A kinetostatic model able to replicate both the natural unloaded motion of the tibiotalar (or ankle) joint and the joint behavior under external loads is presented. The model is developed as the second step of a sequential procedure, which allows the definition of a kinetostatic model as a generalization of a kinematic model of the joint defined at the first step. Specifically, this kinematic model taken as the starting point of the definition procedure is a parallel spatial mechanism which replicates the ankle unloaded motion. It features two rigid bodies (representing the tibia–fibula and the talus–calcaneus complexes) interconnected by five rigid binary links, that mimic three articular contacts and two nearly isometric fibers (IFs) of the tibiocalcaneal ligament (TiCaL) and calcaneofibular ligament (CaFiL). In the kinetostatic model, the five links are considered as compliant; moreover, further elastic structures are added to represent all the main ankle passive structures of the joint. Thanks to this definition procedure, the kinetostatic model still replicates the ankle unloaded motion with the same accuracy as the kinematic model. In addition, the model can replicate the behavior of the joint when external loads are applied. Finally, the structures that guide these motions are consistent with the anatomical evidence. The parameters of the model are identified for two specimens from both subject-specific and published data. Loads are then applied to the model in order to simulate two common clinical tests. The model-predicted ankle motion shows good agreement with results from the literature.

References

References
1.
Corazza
,
F.
,
O’Connor
,
J. J.
,
Leardini
,
A.
, and
Parenti-Castelli
,
V.
,
2003
, “
Ligament Fibre Recruitment and Forces for the Anterior Drawer Test at the Human Ankle Joint
,”
J. Biomech.
,
36
(
3
), pp.
363
372
.10.1016/S0021-9290(02)00425-6
2.
Delp
,
S.
,
Anderson
,
F.
,
Arnold
,
A.
,
Loan
,
P.
,
Habib
,
A.
,
John
,
C.
,
Guendelman
,
E.
, and
Thelem
,
D.
,
2007
, “
Opensim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement
,”
IEEE Trans. Biomed. Eng.
,
54
(
11
), pp.
1940
1950
.10.1109/TBME.2007.901024
3.
Siegler
,
S.
,
Block
,
J.
, and
Schneck
,
C. D.
,
1988
, “
The Mechanical Characteristics of the Collateral Ligaments of the Human Ankle Joint
,”
Foot Ankle
,
8
(
5
), pp.
234
242
.10.1177/107110078800800502
4.
Mommersteeg
,
T. J. A.
,
Blankevoort
,
L.
,
Huiskes
,
R.
,
Kooloos
,
J. G. M.
,
Kauer
,
J. M. G.
, and
Hendriks
,
J.
,
1995
, “
The Effect of Variable Relative Insertion Orientation of Human Knee Bone-Ligament-Bone Complexes on the Tensile Stiffness
,”
J. Biomech.
,
28
(
6
), pp.
745
752
.10.1016/0021-9290(94)00121-J
5.
Guess
,
T. M.
,
Thiagarajan
,
G.
,
Kia
,
M.
, and
Mishra
,
M.
,
2010
, “
A Subject Specific Multibody Model of the Knee With Menisci
,”
Med. Eng. Phys.
,
32
(
5
), pp.
505
515
.10.1016/j.medengphy.2010.02.020
6.
Liacouras
,
P. C.
, and
Wayne
,
J. S.
,
2007
, “
Computational Modeling to Predict Mechanical Function of Joints: Application to the Lower Leg With Simulation of Two Cadaver Studies
,”
ASME J. Biomech. Eng.
,
129
(
6
), pp.
811
817
.10.1115/1.2800763
7.
Imhauser
,
C.
,
Siegler
,
S.
,
Udupa
,
J.
, and
Toy
,
J.
,
2008
, “
Subject-Specific Models of the Hindfoot Reveal a Relationship Between Morphology and Passive Mechanical Properties
,”
J. Biomech.
,
41
(
6
), pp.
1341
1349
.10.1016/j.jbiomech.2007.12.017
8.
Wei
,
F.
,
Hunley
,
S.
,
Powell
,
J.
, and
Haut
,
R.
,
2011
, “
Development and Validation of a Computational Model to Study the Effect of Foot Constraint on Ankle Injury Due to External Rotation
,”
Ann. Biomed. Eng.
,
39
(
2
), pp.
756
765
.10.1007/s10439-010-0234-9
9.
Shelburne
,
K. B.
,
Torry
,
M. R.
, and
Pandy
,
M. G.
,
2005
, “
Muscle, Ligament, and Joint-Contact Forces at the Knee During Walking
,”
Med. Sci. Sports Exercise
,
37
(
11
), pp.
1948
1956
.10.1249/01.mss.0000180404.86078.ff
10.
Franci
,
R.
,
Parenti-Castelli
,
V.
, and
Sancisi
,
N.
,
2009
, “
A Three-Step Procedure for the Modelling of Human Diarthrodial Joints
,”
Int. J. Mech. Control
,
10
(
1
), pp.
3
12
.
11.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2011
, “
A Sequentially-Defined Stiffness Model of the Knee
,”
Mech. Mach. Theory
,
46
(
12
), pp.
1920
1928
.10.1016/j.mechmachtheory.2011.07.006
12.
Forlani
,
M.
,
Baldisserri
,
B.
,
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2011
, “
On the Modelling of the Ankle Motion Under Static Loads by a Sequential Procedure: Model Definition and Preliminary Results
,” Atti del XX CONGRESSO dell’Associazione Italiana di Meccanica Teorica e Applicata, pp. 1–10.
13.
Leardini
,
A.
,
O’Connor
,
J. J.
,
Catani
,
F.
, and
Giannini
,
S.
,
1999
, “
A Geometric Model of the Human Ankle Joint
,”
J. Biomech.
,
32
(
6
), pp.
585
591
.10.1016/S0021-9290(99)00022-6
14.
Di Gregorio
,
R.
,
Parenti-Castelli
,
V.
,
O’Connor
,
J. J.
, and
Leardini
,
A.
,
2007
, “
Mathematical Models of Passive Motion at the Human Ankle Joint by Equivalent Spatial Parallel Mechanisms
,”
Med. Biol. Eng. Comput.
,
45
(
3
), pp.
305
313
.10.1007/s11517-007-0160-7
15.
Franci
,
R.
, and
Parenti-Castelli
,
V.
,
2011
, “
A One-Degree-of-Freedom Spherical Wrist for the Modelling of Passive Motion of the Human Ankle Joint
,”
Interdisciplinary Applications of Kinematics
,
Springer
,
Dordrecht, The Netherlands
, pp.
183
195
.
16.
Franci
,
R.
,
Parenti-Castelli
,
V.
,
Belevedere
,
C.
, and
Leardini
,
A.
,
2009
, “
A New One-DOF Fully Parallel Mechanism for Modelling Passive Motion at the Human Tibiotalar Joint
,”
J. Biomech.
,
42
(
10
), pp.
1403
1408
.10.1016/j.jbiomech.2009.04.024
17.
Sancisi
,
N.
,
Baldisserri
,
B.
,
Parenti-Castelli
,
V.
,
Belvedere
,
C.
, and
Leardini
,
A.
,
2014
, “
One-Degree-of-Freedom Spherical Model for the Passive Motion of the Human Ankle Joint
,”
Med. Biol. Eng. Comput.
,
52
(
4
), pp.
363
373
.10.1007/s11517-014-1137-y
18.
Leardini
,
A.
,
O’Connor
,
J. J.
,
Catani
,
F.
, and
Giannini
,
S.
,
2000
, “
The Role of the Passive Structures in the Mobility and Stability of the Human Ankle Joint: A Literature Review
,”
Foot Ankle Int.
,
21
(
7
), pp.
602
615
.
19.
Sancisi
,
N.
, and
Parenti-Castelli
,
V.
,
2010
, “
A 1-DOF Parallel Spherical Wrist for the Modelling of the Knee Passive Motion
,”
Mech. Mach. Theory
,
45
(
4
), pp.
658
665
.10.1016/j.mechmachtheory.2009.11.009
20.
Parenti-Castelli
,
V.
, and
Sancisi
,
N.
,
2013
, “
Synthesis of Spatial Mechanisms to Model Human Joints
,”
21st Century Kinematics
,
M.
McCarthy
, ed.,
Springer
,
London
, pp.
49
84
.
21.
Wu
,
G.
,
Siegler
,
S.
,
Allard
,
P.
,
Kirtley
,
C.
,
Leardini
,
A.
,
Rosenbaum
,
D.
,
Whittle
,
M.
,
DLima
,
D. D.
,
Cristofolini
,
L.
,
Witte
,
H.
,
Schmid
,
O.
, and
Stokes
,
I.
,
2002
, “
ISB Recommendation on Definitions of Joint Coordinate System of Various Joints for the Reporting of Human Joint Motion—Part I: Ankle, Hip, and Spine
,”
J. Biomech.
,
35
(
4
), pp.
543
548
.10.1016/S0021-9290(01)00222-6
22.
Pankovich
,
A. M.
, and
Shivaram
,
M. S.
,
1989
, “
Anatomical Basis of Variability in Injuries of the Medial Malleolus and the Deltoid Ligament. Part 1: Anatomical Studies
,”
Acta Orthop.
,
50
(
2
), pp.
217
223
.10.3109/17453677908989759
23.
Hefzy
,
M. S.
, and
Grood
,
E. S.
,
1983
, “
An Analytical Technique for Modeling Knee Joint Stiffness—Part II: Ligamentous Geometric Nonlinearities
,”
ASME J. Biomech. Eng.
,
105
(
2
), pp.
145
153
.10.1115/1.3138398
24.
Zavatsky
,
A. B.
, and
O’Connor
,
J. J.
,
1992
, “
A Model of Human Ligaments in the Sagittal Plane. Part 2: Fibre Recruitment Under Load
,”
Proc. Inst. Mech. Eng.
, Part H,
206
(
3
), pp.
135
145
.10.1243/PIME_PROC_1992_206_281_02
25.
Sindel
,
M.
,
Demir
,
S.
,
Yildirim
,
A.
, and
Ucar
,
Y.
,
1998
, “
Anatomy of the Lateral Ankle Ligaments
,”
Turk. J. Med. Sci.
,
28
(
1
), pp.
53
56
.
26.
Taser
,
F.
,
Shafiq
,
Q.
, and
Ebraheim
,
N. A.
,
2006
, “
Anatomy of Lateral Ankle Ligaments and Their Relationship to Bony Landmarks
,”
Surg. Radiol. Anat.
,
28
(
4
), pp.
391
397
.10.1007/s00276-006-0112-1
27.
Primal Pictures
,
2003
,
Primal 3D Interactive Series
,
Primal Pictures Ltd.
,
London
.
28.
Netter
,
F. H.
,
2010
,
Atlas of Human Anatomy
,
Saunders Elsevier
,
Philadelphia
.
29.
Siegler
,
S.
,
Udupa
,
J. K.
,
Ringleb
,
S. I.
,
Imhauser
,
C. W.
,
Hirsch
,
B. E.
,
Odhner
,
D.
,
Saha
,
P. K.
,
Okereke
,
E.
, and
Roach
,
N.
,
2005
, “
Mechanics of the Ankle and Subtalar Joints Revealed Through a 3D Quasi-Static Stress MRI Technique
,”
J. Biomech.
,
38
(
3
), pp.
567
578
.10.1016/j.jbiomech.2004.03.036
30.
Leardini
,
A.
,
O’Connor
,
J. J.
,
Catani
,
F.
, and
Giannini
,
S.
,
1999
, “
Kinematics of the Human Ankle Complex in Passive Flexion: A Single Degree of Freedom System
,”
J. Biomech.
,
32
(
2
), pp.
111
118
.10.1016/S0021-9290(98)00157-2
31.
Moissenet
,
F.
,
Chèze
,
L.
, and
Dumas
,
R.
,
2012
, “
Anatomical Kinematic Constraints: Consequences on Musculo-Tendon Forces and Joint Reactions
,”
Multibody Syst. Dyn.
,
28
(
1–2
), pp.
125
141
.10.1007/s11044-011-9286-3
32.
Jend
,
H. H.
,
Ney
,
R.
, and
Heller
,
M.
,
1985
, “
Evaluation of Tibiofibular Motion Under Load Conditions by Computed Tomography
,”
J. Orthop. Res.
,
3
(
4
), pp.
418
423
.10.1002/jor.1100030404
33.
Beumer
,
A.
,
Valstar
,
E.
,
Garling
,
E.
,
Niesing
,
R.
,
Ranstam
,
J.
,
Löfvenberg
,
R.
, and
Swierstra
,
B.
,
2003
, “
Kinematics of the Distal Tibiofibular Syndesmosis: Radiostereometry in 11 Normal Ankles
,”
Acta Orthop.
,
74
(
3
), pp.
337
343
.10.1080/00016470308540850
34.
Leardini
,
A.
,
Stagni
,
R.
, and
O’Connor
,
J. J.
,
2001
, “
Mobility of the Subtalar Joint in the Intact Ankle Complex
,”
J. Biomech.
,
34
(
6
), pp.
805
809
.10.1016/S0021-9290(01)00031-8
35.
Beimers
,
L.
,
Maria Tuijthof
,
G. J.
,
Blankevoort
,
L.
,
Jonges
,
R.
,
Maas
,
M.
, and
van Dijk
,
C. N.
,
2008
, “
In-Vivo Range of Motion of the Subtalar Joint Using Computed Tomography
,”
J. Biomech.
,
41
(
7
), pp.
1390
1397
.10.1016/j.jbiomech.2008.02.020
36.
Bahr
,
R.
,
Pena
,
F.
,
Shine
,
J.
,
Lew
,
W. D.
,
Lindquist
,
C.
,
Tyrdal
,
S.
, and
Engebretsen
,
L.
,
1997
, “
Mechanics of the Anterior Drawer and Talar Tilt Tests: A Cadaveric Study of Lateral Ligament Injuries of the Ankle
,”
Acta Orthop.
,
68
(
5
), pp.
435
441
.10.3109/17453679708996258
37.
Lapointe
,
S. J.
,
Siegler
,
S.
,
Hillstrom
,
H.
,
Nobilini
,
R. R.
,
Mlodzienski
,
A.
, and
Techner
,
L.
,
1997
, “
Changes in the Flexibility Characteristics of the Ankle Complex Due to Damage to the Lateral Collateral Ligaments: An in vitro and in vivo Study
,”
J. Orthop. Res.
,
15
(
3
), pp.
331
341
.10.1002/jor.1100150304
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