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Mechanistic Study of Ventricular Hook Anchor For Heart Valve Replacement or
Repair
Ran Zhang, Xingguang Liu, Si Chen, Shamini Parameswaran, Zhaoming He
PII: S2590-0935(20)30007-2
DOI: https://doi.org/10.1016/j.medntd.2020.100033
Reference: MEDNTD 100033
To appear in: Medicine in Novel Technology and Devices
Received Date: 11 February 2020
Revised Date: 23 March 2020
Accepted Date: 31 March 2020
Please cite this article as: Zhang R, Liu X, Chen S, Parameswaran S, He Z, Mechanistic Study of
Ventricular Hook Anchor For Heart Valve Replacement or Repair, Medicine in Novel Technology and
Devices, https://doi.org/10.1016/j.medntd.2020.100033.
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© 2020 The Author(s). Published by Elsevier B.V.
Author Contribution to Study:
Ran Zhang: Formal analysis; Funding acquisition; Investigation; Writing original
draft
Xingguang Liu: Methodology; Data curation
Si Chen: Data curation
Shamini Parameswaran: Data interpretation and Editing
Zhaoming He: Conceptualization; Supervision
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
1
Mechanistic Study of Ventricular Hook Anchor For Heart Valve
1
Replacement or Repair
2
Ran Zhang
1
, MS, Xingguang Liu
2
, MD, Si Chen
1
, PhD, Shamini Parameswaran
3
MD, Zhaoming
3
He
4,5
, PhD
4
1 Research Center of Fluid Machinery Engineering & Technology, Jiangsu University, Zhenjiang,
5
Jiangsu Province 212013, P. R. China
6
2 Division of Cardiac Surgery of People’s Hospital of Gansu Province, Lanzhou 730000, P. R. China
7
3 Division of Cardiothoracic Surgery, Yale University, New Haven, CT 06519
8
4 Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409
9
5 Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing,
10
100083, P.R. China
11
12
Running Head: Ventricular Anchor Mechanics
13
Word count: 3621 (excluding references, tables, caption)
14
The paper is submitted to Medicine in Novel Technology and Devices as a full length research paper.
15
Corresponding author:
16
Zhaoming He
17
Department of Mechanical Engineering, Texas Tech University
18
2703 7
th
street, PO Box 41021, Lubbock, TX 79409-1021
19
Phone: 806-834-7480
20
Fax: 806-742-3540
21
Email: zhaoming.he@ttu.edu
22
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
2
Highlights
23
24
• Maximal strain depends on tooth width, thickness, radius of curvature and tip angle.
25
26
• Peak pulling force depends on the tooth width, thickness, radius of curvature.
27
28
• Axial bite depth depends on tip length at tip length >= 3 mm.
29
30
• Radial bite depth depends on radius of curvature and tip length at tip length >3mm.
31
32
33
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
3
Abstract
34
Objective: The objective of this study was to investigate the mechanics of ventricular anchor for heart
35
valve repair or replacement.
36
Methods: Thirteen anchors were designed based on six geometric parameters of the anchor teeth:
37
width, thickness, root length, radius of curvature, tip angle, and tip length. Finite element method was
38
applied to simulate the process of the anchor compressing into a sheath. The Von-Mises strain, peak
39
pulling force, and bite depth were evaluated. An experiment was performed to validate the simulation.
40
Results: The maximum Von-Mises strain was at the contact region of the anchor in a sheath where the
41
teeth were compressed against one another and were distorted. The maximum strain increased with an
42
increase in tooth width, thickness, radius of curvature and tip angle. The peak pulling force increased
43
as tooth thickness and width increased, and radius of curvature decreased. Both the radial and axial
44
bite depths increased with an increase in the tip length at the tip length >=3 mm. The radial bite depth
45
increased with an increase in the radius of curvature.
46
Conclusion: 1) the maximum strain depends primarily on the tooth width, thickness, radius of
47
curvature and tip angle; 2) the peak pulling force depends primarily on the tooth width, thickness,
48
radius of curvature; 3) the axial bite depth depends primarily on the tip length at the tip length >= 3
49
mm. The radial bite depth depends on the radius of curvature and the tip length at the tip length >3mm.
50
The study provides guidance for ventricular anchor design.
51
52
Keywords: Heart valve repair, anchor, finite element analysis, mechanics.
53
54
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
4
1. Introduction
55
Mitral and tricuspid regurgitation are caused by leaflet malcoaptation and have the potential to
56
cause irreversible structural heart issues including the dilatation of the atrium and ventricle leading to
57
eventual heart failure[1, 2]. In order to avoid these irreversible effects, surgical correction is desired,
58
specifically minimally invasive techniques that can correct mitral and tricuspid regurgitation including
59
valve repair or replacement [3-8]. However, anchoring methods for valve repair or replacement
60
devices [9-12] are challenging because the mitral or tricuspid annulus is composed of soft tissue
[13, 61
14]
which does not provide strong supporting foundation for these devices. Forces needed to support
62
these devices can be in the transverse direction and/or in the longitudinal direction. A transverse force
63
is required in direct mitral annuloplasty techniques to shrink the annulus by multiple anchors
64
distributed in the mitral annulus such as the screws in CardioBand System (Valtech Cardio LTD,
65
Israel) [15] and needles in Millipede IRIS Transcatheter Annuloplasty Ring (Millipede, Inc., Santa
66
Rosa, California ). The longitudinal anchoring force in the valve replacement is required to balance
67
transvalvular pressure force and usually much greater than the transverse force. The ventricular wall
68
or the apex are better anchoring sites to provide direct tension forces along the force action line. An
69
anchor in the left ventricular apex has been used to tether the Tendyne valve in mitral valve
70
replacement [16, 17], and An anchor in the ventricular septal wall has been used to tether the
71
LuX-Valve in tricuspid valve replacement [18]. Valve repair techniques such as the plug devices and
72
artificial chords require a longitudinal tethering force from the ventricular anchors. The plug
73
techniques include Coaptation Plate for the mitral regurgitation and FORMA device (Edwards
74
LifeSciences LLC, Irvine, CA) for tricuspid regurgitation [19-23]. A transcatheter apical anchor has
75
been used to tether the FORMA device. A transseptal anchor has been tried in mitral valve chord
76
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
5
repair
[24, 25]
. These transcatheter anchors are usually required to be deliverable and retractable.
77
There are two designs for the ventricular anchor: hook and screw (spiral) types. The screw anchor is
78
rarely used in the ventricle since it has a risk of detachment in the beating heart and may require a
79
complex anti-rotation locking mechanism. The hook-anchor is commonly used since it is not easily
80
detachable from the ventricle wall. Until now, the hook-anchor has been used to anchor FORMA
81
devices and Micra pacemakers (Medtronic PLC. Minneapolis, Minnesota)[26] in the right ventricle
82
and used in mitral valve chord repair in the left ventricle. No screw anchor has been used most likely
83
due to potential risk of detachment. A transcatheter apical anchor was tried in the Mitral Spacer
84
technique without success due to tissue dehiscence
[27]
. Therefore, a ventricular anchor design is
85
crucial to these valve repair or replacement techniques.
86
The hook-anchor is usually cut from a Nitinol tube to form straight teeth which are bent into
87
hooks. The hook-anchor needs to be compressed into a sheath tube and undergoes large deformation
88
which may cause fracture of the hook teeth in delivery. The large pulling force in compression may
89
cause buckling of a sheath tube as well. When the hook-anchor is released, it should restore its
90
original shape and bite the ventricular wall or apex firmly and provide sufficient supporting anchoring
91
force without penetrating the epicardium
[26]
. Therefore, hook-anchor mechanics warrant
92
investigation. In this paper, a parametric study of the hook-anchor was performed to provide guidance
93
for the ventricular anchor design.
94
2. Materials & Methods
95
2.1 Geometric parameter of hook-anchor
96
A Nitinol tube of 5 mm in diameter was selected to design a hook anchor which could be
97
compressed into a sheath of 6 mm in diameter. The anchor root region was 5 mm in diameter. The
98
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
6
anchor was designed with 6 teeth evenly distributed in order to bite ventricular tissue in all directions
99
even if not all the teeth bite the ventricular tissue. An anchor tooth was designed with 3 segments
100
which were straight root, arc and straight tip, and defined by 6 geometric parameters: tooth width,
101
thickness, root length, radius of curvature, tip length and angle, as shown in Fig. 1. A total of 13
102
anchors were designed and are shown in Table 1.
103
2.2 Finite element analysis
104
Eight percent of Von-Mises strain of Nitinol was allowed before plastic deformation occurred
105
[28]. Nitinol density is 6.59 g/mm
3
and Poisson ratio is 0.33. Its constitutive relation is shown in Fig.
106
2 with Table 2 defining parameter values in Fig.2 [29]. SolidWorks (Dassault Systemes S.A, Suresnes,
107
France) was used to build a three-dimensional model of the anchors and a sheath tube, as shown in
108
Fig. 3(a).
109
The effect of geometric asymmetry on tooth compressing and overlapping in a sheath was
110
simulated. Width of every other tooth was reduced by 0.06 mm. Angular displacement of the three
111
wider teeth were also shifted by 0.024 rad. The anchor model was imported into ABAQUS (Dassault
112
Systemes, Velizy, France) for finite element analysis of anchor pulling into a sheath. The anchor model
113
was discretized into hexahedral elements (C3D8R). The sheath tube was defined as a rigid material and
114
had an inner diameter 6 mm. The anchor was pulled into the sheath at a speed of 10 mm/s.
115
ABAQUS/Explicit module was used. The surface-to-surface contact between the anchor and sheath
116
was Penalty Contact method in ABAQUS. The self-contact between the teeth was Kinematic Contact
117
method in ABAQUS. No friction was considered. More than 45,000 elements were used in the
118
simulation because the grid independence verification showed that the error of the peak pulling force
119
of the anchor at 45,000 or greater elements was less than 0.92%. The axial and radial bite depths are the
120
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
7
maximum distances of the tooth tip from the sheath end in the axial direction and radial directions,
121
respectively, in anchor compression process. The maximum strain, peak pulling force, radial and axial bite
122
depths were obtained at 13 anchors which were designed based on six geometric parameters. To evaluate
123
dependence of output results on these parameters, sensitivity is defined as a maximum change of these
124
output parameters divided by average of the geometric parameter over a range. Sensitivity greater than 12%
125
means dependence of output results on the tooth design parameters.
126
2.3 Experiment
127
In order to validate simulation results, an anchor was made with its design shown in Table 1 and
128
compressed into a stainless sheath tube with inner diameter of 6.0 mm. The anchor with a cable, as
129
shown in Fig. 3(b), was pulled into the sheath by a tensile test machine at a speed of 10 mm/s. The
130
pulling force was measured by a force transducer (AIGU ZP-100 dynamometer, Aigu Detecting
131
Instrument Co., Ltd., Dongguan, Guangdong Province, P. R. China) in the anchor compression.
132
3. Results
133
Fig.4(a) shows the Von-Mises strains of the #13 anchor at eight instances of the process of
134
anchor compression into the sheath. The maximum strain was in the root of the teeth and increased as
135
the anchor entered the sheath. It reached 3.3% when the teeth were compressed against one another at
136
the time of 0.36 s. As the anchor further entered the sheath, the maximum strain was obtained at the
137
contact region of the teeth and reached 4.0% at time of 0.46 s, this occurred when the arc segment
138
finished moving into the sheath and the straight tip began to enter the sheath. The maximum strain at
139
the contact region of the teeth increased up to 5.2% at time 1.00 s, when the teeth had entered the
140
sheath completely. Fig.4(b) shows asymmetric tooth overlapping and distortion when the #13 anchor
141
was compressed inside the sheath. Fig.4(c) shows the pulling force in the simulation of # 13 and
142
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
8
experiment anchors. It can be seen that the pulling force of #13 anchor reached the maximum at time
143
0.46 seconds, when the arc segment finished moving into the sheath and the straight tip began to enter
144
sheath, and then decreased afterwards. The peak pulling force was thus independent of the tip length.
145
The peak pulling forces of #13 and experiment anchors were comparable. The other anchors
146
demonstrated similar strain and pulling force behavior in the compression process. Fig. 5 (a) shows a
147
picture of the experiment anchor compressed inside the sheath which confirmed overlapping of the
148
teeth, and Fig.5(b) shows a series of pictures of experimental anchor compression into the sheath. The
149
tooth profile of the experimental anchor was similar to that in the simulation in Fig.4(a).
150
Fig.6 shows the maximum Von-Mises strain, bite depths and peak pulling force in anchor
151
compression process in the simulation. Fig.6(a) shows the data of #1, 2, 3 anchors which differed in
152
the tooth width. The maximum strain and peak pulling force of the anchor increased with increase of
153
the tooth width. Neither the radial nor axial bite depth was sensitive to the tooth width. Fig.6(b) shows
154
the data from #1, 8, 9, and 10 anchors which differed in the root length. The maximum strain was 7.0%
155
at the root length 0 mm and decreased remarkably at the root length 1 mm. It was insensitive to the
156
root length from 1 to 3 mm. The radial bite depth demonstrated a similar trend. Neither the peak
157
pulling force nor axial bite depth was sensitive to the root length. Fig.6(c) shows the data from #1, 6,
158
and 7 anchors which differed in the tooth thickness. The maximum strain and peak pulling force
159
increased with increase of the tooth thickness. Neither the radial nor axial bite depth was sensitive to
160
the tooth thickness. Fig.6(d) shows the data from #1, 4, and 5 anchors which differed in the radius of
161
curvature. The maximum strain and peak pulling force decreased with increase of the radius of
162
curvature. The radial bite depth increased with increase in the radius of curvature. The axial bite depth
163
was insensitive to the radius of curvature. Fig.6(e) shows the data from #1, 11 and 12 anchors which
164
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
9
differed in the tip angle. The maximum strain increased with increase in the tip angle. None of the
165
peak pulling force, radial and axial bite depths was sensitive to the tip angle even when the tip angle
166
was up to 120°. Fig.6(f) shows the data from #13 anchor which differed in tip length. The maximum
167
strain was sensitive to the tip length at the tip length <3 mm and insensitive at the tip length >=3 mm.
168
The radial and axial bite depths were insensitive to the tip length at the tip length < 3 mm and
169
sensitive at the tip length >=3 mm. They increased up to 6.2 and 2.5 mm, respectively, at the tip
170
length 5 mm. The radial and axial bite depths of the experiment anchor measured from Fig.5(b) were
171
similar to those of #13 anchor, and reached 6.3 and 2.4 mm, respectively, at a tip length of 5 mm.
172
Table 3 shows a summary of dependences of the maximum strain, pulling force, radial and axial bite
173
depth.
174
4. Discussion
175
In the current study, a retrievable ventricular hook-anchor was investigated in terms of
176
mechanics in the delivery for tricuspid or mitral valve replacement/repair. Compression of the various
177
hook-anchor designs was simulated by the finite element method. All the designs have been evaluated
178
in terms of the maximum strain, peak pulling force and bite depths based on the geometric parameters
179
of the hook-anchor: tooth width, root length, thickness, radius of curvature, tip angle and length, in
180
order to provide guidance for anchor design in valve repair or replacement. Sensitivity of the
181
maximum strain, peak pulling force and bite depths to the geometric parameters was highlighted. In
182
general, the ventricular hook anchor is probably a viable design based on the clinical use of the
183
similar product
[19, 26]
. Animal experiment and clinical trial are required to confirm its long term
184
compatibility in the future.
185
4.1 Strain
186
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
10
The compression of an anchor into a sheath led to the largest deformation which occurred in the
187
contact region where tooth distortion occurred. The maximal Von-Mises strain should be less than 8%
188
which is the elastic limit of Nitinol. Increase in the tooth width induced increase in the maximum
189
strain which was caused by bending stress in the tooth cross-section which was fan-shaped. The tooth
190
width was approximately the length of outer arc. The wider the tooth, the more fan-shaped the
191
cross-section and hence, the more bending stress. Cutting of 6 hook teeth from a tube in 5 mm
192
diameter ideally leads to the maximum width of 2.7 mm in each tooth regardless of material loss.
193
Generally the wider teeth the stronger tissue biting force. However, allowable maximal strain restricts
194
the teeth wider than 2 mm based on the finding that the maximal strain exceeded 8% at the tooth
195
width > 2.0 mm. This width limit indicates that even 4-tooth design of the hook anchor does not allow
196
wider teeth. Therefore, 6-tooth design is a better choice than 4-tooth design in terms of strain limit and
197
potential biting of 2 more teeth.
198
4.2 Pulling force
199
A cable is used in anchor delivery to move the anchor into or out of a sheath. The peak pulling
200
force occurs in both deployment and withdrawal. To release the anchor, a little pushing force is
201
provided to the control cable to push the anchor out of the sheath. When the teeth partially go out of
202
the sheath, the anchor hooks start to push the anchor out of the sheath under their stored elastic energy.
203
The cable force is then changed from a pushing to pulling force to control release of the anchor. The
204
hook anchor is also fully retrievable if the anchor position is not appropriate after deployment. This
205
withdrawal process is a reverse process of the deployment. The anchor can be pulled back into the
206
sheath. In both deployment and withdrawal processes, a compressive force in the sheath caused by a
207
tensile cable pulling force might induce buckling of the sheath. The peak pulling force should be less
208
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
11
than the allowable buckling force in the sheath design.
209
The pulling force should be greater than the tissue biting force which is the force the anchor
210
provides without detachment from the tissue under a required tethering force. The tissue biting force
211
is measured by pulling the anchor out of tissue in a biting condition. This test ends up with a force at
212
two scenarios: tissue dehiscence for a hard hook anchor or tooth straightening and coming out of a
213
strong tissue without much tissue dehiscence. In either case, the tissue biting force should not be
214
greater than the peak pulling force. The soft teeth of the anchor reduce the pulling force and tethering
215
force, but has a risk of detachment from the tissue. Usually anchor is designed to be hard enough so
216
that the tissue dehiscence occurs in anchor detachment. The factors which affect hardness of the
217
anchor are the same as those influencing the peak pulling force, which include thickness, radius of
218
curvature and tooth width. They play a primary role and should be selected for appropriate design. A
219
non-retrievable anchor can be designed with a barb and has been used the ChordArt system
220
(CoreMedic, Radolfzell, Germany).
221
The required tethering force for the anchor is estimated from a typical hook model which was
222
similar to one used in the FORMA device. Diameter of the FORMA device was 1.5 cm. The
223
transvalvular pressure force was estimated to be 0.94 N if the transvalvular pressure 40 mmHg was
224
assumed in the right ventricle. This force should be 2.8N in the mitral valve repair if the transmitral
225
pressure is assumed to be 120 mmHg in the left ventricle in the Mitral Spacer technique
[27]
. The
226
anchors in the current study were based on a range of the peak pulling force to be 6-15 N which is
227
greater than the required tethering force. A smaller anchor can be designed for the mitral valve chord
228
repair if the tethering force is lower than 2.8 N.
229
4.3 Bite depth
230
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
12
Usually the anchor is designed to be hard enough so that tissue dehiscence occurs instead of
231
anchor straightening
and coming out of the tissue in anchor detachment. This tissue biting or holding
232
force depends on the interaction between the ventricular tissue and anchor, specifically on volume of
233
the tissue involved in the tissue-anchor interaction [30]. In case all the teeth bite ventricular tissue, the
234
bite depths are proportional to volume of the tissue involved in tissue-anchor interaction. The axial
235
bite depth measures the buried depth of the anchor and the radial bite depth measures buried area of
236
ventricular tissue. According to the findings, both the axial and radial bite depths could be changed by
237
choosing the appropriate tip length. However, the radial bite depth was basically unchanged when the
238
tip length was less than 3 mm. In this case, the radius of curvature could be reduced in order to
239
increase the radial bite depth. The radius of curvature of the anchor teeth always affected the radial
240
bite depth markedly. The axial bite could only be controlled by the tip length at the tip length >3 mm.
241
4.4 Limitations
242
Only anchor root tube with diameter of 5 mm was studied. Other anchor root tube sizes may
243
cause different parametric relationship. The Nitinol and sheath constitutive relationship may vary and
244
cause differences in maximum strain and peak pulling force, especially when at a temperature other
245
than 37C. Friction between the anchor and sheath may cause minor differences in results. For the
246
simulation of #13 anchor, the errors of the maximal strain, maximal stress and peak pulling force were
247
0.9%, 0.1% and 3.4% for coefficient of friction of 0.1. The interaction of the anchor teeth and
248
ventricular tissue affects the tissue dehiscence force which depends on how many teeth interact with
249
the tissue and how the teeth interact with the tissue.
250
5. Conclusion
251
The finite element analysis of ventricular hook anchors for heart valve replacement or repair has
252
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
13
been performed to elucidate the effect of 6 geometric parameters: tooth width, tooth thickness, root
253
length, radius of curvature tip length and angle on the maximum strain, axial and radial bite depths,
254
pulling force. It is concluded that 1) the maximum strain depends primarily on the tooth width,
255
thickness, radius of curvature and tip angle; 2) the peak pulling force depends primarily on the tooth
256
width, thickness, radius of curvature; 3) the axial bite depth depends primarily on the tip length at the
257
tip length >= 3 mm. The radial bite depth depends also on the radius of curvature and the tip length at
258
the tip length >3mm. The study provides guidance for ventricular hook anchor design.
259
6. Acknowledgments
260
The work was supported by Youth Project of Jiangsu Natural Science Foundation of China
261
(BK20170552).
262
7. Disclosure Statement
263
Authors do not have a conflict of interest.
264
8. Statement of Human Studies
265
No human studies were carried out by the authors for this article.
266
9. Statement of Animal Studies
267
No animal studies were carried out by the authors for this article.
268
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269
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Miller,Y Joseph, Woo,David A, D'Alessandro,Gorav, Ailawadi,Francois, Dagenais,Timothy J,
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S. Baldus, M. Huntgeburth, O. Alfieri, A. Colombo, G. La Canna, E. Agricola, M. Zuber, F. C.
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17. N. E. Moat, A. Duncan,C. Quarto, Transcatheter mitral valve implantation: Tendyne.
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Interventional Cardiology of the European Society of Cardiology, 2016. 12(Y): p. Y75-Y77.
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11. Figure caption list
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Figure 1: Anchor tooth design has 6 geometric parameters. a) anchor tooth profile parameters. b)
374
anchor 3D model.
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Figure 2: Nitinol constitutive relationship.
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Figure 3: (a) 3D model of anchor and sheath tube. b) anchor assembly in the experiment.
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Figure 4: (a) Von-Mises stress and strain of #13 anchor in 4 instants during the process of anchor
378
compression into the sheath. (b) tooth overlapping and squeezing when the #13 anchor was
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compressed into the sheath. (c) pulling force of #13 anchor in the simulation and the experiment
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anchor.
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Figure 5: (a) a picture of the experiment anchor inside the sheath which confirmed the overlapping. (b)
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a series of pictures of the experiment anchor compression into the sheath.
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Figure 6: The variation maximum Von-Mises strain and bite depth and peak pulling force of the
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anchors in the simulation. (a) data of #1, 2, 3 anchors which differed in the tooth width. (b) data of #1,
385
8, 9, and 10 anchors which differed in the root length. (c) data from #1, 6, and 7 anchors which
386
differed in the tooth thickness. (d) data from #1, 4, and 5 anchors which differed in radius of curvature.
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(e) data from #1, 11 and 12 anchors which differed in the tip angle. (f) data from #13 anchor and the
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experiment anchor which differed in the tip length.
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12. Table caption list
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392
Table 1 Parametric anchor designs
393
Table 2 Nitinol mechanical properties
394
Table 3 Summary of sensitivities of the anchor output results to 6 geometric parameters of the anchor
395
teeth
396
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He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
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Table 1
398
399
400
401
402
403
404
Anchor
number Tooth width
(mm) Radius of
curvature
(mm)
Thickness
(mm)
Root length
(mm)
Tip angle
(°)
Tip length
(mm)
1 1.50 2.5 0.20 2.0 90 5.0
2 1.00 2.5 0.20 2.0 90 5.0
3 2.00 2.5 0.20 2.0 90 5.0
4 1.50 2.0 0.20 2.0 90 5.0
5 1.50 3.0 0.20 2.0 90 5.0
6 1.50 2.5 0.15 2.0 90 5.0
7 1.50 2.5 0.30 2.0 90 5.0
8 1.50 2.5 0.20 0.0 90 5.0
9 1.50 2.5 0.20 1.0 90 5.0
10 1.50 2.5 0.20 3.0 90 5.0
11 1.50 2.5 0.20 2.0 80 5.0
12 1.50 2.5 0.20 2.0 120 5.0
13 1.25 2.5 0.25 2.0 90 5.0
Experiment
1.21 2.5 0.24 2.1 94 4.8
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He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
20
Table 2
406
407
408
409
410
Material parameters Value
Young's modulus of austenite (E
A
) 32481MPa
Young's modulus of martensite (E
M
) 12950MPa
Poisson ratio (ν) 0.33
Start stress during loading (
࣌
࢚ࡸ
ࡿ
) 360MPa
Finish stress during loading (
࣌
࢚ࡸ
ࡱ
) 410MPa
Start stress during unloading (
࣌
࢚ࢁ
ࡿ
) 232MPa
Finish stress during unloading (
࣌
࢚ࢁ
ࡱ
) 160MPa
Maximum residual strain (ε
L
) 3.4%
Start stress during loading and compression (
࣌
ࢉࡸ
ࡿ
) 480MPa
411
He, Ventricular Anchor Mechanics MS# MEDNTD-D-20-00003Rev#1
21
Table 3
412
413
414
415
416
417
418
Parameter
Sensitivity
Output
tooth
width Root
length Thickness Radius of
curvature Tip angle
Tip length
<3 ≥3
(mm) (mm) (mm) (mm) (°) (mm)
Max strain Y N Y Y Y Y N
Peak pulling force Y N Y Y N N N
Axial bite depth N N N N N N Y
Radial bite depth N N N Y N N Y
419
