial rotation, and femoromeniscal contact forces were evaluated during gait simulation for a CrCL-intact and CrCL-deficient stifle. 2.2. Canine subject A five-year-old neutered male Golden Retriever (33 kg) with no orthopedic or neurologic disease was included in this study. All procedures involving the canine subject were performed in accordance with an approved Institutional Animal Care and Use Committee protocol, and owner consent was obtained. 2.3. Canine subject computed tomography scan The canine subject was administered anesthesia and positioned in dorsal recumbency with the stifle fixed in 135 extension as determined using a goniometer. A pelvic limb computed tomography (CT) scana including the pelvis was performed a GE

CT/i Base Single Slice CT Scanner, GE Medical Systems, Little Chalfont, United Kingdom. 1350043-3

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

using 5-mm slice thickness and 0.78 mm  0.78 mm pixel size to obtain skeletal geometry and tissue distributions. A higher-resolution second stifle CT scana was performed from the distal femur (femoral shaft proximal to the femoral condyles) to the proximal tibia (distal to the tibial tuberosity) using 1-mm slice thickness and 0.78 mm  0.78 mm pixel size. The high-resolution stifle scan captured connective tissue features and stifle articulating surface geometry not adequately defined in the 5-mm pelvic limb scan. 2.4. Canine subject kinematics and kinetics Six walking kinematic gait trials were captured and recorded in a 3D test space using a motion capture and tracking systemb which was equipped with eight infrared cameras sampling at 100 Hz. An orthogonal right-hand global space was defined with positive x directed medially for the left pelvic limb, y directed cranially, and z directed vertically. Spherical reflective markers (1 cm diameter) were placed on the left pelvic limb (Table 1). Marker locations were chosen in accordance with a previous canine gait analysis study to improve visibility, repeatability, non-collinearity, skin movement reduction, and clinical plane distinction.26 To reduce motion artifact, the markers were placed directly on the skin using double-sided adhesive tape. Small areas (approximately 3 cm  3 cm) were shaved in the marker locations and hair was trimmed near the markers to prevent obstruction. A static trial was recorded in weight-bearing stance, and four markers (Table 1) were removed following the static trial given the inability to track these markers during dynamic trials. These removed markers were implemented as virtual markers in the dynamic trials using the motion capture software.c The canine subject was leash walked at its preferred velocity (1.1 m/s) through a straight distance of 6 m. Measured marker locations were smoothed using a low-pass Butterworth filter (6 Hz cutoff frequency). Pelvic limb vertical, craniocaudal, and mediolateral ground reaction forces and the free vertical ground moment were measured at 1,000 Hz using a single force platformd positioned level with the ground surface midway along the walking path (Table 2). Walking trials were retained only if the left pelvic limb was in contact with the force platform throughout the stance phase of a complete gait cycle. Trials with inconsistent gait patterns resulting from excessive head turning, excessive lateral motion or inconsistent walking speed were discarded. Six trials were recorded and a representative trial was used for model development. 2.5. CPL segment parameters The Digital Imaging and Communications in Medicine (DICOM) images produced by the CT scan were imported into medical imaging software.e Tissues were b Hawk Camera System, Motion Analysis Corp., Santa Rosa, c EVaRT v. 5.0, Motion Analysis Corp., Santa Rosa, CA d FP4060-08, Bertec Corporation, Columbus, e Mimics v. 14.0, Materialise, Ann Arbor, MI

OH

1350043-4

CA

Canine Stifle Computer Model to Evaluate CrCL Deficiency Table 1. Canine pelvic limb motion capture reflective marker locations. Segment

Location

Pelvis

Left cranial dorsal iliac spine Left ischiatic tuberosity Right cranial dorsal iliac spine Right ischiatic tuberosity

Femur

Left Left Left Left

greater trochanter craniolateral aspect of the quadriceps medial femoral epicondylea lateral femoral epicondyle

Tibia

Left Left Left Left Left

fibular head proximal tibial cresta distal tibial crest lateral malleolus medial malleolusa

Tarsus and Metatarsus

Left caudolateral calcaneous Left 5th metatarsophalangeal joint Left 2nd metatarsophalangeal jointa

Digits

Left dorsal surface of the 4th digit

a Marker

removed following the static trial.

Table 2. Discrete ground reaction forces during phases of stance at a walk in a 33-kg dog.

Phase of stance (%)

Vertical GRF (N)

Craniocaudal GRF (N)

Mediolateral GRF (N)

Vertical moment (Nmm)

0 10 20 30 40 50 60 70 80 90 100

0.0 83.0 153.3 141.1 111.3 94.7 100.6 120.6 121.1 64.5 0.0

0.0
20.8
27.8
9.0 1.5 6.8 12.2 19.3 26.4 14.9 0.0

0.0
5.9 9.3 11.7 9.3 8.1 8.0 8.1 10.3 5.1 0.0

0.0
406.0
522.5
533.0
424.5
552.5
430.4
315.0
269.3
84.9 0.0

delineated for each pelvic limb segment using Hounsfield unit threshold ranges for bone (>226), muscle (
25 to 225), and fat (
205 to
51). Average tissue densities for bone (1.80 g/cm3 Þ, muscle (1.06 g/cm3), and fat (0.95 g/cm3) were assumed.27 Total tissue mass for each segment was determined using mi;j ¼
j P1 P2 SNj ;

ð1Þ

where i ¼ 1; 2; 3; 4 corresponds to the thigh, crus, tarsus and metatarsus, and digits, respectively, j ¼ 1; 2; 3 corresponds to bone, muscle, and fat, respectively,
is the 1350043-5

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little Table 3. Canine pelvic limb segment parameters. Segment Femur Tibia Tarsus Digits  Directions

Mass (g)

I x (kgmm2 )

I y (kgmm2 )

I z (kgmm2 )

1860 434 114 59

5430 1430 129 22

4060 561 16 8

6310 1780 132 18

correspond to anatomical axes previously defined.26

tissue density, P1 and P2 are the pixel dimensions (0.78 mm), S is the slice thickness (5 mm), and N is the number of pixels. Total segment mass is therefore Mi ¼

3 X

mi;j ;

ð2Þ

j¼1

which was evaluated for each segment. Pelvic limb segment inertial parameters were determined for the femur, tibia, tarsus, and digits segments (Table 3). Segments were distinguished by a plane through each joint center, and moments of inertia were determined about the segment center of mass based on tissue volume, density, and distribution as previously described.27,28 2.6. CPL geometry DICOM images from the 1-mm and 5-mm CT scans were converted to 3D geometry using medical image segmentation softwaree and the bone threshold algorithm described. Pelvis, femur, patella, medial meniscus, lateral meniscus, tibia and fibula, tarsus and metatarsus, and digit 3D geometries were exported as point clouds and reconstructed as solid models.f The 1-mm and 5-mm scans were combined and oriented based on bony landmark congruency. Bones were modeled as rigid bodies and menisci were modeled as penetrable bodies. Connective tissue origins and insertions determined from the CT image data described muscle and ligament lines of action. Ligaments and muscles were delineated from other tissues using masks within the medical image segmentation software.e The cross sectional areas (CSA) were determined at the midpoint of ligament length and at the muscle belly. A CPL assembly model was developed with segments oriented based on the reconstructed motion capture marker locations relative to bony landmarks for each 10% discrete stance phase (Fig. 1). The femoral condyles and menisci were assumed to be in contact throughout stance. 2.7. Inverse dynamics analysis Using the CPL anatomy, kinematics, kinetics, and segment inertial parameters, a 3D inverse dynamics analysis29,30 was conducted. Inverse dynamics analysis is the f SolidWorks

v. 2010, SolidWorks Corp., Concord, MA. 1350043-6

Canine Stifle Computer Model to Evaluate CrCL Deficiency

Fig. 1. Three-dimensional (3D) canine pelvic limb model.

process by which the equations of motion are solved for a body segment using known distal reactions and moments to determine proximal reactions and moments. Beginning with the digits segment, reaction moments and forces about the tarsal joint were determined. Subsequently, reaction moments and forces about the stifle joint were determined (Table 4). 2.8. Muscle modeling Stifle joint reaction moments determined by inverse dynamics analysis were used to determine pelvic limb muscle forces crossing the stifle prior to model simulation (Table 4). Muscle forces were approximated as linear force vectors acting along a straight line connecting muscle origin and insertion. Muscles which anatomically do not follow a straight line of action from origin to insertion were approximated as linear force vectors acting along the muscle attachment at the tendon
bone interface. Because the CPL muscle forces were indeterminate, a muscle force optimization strategy and optimization softwareg were used to determine one g Optimization

Toolbox, MATLAB R2010a, MathWorks, Natick, MA 1350043-7

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little Table 4. Calculated stifle joint moments (Nmm) determined by inverse dynamics analysis and calculated muscle forces (N) determined using the minimization of maximal muscle stress optimization strategy. Phase of stance 10% Stifle moment Vertical axis Craniocaudal axis Mediolateral axis Muscle force Cranial tensor fasciae latae Caudal tensor fasciae latae Cranial sartorious Caudal sartorious Rectus femoris Biceps femoris (patellar) Biceps femoris (tibial) Biceps femoris (tarsal) Caudal crural abductor Semimembranosus (femoral) Semimembranosus (tibial) Semitendinosus (tibial) Semitendinosus (tarsal) Gracilis (tibial) Gracilis (tarsal) Lateral and intermediate vastus Medial vastus Long digital extensor Medial gastrocnemius Lateral gastrocnemius Popliteus Superficial digital flexor 

20%

30%


825 1650 1270
959
260
212
4150
6120
5880 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50.2 2.2 43.4 0.0 25.3 25.3 25.6 48.7 0.0 0.0 15.9 0.0 58.5 24.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 109.0 77.0 3.9 70.3 0.0 44.7 44.7 0.0 86.0 0.0 0.0 28.0 0.0 103.2 42.3 0.0

0.0 0.0 0.0 0.0 0.0 0.0 89.9 82.3 3.2 61.7 0.0 36.5 36.5 35.8 70.3 0.0 0.0 22.9 0.0 84.4 34.6 0.0

40%

50%

60%

676 135
3660

545
113
2690

198 53
1570

0.0 0.0 0.0 0.0 0.0 0.0 44.0 47.0 1.7 6.8 35.7 19.1 19.1 36.7 22.0 0.0 0.0 11.9 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 32.5 38.9 1.4 2.2 0.0 16.0 16.0 0.0 30.8 0.0 0.0 10.0 0.0 37.0 15.2 0.0

0.0 0.0 0.0 0.0 0.0 0.0 14.0 20.7 0.7 14.6 0.0 8.4 8.4 0.0 16.2 0.0 0.0 5.3 0.0 5.3 8.0 0.0

70%

80%

90%


284
794
512
91
595 469 1310 2280 2250 1.2 0.0 0.1 1.4 2.1 1.9 0.0 0.2 0.0 5.9 11.7 6.2 0.0 12.0 0.0 19.1 0.1 0.0 12.0 0.0 0.0 0.0

0.4 5.5 9.9 3.4 2.2 12.0 0.0 8.7 0.0 27.1 27.6 14.7 0.0 28.4 0.0 1.4 17.0 9.2 28.3 0.0 0.0 0.0

5.7 0.8 1.5 0.5 7.4 5.4 5.2 5.4 0.2 1.9 4.1 0.0 0.0 4.2 0.0 8.9 4.4 1.2 4.2 0.0 0.0 0.0

Muscle insertion location.

possible solution for the force exerted by each muscle crossing the stifle. The minimization of maximal muscle stress strategy19 was used with the 3D constraint equation M¼

n X

F i  ri ;

ð3Þ

i¼1

where M is the stifle reaction moment determined by inverse dynamics analysis (Table 4), Fi is the muscle force, and ri is the moment arm of the ith muscle. All muscle forces were assumed positive acting along the muscle line of action and to not exceed 60% maximal contraction force which was set as the product of muscle CSA and 350 kPa.31 Intersegmental optimized muscle forces (Table 4) were used to actuate the model to determine internal ligament loads during model simulation.32 1350043-8

Canine Stifle Computer Model to Evaluate CrCL Deficiency

2.9. Ligament modeling Tension-only, nonlinear springs were used to represent stifle ligaments. Seven ligament elements were included in this model: the CrCL, CaCL, lateral collateral ligament (LCL), medial collateral ligament (MCL), patellar ligament (PL), lateral femoropatellar ligament (LFPL), and medial femoropatellar ligament (MFPL) (Table 5). Each ligament was treated as a single line element that was directed along the vector from the ligament origin to the ligament insertion. Ligament element load response functions were F ¼ kj ð"j
"m Þ; F¼

" 2j

1 k ; 4 j "m

F ¼ 0;

2"m < "j ;

0 < "j  2"m ;

ð4Þ ð5Þ

and

"j  0;

ð6Þ

where kj is the stiffness value for ligament j, "j is the strain in ligament j and "m is the parameter that defines the ligament response transition from the toe region to the linear region.19,33 The parameter "m was set at 0.03.19,33 Ligament stiffness values were approximated as the product of the mean longitudinal CrCL tangent modulus reported for a Rottweiler (198 MPa)34 and each ligament CSA at the midpoint along the ligament length. The strain within each ligament, "j , was determined using "j ¼

ðLj
L0j Þ ; L0j

ð7Þ

where Lj is the length of ligament j during simulation and L0j is the ligament zero strain length. The zero strain lengths for the CrCL, CaCL, LCL, MCL, and femoropatellar ligaments were the respective minimum element lengths during stance. The patellar ligament was assumed inextensible and its zero strain length was 37 mm as determined from the CT image data.

Table 5. Canine pelvic limb ligament element properties. Ligament and elastic element CrCL CaCL LCL MCL PL LFPL MFPL Passive quadriceps

L0j (mm)

CSA (mm2 )

Stiffness (N/")

19.0 17.3 21.7 28.2 37.0 38.6 41.4 156

30.4 45.0 23.0 34.8 56.6 14.2 14.2 NA

6020 8920 4560 6890 11,200 2800 2800 2800

Note: strains for all elements were zero at L0j . 1350043-9

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

2.10. Contact properties The menisci surface contours from CT imaging were adapted to the tibial plateau. The tibiomeniscal complex interacted with the femoral condyles with static and dynamic frictional coefficients set to 0.001.35 Contact was included in the model to prevent overlap between stifle articulating components. If during simulation the solver detected overlap between surfaces, a contact force was applied in opposing directions on both bodies at the overlap.36 The contact force, Fn , was determined using
 dg Fn ¼ kge þ ð8Þ fðg; cmax ; dmax Þ; dt where k is the stiffness, g is the contact penetration during simulation, e is the elastic component exponent, and fðcmax ; dmax Þ is a contact penetration step function where cmax is the maximum damping, and dmax is the penetration at which cmax occurs. Femoromeniscal contact penetration, stiffness, maximum damping, and elastic component exponent were 0.8 mm, 1,500 N/mm, 0.5 N  s/mm, and 1.1, respectively. Femorotibial and femoropatellar contact penetration, stiffness, maximum damping and elastic component exponent were 0.1 mm, 30,000 N/mm, 28 N  s/mm and 1.5, respectively.

2.11. Joint modeling The pelvis and femur components were positioned for each discrete stance phase and then held constant during simulation. The tibia and fibula acted as a single body. The tarsus, metatarsus, and digits were fixed relative to each other and acted as a single rigid body during simulation. The digits were constrained to vertical translation and horizontal rotation relative to the ground to represent a no-slip condition. The tarsal joint was a frictionless hinge joint allowing flexion
extension. The stifle had five degrees of freedom (flexion
extension, internal
external rotation and vertical, craniocaudal, and mediolateral translation). The patella had five degrees of freedom but was constrained to the sagittal mid-plane of the trochlear groove. Femoropatellar contact occurred within the trochlear groove while the medial and lateral femoropatellar ligaments and an additional passive quadriceps element (Table 5) constrained the patella in the trochlear groove during simulation. The tension-only, passive quadriceps element was attached between the pelvis and patella along the rectus femoris line of action and represented noncontractile, passive resistance from the quadriceps to the patella. This element was included to prevent distal patellar luxation when the quadriceps muscles were determined inactive by muscle force optimization. The inextensible patellar ligament length (37 mm) located the patella in the trochlear groove relative to the tibial tuberosity.

1350043-10

Canine Stifle Computer Model to Evaluate CrCL Deficiency

2.12. Three-dimensional computer model simulation Stance phase analysis was conducted using motion simulation softwareh which simulated rigid body motion using physics solver softwarei and allowed for the input of external forces. The equations of motion were solved based on input forces and segment geometries. A Newton
Raphson-based iterative numerical differential equation solver37 was used with a variable integration step size (initial, minimum, and maximum sizes set to 10
4 , 10
7 , and 10
2 , respectively). Convergence was obtained using a maximum of 25 iterations, and the Jacobian re-evaluation parameter was set at maximum. Intact and CrCL-deficient stifle joints were evaluated, and CrCL rupture was simulated by suppressing the model CrCL. Stifle ligament loads, tibial translation, tibial rotation, and femoromeniscal contact forces outcome measures were evaluated at 10% discrete intervals throughout stance. Relative tibial translation (RTT) was defined as RTT ¼ ðFTdeficient Þ
ðFTintact Þ;

ð9Þ

where the fixed point tibial translation, FT, is the distance between the tibial tuberosity position relative to a fixed point on the femur along the y (cranio
caudal) axis, with deficient and intact denoting the CrCL status. Tibial translation was normalized by calculating RTT/body mass (mm/kg). Relative tibial rotation (RTR) was defined as RTR ¼ ðRdeficient Þ
ðRintact Þ;

ð10Þ

where R is the internal
external rotation defined by Grood and Suntay.38 Tibial rotation was normalized by calculating RTR/body mass (degrees/kg). 2.13. Three-dimensional computer model verification Hip, stifle, and tarsus flexion
extension joint angles defined by bony landmarks (Table 1) were determined in the CrCL-intact model following simulation using the joint coordinate system method developed by Grood and Suntay.38 Model flexion
extension angles were compared to surface marker motion capture joint angles determined using both the joint coordinate system method (comparison 1) and the 3D arccosine method (comparison 2) available in the motion capture software. The 3D arccosine method determines the angle between two vectors along the respective segment axes in 3D space. Arccosine segment vectors for the left pelvic limb were defined by the motion capture surface markers for the cranial dorsal iliac spine, ischiatic tuberosity, greater trochanter, lateral femoral epicondyle, lateral malleolus, and 5th metatarsophalangeal joint. Marker motion capture joint angles using both methods were also compared (comparison 3). Root mean square (RMS) error for each of the three comparisons was calculated for 10% discrete stance phase increments for the hip, stifle, and tarsus. h SolidWorks Motion v. 2010, Structural Research i ADAMS, MSC Software Corp, Santa Ana, CA

and Analysis Corp, Santa Monica, CA

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N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

Additionally, model outcome measures were compared to tibial translation and rotation following CrCL transection reported in vivo and in vitro,3,9,21
25,39 ligament loading reported in vivo and in vitro40
42 and stifle ligament loads determined during stance for intact and CrCL-deficient stifles using a mathematical model.19 2.14. CPL sensitivity analysis To demonstrate model capabilities, two key ligament parameters were independently varied from baseline values across the entire stance phase to investigate their effect on model outcome measures. Ligament stiffness was varied between 20% in 10% increments in the first analysis. Ligament pre-strain was varied between 4% in 2% increments in the second analysis. Model sensitivity for each parameter varied compared to baseline was reported as the \sensitivity index," or the ratio of the normalized change in outcome measure to the normalized change in input parameter. 3. Results 3.1. Model and motion capture kinematic comparison Hip, stifle and tarsus flexion
extension following simulation in the CrCL-intact model showed agreement with the joint angles determined using motion capture markers for both the joint coordinate system and the 3D arccosine joint angle determination methods (Fig. 2). Flexion
extension RMS errors between the model data points and motion capture markers using the joint coordinate system method (comparison 1) were 4.8 , 4.0 , and 2.6 for the hip, stifle, and tarsus angles, respectively. Flexion
extension RMS errors between the model data points and motion capture markers using the 3D arccosine method (comparison 2) were 10.0 , 4.7 , and 7.4 for the hip, stifle, and tarsus angles, respectively. Flexion
extension RMS errors between the joint coordinate system method and the 3D arccosine method (comparison 3) were 11.4 , 7.2 , and 6.2 for the hip, stifle, and tarsus angles, respectively. Therfore, the RMS error is greater across experimentally derived kinematics methods (comparison 3) than between the model and each experimentally derived kinematics method (comparisons 1 and 2). 3.2. Ligament loads Intact and CrCL-deficient stifle resultant ligament loads were determined for discrete stance phases. In the intact stifle, the peak CrCL and CaCL loads were 41% body weight (BW) and 28% BW, respectively, and occurred at 10% stance (Fig. 3). The peak LCL load was 15% BW, occurring at 90% stance, and the peak MCL load was 10% BW, occurring at 40% stance. In the CrCL-deficient stifle, the peak CaCL, LCL, and MCL loads were 183% BW, 104% BW, and 37% BW, respectively, and occurred at 50% stance. 1350043-12

Canine Stifle Computer Model to Evaluate CrCL Deficiency

Fig. 2. Hip, stifle, and tarsus flexion
extension angle comparison between the CrCL-intact model predicted angles, the 3D arccosine method, and the joint coordinate system (JCS) method.

3.3. Tibial translation and rotation In the CrCL-deficient stifle, peak RTT was 20.2 mm at 50% stance (Fig. 4). This corresponded to an RTT/body mass of 0.61 mm/kg. RTT was 1.1 mm at 10% stance while all other stance phases had an RTT less than 1 mm. In the CrCL-deficient stifle, peak RTR was 4.6 internal rotation occurring at 50% stance (Fig. 4). RTR varied between 1 for other stance phases. 3.4. Femoromeniscal contact forces Intact and CrCL-deficient stifle femoromeniscal contact forces were determined for discrete stance phases. In the intact stifle, the peak lateral contact force was 80% BW occurring at 80% stance and the peak medial contact force was 88% BW occurring at 20% stance (Fig. 5). Femoromeniscal contact forces follow a similar trend to ground reaction forces with the primary peak occurring at 20% stance and the secondary peak occurring at 80% stance. In the CrCL-deficient stifle, the peak lateral contact force was 68% BW occurring at 30% stance and the peak medial contact force was 105% BW occurring at 20% stance. Because the tibia subluxates at 50% stance in the CrCL-deficient stifle, femoromeniscal contact forces reported for this scenario correspond to the peak medial femoromeniscal contact force acting on the caudal meniscal horns during simulation prior to tibia subluxation. 1350043-13

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

Fig. 3. Ligament loads in the intact (a) and CrCL-deficient stifle (b) during stance. In the intact stifle, a peak load of 41% BW occurs in the CrCL. In the CrCL-deficient stifle, a peak load of 183% BW occurs in the CaCL.

Fig. 4. Relative tibial translation and relative tibial rotation during stance. Peak translation and rotation are 20.2 mm and 4.6 , respectively. 1350043-14

Canine Stifle Computer Model to Evaluate CrCL Deficiency

Fig. 5. Femoromeniscal contact forces in the intact and deficient stifle.

3.5. CPL sensitivity analysis Peak ligament loads (Fig. 6), peak tibial translation and rotation (Fig. 7), and peak femoromeniscal contact forces (Fig. 8) during stance following ligament stiffness and ligament pre-strain variation were compared to baseline in the intact and CrCL-deficient stifle. Sensitivity indices for each parameter (Table 6) compared the change in outcome measure to baseline.

Fig. 6. Peak ligament loads in the intact and CrCL-deficient stifle following ligament stiffness and prestrain variation compared to baseline (0% change). 1350043-15

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

Fig. 7. Peak tibial translation and rotation in the intact and CrCL-deficient stifle following ligament stiffness and pre-strain variation compared to baseline (0% change). Note: The difference between the intact and deficient tibial translation and rotation represents RTT and RTR, respectively.

Fig. 8. Peak femoromeniscal contact forces in the intact and CrCL-deficient stifle following ligament stiffness and pre-strain variation compared to baseline (0% change).

1350043-16

Canine Stifle Computer Model to Evaluate CrCL Deficiency Table 6(a). Sensitivity indices for ligament stiffness variation in the intact (I) and deficient (D) stifle. CrCL load

CaCL load

LCL load

MCL load

Change (%)

I

D

I

D

I

D

I

D


20
10 10 20

0.70 0.68 0.66 0.65

NA NA NA NA


0.13 0.94 0.91 0.89

0.53 0.43 0.59 0.51

1.80 0.94 0.84 0.87

0.24
0.10 0.54 0.42

0.83 0.86 0.75 0.76

1.25 1.28 0.75 0.90

Table 6(b). Sensitivity indices for ligament stiffness variation in the intact (I) and deficient (D) stifle. Medial femoromeniscal contact force

Lateral femoromeniscal contact force

Change (%)

I

D

I

D


20
10 10 20

0.31 0.31 0.26 0.27


0.02
0.02
0.06
0.02


0.10
0.06
0.30 0.40


0.99
2.00 0.20 0.26

RTT

RTR


0.06
0.04
0.04
0.04


0.47
1.07 0.04 0.03

Table 6(c). Sensitivity indices for ligament pre-strain variation in the intact (I) and deficient (D) stifle. CrCL load

CaCL load

LCL load

MCL load

Change (%)

I

D

I

D

I

D

I

D


4
2 2 4


32.93
54.53 34.39 35.03

NA NA NA NA


79.41
106.31 52.87 60.27

8.11 7.10
7.01
14.25


17.35 33.84 58.08 64.45

5.26 7.01 11.99
14.56


245.33
179.27 94.53 110.10

25.00 34.86 29.39 15.02

Table 6(d). Sensitivity indices for ligament pre-strain variation in the intact (I) and deficient (D) stifle. Medial femoromeniscal contact force

Lateral femoromeniscal contact force

Change (%)

I

D

I

D


4
2 2 4


15.43
43.23 16.03 18.09

10.82 5.01
9.34
1.66


56.37
26.19 14.18 19.76


4.84
6.30 25.20 37.03

RTT

RTR

0.22 3.22
0.94
22.17

166.45 157.95 35.08
19.01

Note: Bold values represent the largest absolute value sensitivity index across both parameters for each outcome measure in the intact and deficient stifle.

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N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

4. Discussion 4.1. Model description Despite the challenges of biomechanical simulation, a computer model can be used to investigate joint biomechanics43 and evaluate specific therapeutic approaches44 in silico, thereby reducing the need for and better informing in vivo or in vitro studies. The model developed in this study simulated both an intact and CrCLdeficient stifles. To our knowledge, this is the first anatomical, kinematic, and kinetic subject-specific CPL rigid body motion computer model capable of predicting ligament loads, tibial translation, tibial rotation, and femoromeniscal contact forces for both the intact and CrCL-deficient stifles for discrete stance phases. Model capabilities were also demonstrated through a parametric sensitivity analysis of key ligament properties; an analysis not feasible through in vivo or in vitro studies. 4.2. CrCL-intact stifle kinematics CPL model-predicted kinematics during stance showed agreement with measured motion capture kinematics. Hip, stifle, and tarsus flexion-extension joint angles determined by model bony geometry were compared to two common surface marker motion capture 3D joint angle determination methods. Our model predicted flexion
extension joint angles that matched joint angles determined using both the joint coordinate system method (comparison 1) and the 3D arccosine method (comparison 2) with less RMS error than when comparing the joint coordinate system method to the 3D arccosine method (comparison 3). Therfore, RMS error is greater across experimentally derived kinematics methods (comparison 3) than between the model and each experimentally derived kinematics method (comparisons 1 and 2). RMS errors between motion capture fluoroscopy and skin surface marker measurement methods were reported between 2.7 and 9 for human knee flexion
extension during walking.45 Our results were similar to this human study for all three comparisons (comparison 1, 2.6 to 4.8 RMS error; comparison 2, 4.7 to 10.0 RMS error; and comparison 3, 6.2 to 11.4 RMS error). Our model was therefore able to reproduce measured kinematics. 4.3. Ligament loads The CrCL was the primary load-bearing ligament in the CrCL-intact stifle. Our model predicted peak CrCL loads at 10% stance (corresponding to 138 stifle extension) and similar CrCL loads at 50% stance (corresponding to 134 stifle extension), while CrCL loads were reduced after 50% stance. Similar temporal patterns were found in vivo with goat CrCL peak loads occurring in the first 40% of stance.41 Additionally, in vivo goat CrCL loads exhibited a characteristic double peak profile which was also present in our model.41 Stifle ligament load stance history profiles predicted by our model were similar to those reported previously 1350043-18

Canine Stifle Computer Model to Evaluate CrCL Deficiency

using a mathematical model.19 Furthermore, a mathematical model also indicated peak canine stifle CrCL loads at 40% stance, corresponding with the occurrence (50% stance) of peak CrCL loads predicted by our model.19 The CrCL is generally taut in extension and loose in flexion.2 Our findings supported the view that the CrCL is in greater tension in early stance when the stifle is in maximal extension. Peak ligament loads predicted by our model corresponded to strains of 2.3% (CrCL), 1.1% (CaCL), 1.0% (LCL), and 0.5% (MCL). CrCL strains measured during flexion
extension in vivo and in vitro varied between approximately 0%
6% at stifle angles during stance.42 Measured CaCL strains were likely less than those for the CrCL, but strain values could not be inferred because the initial ligament length was not reported.42 Human anterior cruciate ligament bundle strains were measured between
4% and 6% during flexion
extension.40 Our model predicted CaCL loading primarily during the first 40% of stance in the intact stifle. The CaCL was previously reported to be unloaded during stance in the intact stifle using a mathematical model.19 However, CaCL ligament bundle tension has been described during flexion and extension, which is consistent with our findings.2 Neither our study nor the mathematical model included separate ligament bundles. The MCL and LCL carried less load than the cruciate ligaments throughout stance for the intact stifle. Unlike the cruciate ligaments, the collateral ligaments remain approximately constant in length throughout stance,46 suggesting less variation in collateral ligament loads during stance. Our model suggested that the CaCL was the primary load-bearing ligament in the CrCL-deficient stifle. Peak CaCL load (183% BW) occurred at 50% stance (corresponding to 134 stifle extension). Similarly, peak CaCL loading was predicted at 50% stance using a mathematical model.19 The LCL and MCL also contributed to CrCL-deficient stifle stability at 50% stance as peak loads increased to 104% BW (LCL) and 37% BW (MCL). Peak ligament loads predicted by our model in the deficient stifle corresponded to strains of 6.7% (CaCL), 7.4% (LCL), and 1.8% (MCL). Maximum in vitro strains for human knee ligaments at rupture have been reported between 11% and 19%.47 Ligament strains predicted by our model remained below potential rupture levels in the CrCL-deficient stifle. Our model predicted a peak CaCL load in the deficient stifle approximately 4.5 times the peak intact stifle CrCL load with 2.9 times more strain. However, our study did not attempt to model additional constraining tissues such as the joint capsule and musculotendinous structures that further aid stifle stability in vivo. Instability following CrCL suppression at mid-stance resulted in increased tibial translation and rotation opposed primarily by the CaCL and LCL. Despite prediction of higher ligament loads in the deficient stifle, all ligament loads remained well below the reported failure threshold (four times BW) established through canine CrCL cadaveric specimen testing.34 CaCL failure loads are currently unknown, but increased CaCL load following CrCL deficiency predicted by our model at mid-stance may represent deleterious effects on CaCL morphology, especially over time.48 Furthermore, peak LCL and MCL loads increased by factors 1350043-19

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

of seven and three, respectively, following CrCL deficiency. These increases may in part be responsible for mild degenerative effects noted microscopically in the MCL following CrCL deficiency.4 However, these deleterious effects may not be extensive due to the extra-synovial environment and improved blood supply to the collateral ligaments.4 Ligament load magnitudes during stance reported by Shahar et al.19 were consistently less than those predicted by our model. In our model the intact peak stifle CrCL load was 3.4 times higher, and the CrCL-deficient stifle peak CaCL load was 16.6 times higher. Differences in ligament load magnitudes may be due to tibial plateau and femoral condyle conformation geometric differences, muscle force prediction differences, as well as ligament origin and insertion location differences. These disparities may have influenced stifle stabilizing ligament recruitment. Furthermore, our model used different ligament pre-strain values compared to the model developed by Shahar et al.19 Canine stifle ligament strain during stance is currently unknown. It has previously been stated that CrCL and CaCL strains approached a minimum strain of 0% near the standing stifle angle.42 In our study, ligament pre-strain values were set at 0% at the minimum ligament length occurring at a discrete point in stance. The model developed by Shahar et al. used ligament pre-strain values adapted from a human knee model49 based on full knee extension. It is uncertain whether canine stifle and human knee ligaments are strained similarly during stance. Given the differences between the canine stifle and human knee, such as tibial plateau angle and range of motion during stance, it is expected that ligament strains at full extension determined for humans will differ from that in canines. Furthermore, our model included contact between the menisci and femur in addition to femorotibial contact. The previous mathematical model constrained contact between the femoral condyles and tibial plateau as collinear articulating surfaces that must remain in contact.19 These constraining effects may have overstabilized the CrCL-deficient stifle and limited slip conditions between the femur and tibia. Additionally, joint angles were assumed to remain constant during each stance phase solution and to be equal in the intact and CrCL-deficient stifle in the model developed by Shahar et al.19 Stifle kinematics have been reported to vary following CrCL deficiency.50,51 We implemented stance phase initial joint angle conditions, but during simulation, our model was allowed to reach equilibrium based on applied forces and constraints. These differing factors between our model and the mathematical model developed by Shahar et al. likely led to increased stifle stability in the model developed by Shahar et al.19 Therefore, tibial translation may have been reduced, leading to a corresponding lower CaCL load as compared to our model. 4.4. Tibial translation and rotation CrCL load in the intact stifle during stance, as well as RTT and RTR following CrCL suppression supports the CrCL functional role in our model. These findings 1350043-20

Canine Stifle Computer Model to Evaluate CrCL Deficiency Table 7. Model outcome measures during stance compared to previous studies.

Study

Study type

Normalized tibial translation (mm/kg)

Normalized tibial rotation (degrees/kg)

Current study Apelt et al.9 Hagemeister et al.21 Kim et al.22 Korvick et al.23 Kowaleski et al.24 Tashman et al.25 Warzee et al.3

Computer model In vitro In vitro In vitro In vivo In vitro In vivo In vitro

0.61 0.41 0.13
0.14 0.43
0.54 0.26
0.30 0.60
0.80 0.33
0.66 0.59

0.14 NA 0.16
0.18 0.40
0.50 0.05
0.06 NA 0.10
0.20 0.71

 Value obtained in the data range during stance corresponding to peak cranial tibial translation.

illustrated that the CrCL serves to prevent cranial tibial translation and internal tibial rotation while acting as a primary stifle stabilizer.2,52 Due to differences in dog mass between our computer model and other studies, a normalized tibial translation and rotation were compared (Table 7). Comparing normalized tibial translation, our model predicted RTT/body mass of 0.61 mm/kg and met the criteria suggested by Pipkorn and Eriksson53 for the studies conducted by Kim et al.,22 Kowaleski et al.,24 Tashman et al.,25 and Warzee et al.3 Comparing normalized tibial rotation, our model predicted RTR/body mass of 0.14 degrees/kg and met the criteria suggested by Pipkorn and Eriksson53 for the studies conducted by Hagemeister et al.21 and Tashman et al.25 Therefore, normalized tibial translation and rotation measures at mid-stance generated by our model are in reasonable agreement with in vitro and in vivo studies that incorporated stifle ligaments, menisci, a joint capsule, and muscle forces.3 Although both RTT and RTR occurred primarily at 50% stance in our CrCL-deficient stifle model, it should be noted that because this was a quasi-static model, each interval of stance phase simulation was evaluated separately with reset initial conditions. Continuous translation and rotation effects were therefore not represented across the stance phase as it occurs in vivo as indicated by Tashman et al.39 Our CPL model assumed no change between the CrCL-intact and CrCL-deficient initial conditions for all stance phases prior to simulation. Our CrCL-deficient model predicted peak CaCL, LCL, and MCL loads as well as peak RTT and RTR at 50% stance. Although the model is influenced by a multitude of factors, the input ground reaction forces and moments may play an important role in stifle instability at 50% stance. Based on the ligament loading pattern in the intact stifle, the CrCL was most active at 10%, 20% and 50% stance; however, stifle instability was present primarily at 50% stance in the CrCL-deficient stifle. It is important to note that the peak vertical ground reaction moment occurred at 50% stance and the vertical ground reaction force was reduced at this same point of stance. The increased vertical ground reaction moment causes the tibia to internally 1350043-21

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

rotate, increasing the tendency for separation between the lateral femoral condyle and lateral meniscus. The reduced vertical ground reaction force promotes the tendency for separation of the tibia and femur, whereas a higher vertical ground reaction force would compress the tibia and meniscus into the femur, increasing the femoromeniscal contact force and thereby preventing femoromeniscal separation. With the reduced contact surface area occurring at 50% stance, tibial translation and rotation are not prevented by femoromeniscal contact forces. 4.5. Femoromeniscal contact forces Femoromeniscal contact force magnitudes predicted by our model during stance were primarily between 50% BW and 100% BW. Similar stifle contact reaction force magnitudes were predicted by Shahar et al. using a mathematical model.19 Mean in vitro femorotibial contact forces at mid-stance for dogs of similar mass were 232 N (74% BW, medial) and 164 N (52% BW, lateral) in the CrCL-intact stifle and 142 N (45% BW, medial) and 140 N (45% BW, lateral) in the deficient stifle.22 Femoromeniscal contact forces at mid-stance predicted using our model were 222 N (68% BW, medial) and 194 N (59% BW, lateral) in the CrCL-intact stifle and 144 N (44% BW, medial) and 204 N (63% BW, lateral) in the deficient stifle. Total stifle contact force (sum of medial and lateral contact force) at mid-stance measured in vitro was 395 N (126% BW) in the intact stifle and 276 N (88% BW) in the deficient stifle.22 Our model predicted total stifle contact force at mid-stance of 127% BW in the intact stifle and 107% BW in the deficient stifle. Therefore, our model predicted stifle contact forces similar to measured contact forces in the intact stifle and slightly higher contact forces in the CrCL-deficient stifle. Stifle contact forces shifted caudally following CrCL deficiency in both the in vitro study by Kim et al.22 and our computer model indicating joint stability is critical to maintain normal joint contact mechanics. Stifle instability and altered femoromeniscal contact mechanics may increase osteoarthritis and meniscus injury likelihood following CrCL deficiency. The menisci act as passive restraints following CrCL deficiency, and menisci impingement often leads to rupture of the medial caudal horn.17 Our computer model supports this rationale because the femoromeniscal contact force shifted from the cranial horn to the caudal horn prior to tibial subluxation in the CrCL-deficient stifle. However, we did not investigate the distribution of femormeniscal contact forces as interface pressures which may affect injury potential. For instance, at mid-stance, total stifle contact force was reduced in both our model and an in vitro study following CrCL deficiency, but mean and peak pressure increased due to reduced contact area in vitro.22 Finally, although medial femoromeniscal contact forces were reduced at mid-stance following CrCL deficiency, the peak medial femoromeniscal contact force during stance increased by 17% BW. The peak medial femoromeniscal contact force in both the intact and CrCL-deficient stifle occurred at 20% stance which corresponded to the peak vertical ground reaction force. The peak lateral femoromeniscal contact force during 1350043-22

Canine Stifle Computer Model to Evaluate CrCL Deficiency

stance, however, decreased from 80% BW (80% stance) to 68% BW (30% stance) following CrCL deficiency. This medio-lateral disparity present when investigating the entire stance phase may further elucidate the increased likelihood for medial meniscus injury over lateral meniscus injury diagnosed clinically following CrCL deficiency,17 which is not directly apparent when only investigating mid-stance. 4.6. CPL sensitivity analyses Canine stifle ligament stiffness in vivo is currently unknown. Baseline ligament stiffness values used in our model were estimated from previously reported CrCL tensile test data for two breeds.34 To understand the influence of ligament stiffness on outcome measures, we incrementally varied ligament stiffness through 20%. Overall, ligament stiffness appeared to have relatively little influence on outcome measures as indicated by the low sensitivity indices (Table 6) for the range of stiffness that we evaluated. As ligament stiffness increased in the model, ligament loads and femoromeniscal contact forces increased slightly in the CrCL-intact stifle. Similarly, ligament loads slightly increased with increasing ligament stiffness in the deficient stifle. Ligament stiffness variation had little effect on femoromeniscal contact forces in the deficient stifle. Our model showed substantially less sensitivity to ligament stiffness than ligament pre-strain for all outcome measures as indicated by the consistently higher ligament pre-strain sensitivity indices. Canine stifle ligament pre-strain in vivo is currently unknown. It has been reported that canine cruciate ligament strains approached a minimum of zero during joint angles representative of stance in the cruciate ligaments.42 Therefore, the minimum ligament length for each cruciate ligament occurring at a discrete point in stance was assigned zero ligament pre-strain in our model. Collateral ligament strains during stance are also unknown and therefore were similarly assigned 0% ligament pre-strain at the minimum ligament lengths at a discrete point in stance. Knee ligament strains have been reported in the human literature ranging between
4% and 6% during normal range of motion.40 To assess the influence of ligament pre-strain implemented in our model, ligament pre-strain was incrementally varied through 4% from the baseline value. Increased pre-strain represented taut ligaments while decreased pre-strain represented ligaments having slack. Decreased ligament pre-strain may therefore introduce stifle joint laxity in the model. In the CrCL-intact stifle, increasing and decreasing ligament pre-strain served to increase ligament loading although two different mechanisms were identified as being responsible for these increased ligament loads. As ligament pre-strain decreased from baseline in the CrCL-intact stifle, stifle joint laxity increased which resulted in stifle instability leading to increased tibial rotation at
4% and
2% ligament pre-strain. This instability substantially \stretched" the stifle ligaments thereby increasing loading. Similar trends were predicted by our model for femoromeniscal contact forces in the CrCL-intact stifle; stifle instability increased with 1350043-23

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

decreasing ligament pre-strain (from baseline) thus increasing femoromeniscal contact forces due to less optimal joint congruency and menisci impingement. Increasing ligament pre-strain (from baseline) also led to higher femoromeniscal contact forces given greater initial tension in the ligaments drawing the femoral condyles into the menisci. In the CrCL-deficient stifle, ligament load trends were the opposite of the CrCLintact stifle for varying pre-strain; ligament loading tended to decrease for both increasing and decreasing ligament pre-strain. As pre-strain decreased from baseline, tibial translation led to subluxation, thereby eliminating rotational freedom as the tibia was compressed into the femoral condyles. Furthermore, ligament loads decreased from baseline to þ4% ligament pre-strain since stifle joint laxity was reduced as indicated by reduced tibial translation at 2% ligament pre-strain and eliminated tibial translation at 4% ligament pre-strain. Medial and lateral femoromeniscal contact forces generally increased with increasing ligament pre-strain given greater initial tension in the ligaments thus reducing joint laxity. Our sensitivity analysis indicated ligament pre-strain had an appreciable effect on model outcomes as evidenced by relatively higher absolute values of sensitivity indices. Similarly, the laxity of a human knee model was most sensitive to ligament prestrain through a range of flexion, which is consistent with our findings.54 4.7. Model benefits and potential applications Our computer model represents a critical first step towards canine stifle biomechanical simulation and presents a novel clinical tool that can be used to investigate stifle biomechanics, and underlying CrCL deficiency causation, treatment, and management. Canine stifle CrCL deficiency has primarily been investigated through in vivo and in vitro experimental studies with little development in computational analysis methods. Human knee models are essential to formulating and testing research questions associated with ligament injury, surgical intervention, and rehabilitation strategies. In silico simulation of canine stifle biomechanics could therefore augment clinical studies assessing the effects and management of CrCL deficiency by providing predictive functionality to this multifaceted injury. As predicted by our model ligament property sensitivity analysis, biomechanical parameters can affect canine stifle biomechanics. Additional biomechanical parameters associated with CrCL deficiency such as tibial plateau angle and patellar ligament orientation could be investigated in a broader parametric sensitivity analysis that directly compares outcome measures across and within parameters. Individual parameters could therefore be isolated to determine which have the greatest effect on model outcomes. Furthermore, surgical interventions could be assessed and tuned using simulation models to provide confidence through evidencebased biomechanical analyses that optimal outcomes will be achieved following CrCL deficiency stabilization surgery. Surgical osteotomy procedures could effectively be implemented in the CPL model by altering model bony geometry to 1350043-24

Canine Stifle Computer Model to Evaluate CrCL Deficiency

replicate each respective procedure. Finally, although the goal of this study was to investigate CrCL deficiency, future models will likely benefit from the development presented in this study. This model could for example be modified and adapted to investigate other canine stifle injuries such as osteoarthritis, meniscal damage, and patellar luxation. 4.8. Limitations This computer model is a simplification of a complex biomechanical system. Canine pelvic limb kinematics were approximated based on motion capture data which may be affected by marker motion and soft tissue artifact.45 Additionally, the tarsus, metatarsus, and digits were fixed relative to each other during simulation. However, the angle between the digits and the tarsus and metatarsus complex was uniquely set prior to each 10% discrete stance phase simulation based on motion capture data. Ligaments were approximated as single elements as opposed to multiple bundles connecting origin and insertion. Our model did not account for ligament bundle recruitment variation which may occur in vivo,2,46 but rather reported loading of the composite bundle which may fail to identify increased loading on a single bundle. Effects due to ligaments wrapping around bone geometry or ligaments twisting were neglected. Ligaments were modeled as time-independent nonlinear springs with material properties based upon ligament CSA. An identical elastic modulus and pre-strain were used for all ligaments which may vary depending upon ligament structure, age-related degeneration, or changes over time or in association with CrCL loss.4 The CaCL morphology, for example, is altered with CrCL loss, possibly as a result of repetitive microtrauma48 or changes to the synovial environment.55 A range of discrete points was chosen for ligament stiffness and ligament pre-strain variation in our parametric sensitivity analysis. A wider range may show trends not predicted in our sensitivity analyses. Muscle actuation was simplified by estimating muscle force magnitudes using an optimization technique.19 These optimized forces represent one possible solution set to achieve the stifle reaction moments determined by inverse dynamics. Canine pelvic limb muscle forces during a walk in vivo are currently unknown, but muscle activation electromyography results have been reported.56 The optimization method in this study predicted similar activation patterns and duration for the lateral gastrocnemius, popliteus, gracilis, semimembranosus (femoral insertion), semitendinosus, biceps femoris, rectus femoris, tensor fasciae latae, and sartorious. However, the medial gastrocnemius, superficial digital flexor, semimembranosus (tibial insertion), and lateral vastus were active for shorter durations than electromyography results, and the long digital extensor was active for a longer duration than electromyography results.56 These differences could be due to breed variation.57 Furthermore, it is expected that muscle activation may be altered in the CrCL-deficient stifle to compensate for instability as noted in the human knee following anterior cruciate ligament rupture.58 1350043-25

N. P. Brown, G. E. Bertocci & D. J. Marcellin-Little

The stifle joint capsule and meniscofemoral ligament were not represented in our model which may reduce tibial translation. Additionally, stifle cartilage and menisci biomechanical properties were simplified, and contact between the femur and menisci was representative of the contact and deformation between the femur and combined menisci and tibial cartilage. Finally, attempts to verify our computer model were partially based on previously reported in vivo, in vitro, and mathematical modeling studies, each with their own inherent limitations (e.g., in vitro studies often simplify or neglect muscle forces and present ethical concerns.) However, model-predicted kinematics were comparable to experimental kinematics with less RMS error between the model and each experimental kinematic determination method than between experimental kinematic determination methods. 5. Conclusions The 3D rigid body computer model developed in this study provides a first approximation of the CPL during the stance phase of walking that can be used to investigate ligament loads, tibial translation, tibial rotation, and femoromeniscal contact forces in the intact and CrCL-deficient stifle. Model verification was confirmed through reasonable agreement with measured kinematics and previously reported studies. Application of the model was demonstrated through a parametric sensitivity analysis evaluating the sensitivity of outcome measures to ligament stiffness and ligament pre-strain. Model outcomes were more sensitive to ligament pre-strain than ligament stiffness. This model serves as a basis from which future CPL models could be developed to study stifle biomechanics, as well as CrCL deficiency causation and surgical management. Acknowledgments This project was supported by the AKC Canine Health Foundation, Grant No. 01533-A. The contents of this publication are solely the responsibility of the authors and do not necessarily represent the views of the Foundation. Resources in support of this study were also provided by the University of Louisville Grosscurth Biomechanics Endowment. The authors thank Dr. Scott Rizzo, Lindsey Scanson, and Laura Prezocki at Louisville Veterinary Specialty and Emergency Services for their clinical expertise and technical assistance. References 1. Aragon CL, Budsberg SC, Applications of evidence-based medicine: Cranial cruciate ligament injury repair in the dog, Vet Surg 34:93
98, 2005. 2. Arnoczky SP, Marshall JL, The cruciate ligaments of the canine stifle: An anatomical and functional analysis, Am J Vet Res 38:1807
1814, 1977. 3. Warzee CC, Dejardin LM, Arnoczky SP, et al., Effect of tibial plateau leveling on cranial and caudal tibial thrusts in canine cranial cruciate-deficient stifles: An in vitro experimental study, Vet Surg 30:278
286, 2001. 1350043-26

Canine Stifle Computer Model to Evaluate CrCL Deficiency

4. Vasseur PB, Pool RR, Arnoczky SP, et al., Correlative biomechanical and histologic study of the cranial cruciate ligament in dogs, Am J Vet Res 46:1842
1854, 1985. 5. Vasseur PB, Clinical results following nonoperative management for rupture of the cranial cruciate ligament in dogs, Vet Surg 13:243
246, 1984. 6. Witsberger TH, Villamil JA, Schultz LG, et al., Prevalence of and risk factors for hip dysplasia and cranial cruciate ligament deficiency in dogs, J Am Vet Med Assoc 232:1818
1824, 2008. 7. DeAngelis M, Lau RE, A lateral retinacular imbrication technique for the surgical correction of anterior cruciate ligament rupture in the dog, J Am Vet Med Assoc 157:79
84, 1970. 8. Kim SE, Pozzi A, Kowaleski MP, et al., Tibial osteotomies for cranial cruciate ligament insufficiency in dogs, Vet Surg 37:111
125, 2008. 9. Apelt D, Kowaleski MP, Boudrieau RJ, Effect of tibial tuberosity advancement on cranial tibial subluxation in canine cranial cruciate-deficient stifle joints: An in vitro experimental study, Vet Surg 36:170
177, 2007. 10. Apelt D, Pozzi A, Marcellin-Little DJ, et al., Effect of cranial tibial closing wedge angle on tibial subluxation: An ex vivo study, Vet Surg 39:454
459, 2010. 11. Conzemius MG, Evans RB, Besancon MF, et al., Effect of surgical technique on limb function after surgery for rupture of the cranial cruciate ligament in dogs, J Am Vet Med Assoc 226:232
236, 2005. 12. Jandi AS, Schulman AJ, Incidence of motion loss of the stifle joint in dogs with naturally occurring cranial cruciate ligament rupture surgically treated with tibial plateau leveling osteotomy: Longitudinal clinical study of 412 cases, Vet Surg 36:114
121, 2007. 13. Lazar TP, Berry CR, deHaan JJ, et al., Long-term radiographic comparison of tibial plateau leveling osteotomy versus extracapsular stabilization for cranial cruciate ligament rupture in the dog, Vet Surg 34:133
141, 2005. 14. Pacchiana PD, Morris E, Gillings SL, et al., Surgical and postoperative complications associated with tibial plateau leveling osteotomy in dogs with cranial cruciate ligament rupture: 397 cases (1998
2001), J Am Vet Med Assoc 222:184
193, 2003. 15. Rayward RM, Thomson DG, Davies JV, et al., Progression of osteoarthritis following TPLO surgery: A prospective radiographic study of 40 dogs, J Small Anim Pract 45:92
97, 2004. 16. Robinson DA, Mason DR, Evans R, et al., The effect of tibial plateau angle on ground reaction forces 4
17 months after tibial plateau leveling osteotomy in Labrador Retrievers, Vet Surg 35:294
299, 2006. 17. Slocum B, Slocum TD, Tibial plateau leveling osteotomy for repair of cranial cruciate ligament rupture in the canine, Vet Clin North Am Small Anim Pract 23:777
795, 1993. 18. Shahar R, Banks-Sills L, Biomechanical analysis of the canine hind limb: Calculation of forces during three-legged stance, Vet J 163:240
250, 2002. 19. Shahar R, Banks-Sills L, A quasi-static three-dimensional, mathematical, three-body segment model of the canine knee, J Biomech 37:1849
1859, 2004. 20. Shahar R, Milgram J, Biomechanics of tibial plateau leveling of the canine cruciatedeficient stifle joint: A theoretical model, Vet Surg 35:144
149, 2006. 21. Hagemeister N, Lussier B, Jaafar E, et al., Validation of an experimental testing apparatus simulating the stance phase of a canine pelvic limb at trot in the normal and the cranial cruciate-deficient stifle: An in vitro kinematic study, Vet Surg 39:390
397, 2010. 22. Kim SE, Pozzi A, Banks SA, et al., Effect of tibial plateau leveling osteotomy on femorotibial contact mechanics and stifle kinematics, Vet Surg 38:23
32, 2009.

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23. Korvick DL, Pijanowski GJ, Schaeffer DJ, Three-dimensional kinematics of the intact and cranial cruciate ligament-deficient stifle of dogs, J Biomech 27:77
87, 1994. 24. Kowaleski MP, Apelt D, Mattoon JS, et al., The effect of tibial plateau leveling osteotomy position on cranial tibial subluxation: An in vitro study, Vet Surg 34:332
336, 2005. 25. Tashman S, Anderst W, Kolowich P, et al., Kinematics of the ACL-deficient canine knee during gait: Serial changes over two years, J Orthop Res 22:931
941, 2004. 26. Fu YC, Torres BT, Budsberg SC, Evaluation of a three-dimensional kinematic model for canine gait analysis, Am J Vet Res 71:1118
1122, 2010. 27. Ragetly CA, Griffon DJ, Thomas JE, et al., Noninvasive determination of body segment parameters of the hind limb in Labrador Retrievers with and without cranial cruciate ligament disease, Am J Vet Res 69:1188
1196, 2008. 28. Amit T, Gomberg BR, Milgram J, et al., Segmental inertial properties in dogs determined by magnetic resonance imaging, Vet J 182:94
99, 2009. 29. Dumas R, Aissaoui R, de Guise JA, A 3D generic inverse dynamic method using wrench notation and quaternion algebra, Comput Methods Biomech Biomed Eng 7:159
166, 2004. 30. Winter DA, Biomechanics and Motor Control of Human Movement, 3rd edn., John Wiley & Sons, Inc., pp. 180
202, Hoboken, NJ, 2005. 31. Zajac FE, Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control, Crit Rev Biomed Eng 17:359
411, 1989. 32. Cleather DJ, Bull AM, An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction, Ann Biomed Eng 39:1925
1934, 2011. 33. Blankevoort L, Huiskes R, Ligament
bone interaction in a three-dimensional model of the knee, J Biomech Eng 113:263
269, 1991. 34. Wingfield C, Amis AA, Stead AC, et al., Comparison of the biomechanical properties of rottweiler and racing greyhound cranial cruciate ligaments, J Small Anim Pract 41:303
307, 2000. 35. McCann L, Ingham E, Jin Z, et al., Influence of the meniscus on friction and degradation of cartilage in the natural knee joint, Osteoarthritis Cartilage 17:995
1000, 2009. 36. Majors BJ, Wayne JS, Development and validation of a computational model for investigation of wrist biomechanics, Ann Biomed Eng 39:2807
2815, 2011. 37. Gear CW, The numerical integration of ordinary differential equations, Math Comp 21:146
156, 1967. 38. Grood ES, Suntay WJ, A joint coordinate system for the clinical description of threedimensional motions: Application to the knee, J Biomech Eng 105:136
144, 1983. 39. Tashman S, Anderst W, In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: Application to canine ACL deficiency, J Biomech Eng 125:238
245, 2003. 40. Belisle AL, Bicos J, Geaney L, et al., Strain pattern comparison of double- and singlebundle anterior cruciate ligament reconstruction techniques with the native anterior cruciate ligament, Arthroscopy 23:1210
1217, 2007. 41. Holden JP, Grood ES, Korvick DL, et al., In vivo forces in the anterior cruciate ligament: Direct measurements during walking and trotting in a quadruped, J Biomech 27:517
526, 1994. 42. Stone JE, Madsen NH, Milton JL, et al., Developments in the design and use of liquidmetal strain gages, Exp Mech 23:129
139, 1983. 43. Delp SL, Loan JP, A computational framework for simulating and analyzing human and animal movement, Comput Sci Eng 2:46
55, 2000. 1350043-28

Canine Stifle Computer Model to Evaluate CrCL Deficiency

44. Semadeni R, Schmitt KU, Numerical simulations to assess different rehabilitation strategies after ACL rupture in a skier, J Sport Rehabil 18:427
437, 2009. 45. Akbarshahi M, Schache AG, Fernandez JW, et al., Non-invasive assessment of softtissue artifact and its effect on knee joint kinematics during functional activity, J Biomech 43:1292
1301, 2010. 46. Vasseur PB, Arnoczky SP, Collateral ligaments of the canine stifle joint: Anatomic and functional analysis, Am J Vet Res 42:1133
1137, 1981. 47. Butler DL, Kay MD, Stouffer DC, Comparison of material properties in fascicle-bone units from human patellar tendon and knee ligaments, J Biomech 19:425-432, 1986. 48. Zachos TA, Arnoczky SP, Lavagnino M, et al., The effect of cranial cruciate ligament insufficiency on caudal cruciate ligament morphology: An experimental study in dogs, Vet Surg 31:596
603, 2002. 49. Blankevoort L, Huiskes R, de Lange A, Recruitment of knee joint ligaments, J Biomech Eng 113:94
103, 1991. 50. DeCamp CE, Riggs CM, Olivier NB, et al., Kinematic evaluation of gait in dogs with cranial cruciate ligament rupture, Am J Vet Res 57:120
126, 1996. 51. Ragetly CA, Griffon DJ, Mostafa AA, et al., Inverse dynamics analysis of the pelvic limbs in Labrador Retrievers with and without cranial cruciate ligament disease, Vet Surg 39:513
522, 2010. 52. Slocum B, Devine T, Cranial tibial thrust: A primary force in the canine stifle, J Am Vet Med Assoc 183:456
459, 1983. 53. Pipkorn B, Eriksson M, A method to evaluate the validity of mathematical models, Proc 4th Eur MADYMO Users Meeting, Brussels, Belgium, pp. 7
15, 2003. 54. Bertozzi L, Stagni R, Fantozzi S, et al., Evaluation of a cruciate ligament model: Sensitivity to the parameters during drawer test simulation, J Appl Biomech 24:234
243, 2008. 55. Cook JL, Cranial cruciate ligament disease in dogs: Biology versus biomechanics, Vet Surg 39:270
277, 2010. 56. Wentink GH, The action of the hind limb musculature of the dog in walking, Acta Anat (Basel) 96:70
80, 1976. 57. Colborne GR, Innes JF, Comerford EJ, et al., Distribution of power across the hind limb joints in Labrador Retrievers and Greyhounds, Am J Vet Res 66:1563
1571, 2005. 58. Knoll Z, Kiss RM, Kocsis L, Gait adaptation in ACL deficient patients before and after anterior cruciate ligament reconstruction surgery, J Electromyogr Kinesiol 14:287
294, 2004.

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