Reality-Based Real-Time Cell Indentation Simulator

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Hamid Ladjal, Jean-Luc Hanus, Anand Pillarisetti, Carol Keefer, Antoine Ferreira, et al.. Reality- Based Real-Time Cell Indentation Simulator. IEEE/ASME Transactions on Mechatronics, Institute of Electrical and Electronics Engineers, 2012, 17 (2), pp.239 - 250. �10.1109/TMECH.2010.2091010�.

�hal-00647908�

IEEE Proof

ical and numerical modeling to assure accurate cell deformation

8

and force calculations. Advances in alternative finite-element for-

9

mulation, such as the mass–tensor approach, have reached a state,

10

where they are applicable to model soft-cell deformation in real

11

time. The geometrical characteristics and the mechanical proper-

12

ties of different cells are determined with atomic force microscopy

13

(AFM) indentation. A real-time, haptics-enabled simulator for cell

14

centered indentation has been developed, which utilizes the AFM

15

data (mechanical and geometrical properties of embryonic stem

16

cells) to accurately replicate the indentation task and predict the

17

cell deformation during indentation in real time. This tool can be

18

used as a mechanical marker to characterize the biological state

19

of the cell. The operator is able to feel the change in the stiff-

20

ness during cell deformation between fixed and live cells in real

21

time. A comparative study with finite-element simulations using a

22

commercial software and the experimental data demonstrate the

23

effectiveness of the proposed physically based model.

24

Index Terms—Atomic force microscope (AFM), finite-element

25

modeling (FEM), haptics, modeling, real-time interaction, stem

26

cell.

27

I. I

NTRODUCTION 28

M ECHANICAL manipulation and characterization of bi-

29

ological cells is currently one of the most promising

30

research areas in the field of biorobotics applied to cellular level

31

interactions. The mechanical properties, such as elasticity, mem-

32

brane tension, cell shape, and adhesion strength, may play an

33

Manuscript received March 31, 2010; revised July 7, 2010 and October 5, 2010; accepted October 8, 2010. Recommended by Technical Editor Y. Sun. A portion of this paper was presented at the IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, October 18–22, 2010. This work was supported by the National Science Foundation under Grant CMMI 0826158, in part by STMD-Maryland Technology Development Corporation under Grant 08071517, and in part by the Centre de Recherche en Biologie de Baugy, France.

Q1 H. Ladjal, J.-L. Hanus, and A. Ferreira are with the Institut PRISME, Ecole Nationale Sup´erieure d’Ing´enieurs de Bourges, 18000 Bourges, France (e-mail: hamid.ladjal@ensi-bourges.fr; jean-luc.hanus@ensi-bourges.fr;

antoine.ferreira@ensi-bourges.fr).

A. Pillarisetti is with the Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104 USA (e-mail :anandpi@seas.upenn.edu.)

C. Keefer is with the Department of Animal and Avian Sciences, University of Maryland, College Park, MD 20742 USA (e-mail: ckeefer@umd.edu).

J. P. Desai is with the Robotics, Automation, and Medical Systems (RAMS) Laboratory, Maryland Robotics Center, Institute for Systems Research, Univer- sity of Maryland, College Park, MD 20742 USA (e-mail: jaydev@umd.edu).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2010.2091010

Fig. 1. Stem cells are valuable resources for toxicology, developmental biol- ogy, and regenerative medicine research.

important role in cell development and differentiation [1]–[3].

34

In contrast to adult stem cells, embryonic stem cells differentiate

35

into every cell type in the body, and thus, have a huge therapeutic

³⁶

potential. Stem-cell-based systems offer a very promising and

³⁷

innovative solution for obtaining large number of cells for early

³⁸

efficacy and toxicity screening. Stem cell technology provides

³⁹

a new tool for drug development and a better insight to under-

⁴⁰

stand mammalian gene function (see Fig. 1). The mechanical

41

properties of biological cells have been studied with different

42

techniques [4], the most popular being optical tweezers [5],

43

magnetic beads [6], and micropipette aspiration [7]. Different

44

microrobotic systems with various end effectors have been pro-

45

posed [33], [34]. However, these methods cannot compete with

46

the precision that can be obtained with the atomic force mi-

47

croscopy (AFM) method [8], [32]. AFMs have been widely

48

used in the study of micro- and nanostructures including living

49

cells. Modern AFM techniques allow solving several problems

⁵⁰

of cell biomechanics by simultaneous evaluation of the local

⁵¹

mechanical properties and the topography of living cells, at a

⁵²

high spatial resolution and force sensitivity [9]. In these exper-

⁵³

iments, an AFM cantilever serves as a microindenter to probe

⁵⁴

the cell, and further analysis of force-indentation data yields

⁵⁵

the local Young’s modulus. In addition, the AFM indentation

56

technique can be used to characterize the viscoelastic behavior

57

of the cell cytoskeleton [10], including viscosity [11], loss and

58

storage moduli [12], and stress relaxation times. Mechanical

59

phenotyping prove actually to be a valuable tool in the develop-

60

ment of improved methods of targeted cellular differentiation of

61

embryonic, induced pluripotent (iPS), and adult stem cells for

62

therapeutic and diagnostic purposes [30], [31]. In this study, we

63

propose to characterize the mechanical behavior of an individual

64

mouse embryonic stem cells (mESC) in undifferentiated state

⁶⁵

1083-4435/$26.00 © 2010 IEEE

IEEE Proof

cytoskeleton-disrupted experiments. Therefore, the user per-

75

forms extremely challenging manipulations requiring advanced

76

manual skills. Modeling the physics of the interaction between

77

tip and cell is necessary to realize complicated indentation tasks

78

like cancer cell probing [14].

79

We developed finite-element models (FEMs) that include the

80

topological information of adherent stem cells (shape and di-

81

mensions), AFM tips (conical and spherical), and biological

82

structure (cell models with cytoplasm layers, cytoskeletons, and

83

nucleus) [15]. To validate the viscoelastic and nonlinear dynam-

84

ics of the cell in real time using finite-element procedures, we

85

report herein the mechanical characterization of single mESC

86

indentation-relaxation for different colonies of fixed and live

87

undifferentiated mESCs (termed, undiff mESC). The proposed

88

indentation tests use microsphere-modified AFM probes in or-

89

der to estimate the global elastic modulus of the cell to reflect

90

the true global response of a mESC [14], [15]. This paper is a

91

subsequent contribution to [27], where various analytical mod-

92

els are tested and compared to estimate the mechanical prop-

93

erties of the biological cells. Based on the proposed physical

94

model, we have developed a computer-based training system

95

using force feedback to simulate cell indentation procedures in

96

virtual environments (VEs) for biologist training. The paper con-

97

sists of five sections. In Section II, we present the biomechanical

98

finite-element approach dedicated to real-time indentation. In

99

Section III, we present the methodology of the VE system for

100

cell indentation. In Section IV, we present the experimental

101

setup using the force microscopy. In Section V, we make a

102

comparative study between the physics-based model and ex-

103

perimental data. In Section VI, we present our real-time cell

104

indentation simulator using a spherical tip. Finally, we give

105

some concluding remarks and the directions for future work.

106

II. P

HYSICS

-B

ASED

D

EFORMABLE

M

ODELS FOR

C

ELL 107

N

ANOINDENTATION

S

IMULATION 108

In this section, we present further developments to the linear

109

elastic mass–tensor model introduced by [16], [17] and extended

110

by Schwartz et al. [18]. In our paper, the cell is modeled by a

111

volume object discretized into a conformal tetrahedral mesh as

112

defined by finite-element theory.

113

Using classical notations, inside each tetrahedron T

^k

, the

114

displacement field, defined by a linear interpolation [N

^k

] of the

115

nodal displacement vector {u

^k

} of the four vertices of tetrahe-

116

dron, is written as follows:

117

U(x)

^k

=

N

^k

(x) u

^k

. (1)

follows:

¹²⁵

f

^k

=

K

^k

u

^k

. (3)

This stiffness matrix is composed of a plurality of elementary

126

submatrices, each connecting the elementary force acting on the

127

node i to the displacement of the node j

128

K

^k_ij

= 1

36 V

^k

λ {m

i

} {m

j

}

^T

+ μ {m

j

} {m

i

}

^T

+ μ {m

i

}

^T

{m

j

} [I]

(4) where { m } are unit outward-pointing normals to triangular

¹²⁹

faces and V

^k

is the volume of the tetrahedron T

^k

.

130

Taking into account the contribution of all adjacent tetrahedra,

131

the global internal force acting on a node l can be expressed as

132

follows:

133

F

^l_int

=

k∈Vl

⎛

⎝

⁴

j= 1

K

^k_ij

{u

j

}

⎞

⎠ (5)

where V

l

is the neighborhood of vertex l (i.e., the tetrahedra

134

containing node l).

135

The tensors [K

^l_ij

] depending on the remaining geometry and

136

Lame’s coefficients are constant. They can be precomputed in an

137

offline phase. This is the essential advantage of the mass–tensor

138

approach, which makes it useful for real-time application.

139

A. Cell Modeling Using FEM

140

In our paper, the mESC is meshed with 3-D first-order tetra-

¹⁴¹

hedral elements, as shown in Fig. 2. The geometrical character-

142

istics of the cells were obtained from experimental data using

143

the AFM system. This includes shape, diameter, and height of

144

the cells. The mesh that has been used for the following simu-

145

lations is composed of 835 vertices and 2456 tetrahedra, where

146

all vertices are free to move except the ones in contact with the

147

petri dish, which are fixed.

148

B. Dynamic Model

149

The equation of motion of a vertex l of the cell mesh can be

¹⁵⁰

written as follows:

¹⁵¹

M

^l

{ u ¨

_l

} + γ

^l

{ u ˙

_l

} +

k∈Vl

⎛

⎝

⁴

j= 1

K

^k_ij

{u

j

}

⎞

⎠ = F

^l_ext

(6) where M

^l

and γ

^l

are, respectively, the mass and damping coef-

152

ficients of each vertex.

¹⁵³

IEEE Proof

Fig. 2. Representation of the 3-D mESC mesh using P1 tetrahedral finite elements.

To solve the dynamic system, we tested different integration

154

schemes (implicit and explicit) taking into account the tradeoff

155

between real-time simulation and haptic stability requirements.

156

We choose the explicit centered finite-difference scheme defined

157

by

158

⎧

⎨

⎩

u(t + h) = u(t) + ˙ u(t) h +

¹₂

u(t) ¨ h

²

+ O(h

³

)

˙

u(t + h) = ˙ u(t) +

¹₂

u(t) ¨ h +

¹₂

u(t ¨ + h) h + O(h

³

) (7) where h is the temporal integration step size chosen to satisfy

159

the Courant–Friedrich–Lewy condition.

160

The discrete equation of motion of a vertex l reads

161

M

^l

+ h

2 γ

^l

{ u ¨

_l

}

(t+h)

= F

^l_ext

(t+h)

− γ

^l

{ u ˙

_l

}

(t)

+ h 2 { u ¨

_l

}

(t)

−

k∈Vl

⎛

⎝

⁴

j= 1

K

^k_ij

{u

j

}

(t)

+ h{ u ˙

_j

}

(t)

+ h

²

2 { u ¨

_j

}

(t)

⎞ ⎠

(8) from which we can compute the new vertices for accelerations,

162

velocities, and positions.

163

III. VE S

YSTEM FOR

C

ELL

I

NDENTATION 164

Fig. 3 shows the architecture of the real-time virtual-reality-

165

based cell indentation simulator. This includes the computer

166

generated models of stem cells, the AFM nanoindentor, the col-

167

lision detection algorithm, physics-based models of deformable

168

mESC, and the haptic interaction controller. The operator will

169

be able to interact with the 3-D model of the cell using his

170

sense of vision as well as actively manipulate using his sense

171

of touch. Usually, real-time graphics translates to an update

172

rate of 25 Hz, stable haptic interaction in VE’s requires much

173

higher update rate of around 1 kHz. As soft biological tissues

174

exhibit complex viscoelastic and nonlinear properties, the real-

175

time interaction imposes severe restrictions on the FEM model.

176

Fig. 3. Computational architecture for simulating force-reflecting deformable cell indentation in a VE. The figure shows the two simulation phases used for the real-time indentation of the cell: 1)offlineprecalculations of stiffness matrices and 2) simulation of visual and haptic interaction.

A significant difficulty of using the finite-element technique for

177

real-time simulation is that it is computationally costly. These

178

mesh-based schemes also require an expensive numerical in-

179

tegration operation for the computation of the system stiffness

180

matrices. For this reason, we adopted a computational architec-

¹⁸¹

ture with two simulation stages: 1) an offline computation of

¹⁸²

stiffness matrices for each triangular element and 2) visual and

¹⁸³

haptic interaction for real-time indentation simulation.

¹⁸⁴

A. Offline Computation

185

The proposed computational methodology contains an offline

186

precalculation step. The most costly and time-consuming opera-

187

tions are realized during this step. The database contains various

188

developed models of the different stem cells geometry (bone

¹⁸⁹

marrow, pancreatic, heart muscle, nerve cells, etc.). Using AFM

¹⁹⁰

image analysis (ImagePro software from AFM Asylum), we de-

¹⁹¹

rived different geometric stem cell models based on a commer-

¹⁹²

cial computer-aided design (CAD) package (MARC-ADAMS).

¹⁹³

The meshing of the 3-D internal structure of the mESC is then

¹⁹⁴

carried out through a dedicated 3-D meshing software (GID

195

software) modeled in exact dimensions. Although they were

196

displayed as 3-D texture-mapped objects to the user, they were

197

modeled as connected line segments to reduce the number of

198

collision computations during real-time interactions.

199

The adherent cell was approximated as an assembly of dis-

200

crete tetrahedral elements interconnected to each other through

201

a fixed number of nodes (see Fig. 2). The displacements of

202

these nodal points for applied external indentation forces were

203

the basic unknowns of our FEM analysis. The coordinates

²⁰⁴

IEEE Proof

Fig. 4. Scheme illustrating the multiple collision detection algorithm using a simple sphere-points intersection problem: the distance between the center of the spherical tip and the nodes of the cell surface is calculated in real time.

of vertices, the tetrahedron indexing, and the connectivity of

205

vertices were derived from the geometric model. Then, the

206

mechanical (Young’s modulus and stiffness) and geometrical

207

(height and shape) properties of the cell structure are determined

208

through AFM indentation experiments. Finally, these properties

209

are passed to the FEM algorithm for calculating the physically

210

based behavior of biological soft tissues. The offline calcula-

211

tion of all tensors K

_ij

allows precalculation stiffness values for

212

preselected cells such as, for example, live and fixed cells.

213

B. Real-Time Indentation

214

Since haptics and graphics have different update frequencies,

215

we implemented separate threads to update the loops. During

216

the indentation task, the contact between the tip and the cell

217

must occur at a special set of points (nodal points).

218

1) Collision Detection: An important part of biological can-

219

tilever tip-soft cell modeling is the fast collision detection al-

220

gorithm. The collision detection is the first step to carry out

221

realistic interactions. However, locating the contact primitive

222

(e.g., facets) between two objects may be computationally ex-

223

pensive, especially if the objects are composed of a large number

224

of polygons. In general, to determine a contact between two vir-

225

tual objects, we compute the distance between them. If this

226

distance is negative, then the objects are in contact. We may

227

continue by determining the set of geometric objects or entities

228

that collide. The cantilever tip in VE can be modeled as a com-

229

plex 3-D object, composed of numerous surfaces, edges, and

230

vertices, but this constitutes a challenging task. For the purpose

231

of detecting collisions, we used a point-based representation of

232

the cantilever tip as a simple spherical object and employed a

233

simple sphere-points intersection algorithm with local search

234

technique. It calculates the distance between the center of the

235

spherical tip and the nodes of the cell surface (see Fig. 4).

236

2) Penalty-Based Models: In an interaction model, a colli-

237

sion between two objects may generate local and global defor-

238

mations of the colliding objects, new internal forces, changes

239

in the velocities of the involved objects, and topology modifica-

240

tions, such as punction or cutting. Physical simulations suppose

241

that these events are related to the mechanical properties of the

242

objects. In our simulations, we used the penalty-based models.

243

Fig. 5. Main flowchart for multi collision detection:Mrepresents the position of the center of the spherical tip andRits radius,irepresents the current external cell surface node,di,{F_{re p}ⁱ }and{ni}represent, respectively, the computed distance between the center of the tip and the current node, the repulsive force, and the outward-pointing contact normal at nodei.

These models consider the reactive force that first reduces the

²⁴⁴

relative speed of the two objects, and finally, repulses them from

²⁴⁵

each other, as proportional to the deformation. Thus, the reac-

²⁴⁶

tive force is a function of the local interpenetration depth δ. The

247

normal repulsive force F

_rep

can be written as follows:

²⁴⁸

{F

rep

} = λ δ {n} (9) where λ is the penalty of the interpenetration and {n} is the

249

outward-pointing normal.

²⁵⁰

These contact forces are evaluated at each time step t (see

²⁵¹

Fig. 5). They represent the new updated external forces acting

²⁵²

upon our stem cell.

²⁵³

3) Virtual Coupling for Stability of the Haptic Rendering:

254

The internal operating loop of the haptic interface requires an

²⁵⁵

update frequency around 1 kHz. However, the FEM update fre-

256

quency is in the range of 25–30 Hz. This frequency difference

257

threatens the coherence between both systems leading to insta-

258

bilities of the user haptic rendering. We adopted the solution to

259

use a virtual coupling model defined in [24].

260

This approach introduces a virtual passive link between the

261

simulation model and the haptic interface in order to ensure

262

the stability and the performance of the system [see Fig. 6(a)].

263

When we combine the impedance display implementation with

264

an appropriate virtual coupling network, we get the admittance

²⁶⁵

IEEE Proof

Fig. 6. Stability conditions using the virtual coupling model. (a) Model of virtual coupling. (b) Impedance display virtual coupling.

matrix for the combined interface. The linear two-port is said

266

to be absolutely stable if there exists no set of passive ter-

267

minating one-port impedances for which the system is unsta-

268

ble. Llewellyn’s stability criteria [25] provides both necessary

269

and sufficient conditions for absolute stability of linear two-

270

ports. We get the conditions for absolute stability of the haptic

271

interface

272

Re(Z

di

(z)) ≥ 0, 1

Z

_cvi

(z) ≥ 0 (10)

273

cos(

ZOH(z)) + 2Re(Z

di

(z))Re(1/Z

cvi

(z))

| ZOH(z) | ≥ 1 (11) where Z

cvi

(z) is the virtual coupling impedance (k

c

, b

c

),

274

ZOH(z) is a zero-order holder, and Z

_di

(z) is the PHANToM

275

impedance. The inequality (11) can be rewritten to get an ex-

276

plicit expression of absolute stability of the haptic interface

277

Re 1

Z

cvi

(z)

≥ 1 − cos(

ZOH(z))

2Re(Z

di

(z)) | ZOH(z) | . (12) For the virtual coupling, the impedance display induces a limit

278

on the maximum impedance which can be rendered. We use (12)

279

to find the virtual coupling, which makes the haptic interface

280

absolutely stable. Using the design bound of the best performing,

281

absolutely stabilizing virtual coupling. These parameters are

282

found as b

c

= 0.008 N/(mm/s) and k

c

= 2.3 N/mm (plotted on

283

Fig. 6(a) as a thin red line). The left side of (12) with the resulting

284

values is plotted on Fig. 6(b) as a bold blue line.

285

Fig. 7. Experimental setup based on AFM system for mESC indentation studies. The nanoindentor is constituted by a spherical probe (5μm diameter) attached to a silicon nitride cantilever from Novascan Technologies.

IV. E

XPERIMENTAL

S

ETUP 286

A. Description

287

The experimental tests of the cell indentations were per-

²⁸⁸

formed using an AFM (Model: MFP-3D-BIO, Asylum Re-

²⁸⁹

search, Santa Barbara, CA). The AFM is integrated with a top

²⁹⁰

view module and mounted on an active vibration isolation ta-

²⁹¹

ble manufactured by Herzan (Laguna Hills, CA), as shown in

292

Fig. 7. The top view module enables viewing of cells and easy

293

alignment of the laser beam on the AFM cantilever. The XY

294

stage (manual) allows the user to position the cell beneath the

295

cantilever tip of the AFM. The entire AFM setup is enclosed in

296

an acoustic isolation chamber to prevent acoustic noise from in-

297

terfering with the AFM measurements. The x- and y-axis ranges

298

of the scan head are 90 μm. The z-axis scan range is 40 μm.

299

The AFM system is used to obtain force and cell deformation

300

data from biological samples.

301

The cantilever is moved by the piezoelectric scanner in z-

³⁰²

direction toward the cell. The deflection of the cantilever is

³⁰³

detected by a photodiode when the tip comes in contact with the

³⁰⁴

cell. When the tip of the cantilever is in contact with the cell, the

³⁰⁵

initial cantilever deflection (d

₀

), and initial cantilever movement

³⁰⁶

in (z) direction (z

₀

) are stored. As the cantilever moves further

307

in z-direction and deforms the cell, the final cantilever deflection

308

(d

₁

) and the cantilever movement (z

₁

) are obtained [21].

309

The stiffness depends not only on the Young’s modulus but

310

also on the geometry of the tip-surface contact. Therefore, the

311

geometry and spring constant of the cantilever are calibrated in

312

the same way for live and fixed cells. In the following exper-

313

iments, we employed two types of cantilevers attached with a

314

spherical probe (5 μm in diameter).

315

1) Silicon nitride cantilever with a spring constant of 0.06

³¹⁶

N/m (Novascan Technologies, Inc., Ames, IA) for live

³¹⁷

cells.

³¹⁸

2) Silicon cantilever with a spring constant of 1.75 N/m (No-

³¹⁹

vascan Technologies, Inc.) for fixed cells.

³²⁰

IEEE Proof

Fig. 8. Thermal graph measurement of a spherical tip cantilever (Kc= 1.29 N/m) used for fixed cells indentation. The left corner inset represents the contact slope from a force curve to determine the sensitivity of the can- tilever and (deflection volt=98.01 nm/v) and the right corner inset represents the zoom-in view of the resonant frequency plot (F= 46.043kHz).

B. AFM Calibration

321

Before any experiment is done, it is necessary to perform

322

a calibration of the cantilever to determine its resonant fre-

323

quency. The resonant frequency measurement enables the user

324

to determine if it lies within the specified range provided by

325

the manufacturer in order to detect probe defects. The determi-

326

nation of spring constant K

n

by the thermal method involves

327

both measurements : 1) sensitivity in nanometer per volt and 2)

328

first-resonant frequency of the cantilever.

329

1) Determine the contact slope of the indentation curve on a

330

hard surface to determine the sensitivity of the cantilever

331

(see left corner inset of Fig. 8).

332

2) Measure the thermal power spectral density (PSD) to de-

333

termine the resonant frequency of the cantilever and to

334

confirm that the cantilever and light source are aligned.

335

This confirms that the system is functioning properly. The

336

results are plotted as the deflection amplitude data using

337

Fourier transform in meter per square root hertz versus the

338

frequency in hertz (see right corner inset of Fig. 8). The

339

spring constant of the cantilever was determined experi-

340

mentally for each tip used in our studies using the IGOR

341

software interface supplied by Asylum Research.

342

Finally, the exact K

c

values after the calibration procedure

343

are K

_c

= 0.08745 N/m for live cells and K

_c

= 1.29 N/m for

344

fixed cells.

345

V.

M

ESC C

HARACTERIZATION 346

A. Cell Culture Preparation

347

It is recommended to use specially coated dishes or slides

348

to facilitate adhesion. Such petri dishes or slides are available

349

commercially. Cells should be attached to some rigid substrate,

350

usually either a slide or the bottom of a petri dish. In our study,

351

the mESC R1 (SCRC-1011, American Type Culture Collection

352

(ATCC), Manassas, VA) were grown on 0.1% gelatin-coated

353

plates in the absence of feeder cells. The ES medium consisted

354

of 1000 U/mL leukemia inhibitory factor (LIF, ESGRO, Chemi-

355

con, Temecula, CA), 15% fetal bovine serum (FBS) (Invitro-

356

Fig. 9. How to determine the height of the stem cell through indentation curves? (a) mESC geometric parameters. (b) Force (F) versus piezo movement of the cantilever (Z) on a hard surface. The red and blue lines represent the loading and unloading curve, respectively. (c) Force (F) versus piezo movement of the cantilever (Z) on an mESC surface.

gen), and basic medium that included Knockout Dulbecco’s

³⁵⁷

modified Eagle’s medium (Invitrogen), 2 mM

L

-glutamine, 1x

³⁵⁸

nonessential amino acids, and 0.1 mM mercaptoethanol. Dif-

³⁵⁹

ferentiation was induced by removal of LIF from the medium.

³⁶⁰

Prior to the experiments, cells were dispersed using trypsin to

³⁶¹

obtain single cells and were plated on 60 mm tissue culture petri

362

dish. Fixed mESC were obtained by treating live cells with with

363

4% formaldehyde for 10 min, washed and stored in phosphate

364

buffered saline.

365

B. Geometry of the Cell and Cantilever Interaction

366

With the Surface

367

The cells were determined to be 10 and 15 μm in diameter

368

using the cantilever tip to measure the interaction force between

369

the cell and the tip. The geometric modeling of the cell re-

370

quires the determination of the height, adhesion surface, and

371

cell’s contour [see Fig. 9(a)]. The mESC height was calculated

372

from the force–displacement curve obtained on hard and mESC

373

surfaces. First, the initial height h

0

is measured by bringing

³⁷⁴

IEEE Proof

Fig. 10. How to determine the diameter of the stem cell through image analysis (ImagePro software from Asylum)?

Fig. 11. Hertzian contact with a spherical tip:Fis the loading force, andδ andaare the indentation and contact radius, respectively.

the AFM tip in contact with the hard surface near mESC [see

375

Fig. 9(b)], and then, the second height h

₁

by bringing the AFM

376

tip on mESC surface [see Fig. 9(c)]. The mESC height is the

377

difference h = h

₀

− h

₁

. Second, to determine the mESC shape,

378

AFM imaging experiments are carried out in order to deter-

379

mine the mESC’s contour and diameter using image processing

380

techniques [19]. From Fig. 10, we selected mESC shapes with

381

circular adhesion surfaces. As illustration, the left corner inset

382

shows a typical circular mESC, where D

1

and D

2

stands for the

383

horizontal cells diameters (D

1

D

2

close to 12 μm).

Q2 384

C. Mechanical Characterization of mESC Using Spherical Tip

385

To estimate the mechanical properties of biological cells using

386

the AFM, various analytical models can be used to identify the

387

Young’s modulus of mESC in live as well as fixed cells.

388

1) Hertz Contact: The Hertz contact model has been used

389

extensively by the AFM community to quantify the mechanical

390

property of biological samples using AFM [8], [9]. The Hertz

391

contact model describes the simple case of elastic deformation

392

of two perfectly homogeneous smooth surfaces touching under

393

load (see Fig. 11). The forces measured are dominated by the

394

elastic properties. In our work, the geometry of the tip used for

395

all experiments is spherical. The mechanical interaction between

396

the spherical tip and mESC can be described by the Hertz contact

397

model of two elastic bodies [20]. The model assumes that:

398

1) the material properties of the tip and the cell are isotropic

399

and homogeneous;

400

Fig. 12. Schematic of the microcapsule indented by a sphere with a loading forceF.

2) the normal contact of the two bodies is adhesionless and

401

frictionless;

402

3) the contact geometry is assumed to be axisymmetric,

403

smooth, and continuous.

404

The relationship between the indentation δ, and the loading

405

force F is given by

⁴⁰⁶

F = 4

3 E

^∗

R

¹²

δ

³²

(13) where E

^∗

and R are the combined modulus and the relative

⁴⁰⁷

curvature of the tip and the cell, respectively,

⁴⁰⁸

1

E

^∗

= 1 − ν

₁²

E

₁

+ 1 − ν

₂²

E

₂

(14)

1 R = 1

R

1

+ 1 R

2

(15) where (E

1

, ν

1

, R

1

) and (E

2

, ν

2

, R

2

) represents the elastic mod-

⁴⁰⁹

ulus, Poisson’s ratio, and the radius of the cell and spherical

⁴¹⁰

indenter, respectively. The elastic modulus of the silicon nitride

⁴¹¹

cantilever and silicon cantilever were 222.22 and 168.17 GPa

⁴¹²

used for the live and fixed cells, respectively. The elastic modu-

⁴¹³

lus of the cells is in range of kilopascals [11]. Hence, our assump-

414

tion that the tip used for probing is infinitely stiff (E

₂

E

₁

)

415

compared to the cell and Hertz contact model is valid. Thus,

416

(13) can be rewritten as follows:

417

F = 4E

₁

3(1 − ν

₁²

) R

¹²

δ

³²

(16) where E

1

and ν

1

represent the elastic modulus and Poisson’s

418

ratio of the cell assuming ν

1

= 0.5.

419

2) Capsule Contact: The second model considers the bio-

⁴²⁰

logical cell to be composed of a cell membrane and cytoplasm

⁴²¹

(see Fig. 12). It is the capsule model. The model assumes that

⁴²²

the cell membrane is a thin film and that the inner cytoplasm

⁴²³

provides a uniform hydrostatic pressure on the membrane [22].

⁴²⁴

The model assumes the following.

⁴²⁵

1) The cell membrane is linearly elastic.

426

2) The deformation of the cell membrane is caused by

427

stretching and bending of the cell membrane.

428

3) The cell is free of initial membrane stress or residual stress.

429

4) The cell volume is constant.

430

IEEE Proof

Fig. 13. Load–unload versus time for fixed undiff.

The force (F ) and relative deformation (ε) relationship is

431

given by [22]

432

F = 2πhR

0

[1 + R

0

/(2R

s

)]

²

E

(1 − ν)(1 + R

₀

/R

_s

)

⁴

ε

³

+ π 2 √

2 Eh

²

√

ε (17) where E, ν, and h represent the elastic modulus, Poisson’s ra-

433

tion, and the thickness of the capsule membrane, respectively.

434

R

0

and R

s

are the radius of the capsule and the spherical in-

435

denter, respectively. ε is the relative deformation of the capsule

436

related to the indentation by ε = δ/2R

0

. The first and the second

437

term in (17) represent stretching and bending of the cell mem-

438

brane, respectively, however, in our experiments, the bending

439

deformation term can be neglected for ε > 0.15 [22].

440

D. Comparison Between Experimental Data

441

and Analytical Models

442

We evaluated and compared the different analytical mod-

443

els to determine whether they appropriately predict the force-

444

indentation relationship of mESC. Figs. 13 and 16 present the

445

force (loading and unloading) versus time of fixed and live un-

446

diff mESC. From all these experiments, we observed adhesion

447

force in few of the cases. For live mESC probed by a spherical

448

tip, the adhesion force existed only for one sample. However,

449

their amplitudes were negligible (less than 0.05 times the maxi-

450

mum indentation) compared to the maximum indentation forces

451

(more than 0.1 times the maximum indentation) observed by

452

other researchers [28], [29]. In our experiments, we observed

453

that the adhesion force exists for only one of the live undiff and

454

does not exist for the fixed cells. This could be due to the wear

455

of the spherical tip [26]. Since we did not observe any adhesion

456

forces, we have not used the JKR or DMT models.

Q3 457

Figs. 14 and 15 show the experimental force versus cell inden-

458

tation curves for live and fixed undiff mESC and the simulated

459

ones using the capsule and the Hertz models, respectively, for

460

small and rather larger indentation range. Based on the ex-

Q4 461

perimental investigation, a least-square fit on the dataset (for

462

the whole cells) and the corresponding r

²

values are calcu-

463

lated. These results show that the capsule model is inappropriate

464

for describing mESC indentation. This conclusion is confirmed

465

by the calculation of r

²

values performed on each mESC (see

466

Table I). Finally, from our experiments, we infer that Hertz

467

model appropriately describes the mechanical behavior of the

468

Fig. 14. Fixed undiff (small deformation).

Fig. 15. Live undiff mESC .

TABLE I

LEAST-SQUAREVALUE(COEFFICIENTCORRELATION)r² OBTAINED BYHERTZ FIT ANDCAPSULEFIT FORTENSAMPLES OFLIVE ANDFIXEDUNDIF MESC

Fig. 16. Load–unload versus time for live undiff.

live and fixed undiff mESC (see Figs. 16– 18). Equation (16)

Q5469

was used to determine the global elastic modulus of the mESC.

470

The average elastic modulus were 17.87 and 0.217 kPa for the

471

fixed and live undiff, respectively, (see Fig. 19). The standard

472

deviations for the fixed and live undiff cells were 3.37 and

473

0.05 kPa.

⁴⁷⁴

IEEE Proof

Fig. 17. Live undiff (small deformation).

Fig. 18. Fixed undiff mESC.

Fig. 19. Elastic modulus for live and fixed undifferentiated mESC calculated from the Hertz contact model for a small deformation (range 0.5μm) with error bar.

It should be noticed that alterations in the mechanical proper-

475

ties of cells directly reflect changes in their cellular composition,

476

internal structure (cytoskeleton), and external interactions (cell–

477

cell and/or cell–surface) that occur during differentiation, aging,

478

and other changes in physiological status that are not accounted

479

in the cell indentation model.

480

VI. FEM S

IMULATION OF

C

ELL

I

NDENTATION 481

Fig. 20 presents a photo of the visual and haptic user inter-

482

face setup. To test the accuracy and reliability of the proposed

483

user interface system with haptics-enabled simulation, a set of

484

experiments is designed using the setup given in Section II.

485

The geometrical dimensions of the cell are determined through

486

AFM image processing and force curve deflection (diameter and

487

height), and the mechanical properties through AFM indenta-

488

tion studies due to the use of an analytical Hertz contact model.

489

Fig. 20. Real-time indentation simulator using the Omni haptic interface.

TABLE II

MECHANICAL ANDGEOMETRICALPROPERTIES OFSINGLECELLSSELECTED USED IN THEHAPTICS-ENABLEDSIMULATOR

Fig. 21. Force versus indentation for live mESC: comparison between the real-time FEM, the Hertz contact, the quasi-static FEM, and experimental data.

These properties (see Table II) are passed to the finite-element

⁴⁹⁰

simulations.

⁴⁹¹

In order to demonstrate the validity of our finite-element in-

⁴⁹²

dentation model in real time, we compare the simulation inden-

493

tation using the physics-based FEM model to the incremental

494

data provided by AFM indentation tool and to the response sim-

495

ulated with a commercial FE software. Figs. 21 and 22 present

496

the nonlinear relationship between the penetration distance (in-

497

dentation) and the reaction force for live and fixed undiff cells.

498

The finite-element simulations using the commercial software

499

show good agreement with both Hertz contact model and the ex-

500

perimental indentation data. The developed real-time physics-

501

based FEM simulator demonstrates its accuracy in predicting

⁵⁰²

IEEE Proof

Fig. 22. Force versus indentation for fixed mESC: comparison between the real-time FEM, the Hertz contact, the quasi-static FEM, and experimental data.

Fig. 23. Simulation of the AFM nanoindentation in VEs. The AFM tip and the stem cell was modeled using finite-element methods. A scene is shown from current training method: the 3-D cell deformation simulation before and after force indentation.

indentation forces for large deformations (>25%) of relative

503

nominal strain (see Figs. 21 and 22). Fig. 23 illustrates a real-

504

time cell indentation procedure in a VE for training. It shows a

505

screenshot of the cell surface deformation. The interaction be-

506

tween tip and surface can be visualized to the user in 3-D (sphere

507

and cone represent AFM tip and forces acting on tip, respec-

508

tively). It shows the indentation (elastic deformation) on the

509

cell surface and repulsive contact forces while pressing on the

510

surface. In order to improve the force feedback rendering, we

511

added a visual metaphor on the computer screen.

512

The rendered reflection force is depicted by a cone represent-

513

ing the force vector acting on the AFM tip. The visual metaphor

514

has efficiently proved its effectiveness in AFM-based nanoma-

515

nipulation simulation [23]. The vector amplitude reflects the

516

force feedback amplitude and the vector orientation represents

517

the vertical/horizontal force components. Fig. 24 shows in 3-D

518

real time the probe tip, zoomed cell indentation, and micro-

519

forces. The indentation force rendered to the operator is com-

520

posed of a vertical F

_z

and horizontal F

_x

component. For the

521

specific case corresponding to the center indentation, the tan-

522

gential component is very small F

x

0. Only vertical reflection

523

force is provided to the user. He cannot haptically feel it dur-

524

ing simulated indentation tests (see Figs. 25(a) and 26). In the

525

case, where the AFM probe is pushed away from the center of

526

the cell, a tangential component exists (F

x

= 0) and the reflec-

527

Fig. 24. Depth deformation of the cell: the left picture presents the depth indentation (2μm) of the cell and the right picture shows the zoom of the cell deformation.

Fig. 25. Force indentation, where the probe is put (a) in the center and (b) off center of the cell.

Fig. 26. Horizontal and vertical component force versus indentation: the probe is put in center of the cell.

tion force rendered to the user contains a vertical and tangential

⁵²⁸

component (see Figs. 25(b) and 27). We did not reproduce this

⁵²⁹

specific case in our results since the main interest of the paper is

530

to prove experimentally the real-time explicit simulator results

531

during centered cell indentations (since only vertical compo-

532

nents of the force experiments are measured through the AFM

533

cantilever).

534

IEEE Proof

Fig. 27. Horizontal and vertical component force versus indentation: the probe is put off center of the cell.

VII. C

ONCLUSION 535

We have developed a computer-based training system to sim-

536

ulate real-time cell indentation procedures in VEs for training

537

biologists. The simulator provides the user with visual and hap-

538

tic feedback. The simulation of this procedure involves real-time

539

rendering of computer generated graphical images of the AFM

540

tip, physics-based modeling of soft biological tissue, and dis-

541

play of touch and force sensations to the trainee through the

542

simulation of haptic interactions. The real-time haptics-enabled

543

simulator is realistic, since it is mainly based on experimen-

544

tal AFM data (mechanical and geometrical property of mESC)

545

to accurately replicate the indentation task and predict the cell

546

deformation during indentation. We first investigated the chal-

547

lenging issues in the real-time modeling of the biomechanical

548

properties of the cell indentation through FEMs. Compared to

549

experimental AFM indentation results performed on mESC, we

550

can see clearly that the proposed physically based FEM model

551

is able to simulate the cell deformation through real-time sim-

552

ulation constraints. Currently, we are working on integrating

553

nanoscale effects, such as friction, viscosity, punction, and ad-

554

hesion forces in the nonlinear FEM model. All modalities will

555

be merged in an ergonomic tool and intelligent biological sim-

556

ulator for stem cell characterization.

557

R

EFERENCES 558

[1] J. Settleman, “Tension precedes commitment-even for a stem cell,” Mol.

559

Cell, vol. 14, pp. 148–150, 2004.

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[2] V. E. Meyers, M. Zayzafoon, J. T. Douglas, and J. M. McDonald, “RhoA 561

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commitment,” Dev. Cell, vol. 6, pp. 483–495, 2004.

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[4] J. Desai, A. Pillarisetti, and A. D. Brooks, “Engineering approaches to 568

biomanipulation,” Annu. Rev. Biomed. Eng., vol. 9, pp. 35–53, 2007.

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[13] A. Pillarisetti, C. Keefer, and J. P. Desai, “Mechanical Response of embry- 596 onic stem cells using haptics-enabled atomic force microscopy,” inProc. 597 Int. Symp. Experimental Robot., Athens, Greece, 2008. 598 Q6 [14] R. E. Rudd, M. McElfresh, E. Baesu, R. Balhorn, M. Allen, and J. Belak, 599

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[15] V. Lulevich, T. Zink, H.-Y. Chen, F.-T. Liu, and G.-Y. Liu, “Cell me- 603 chanics using atomic force microscopy-based single-cell compression,” 604 Langmuir, vol. 22, no. 19, pp. 8151–8155, 2006. 605 [16] M. Bro-Nielsen and S. Cotin, “Real-time volumetric deformable models 606 for surgery simulation using finite elements and condensation,” Comput. 607 Graph. Forum (Eurographics), vol. 5, no. 3, pp. 57–66, 1996. 608 [17] S. Cotin, H. Delingette, and N. Ayache, “A hybrid elastic model for real- 609 rime cutting, deformations, and force feedback for surgery training and 610 simulation,” Vis. Comput., vol. 16, pp. 437–452, 2000. 611 [18] J.-M. Schwartz, M. Dellinger, D. Rancourt, C. Moisan, and D. Laurendeau, 612

“Modeling liver tissue properties using a non-linear visco-elastic model 613 for surgery simulation,” Med. Image Anal., vol. 9, no. 2, pp. 103–112, 614

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[19] H. Ladjal, J.-L. Hanus, A. Pillarisetti, C. Keefer, A. Ferreira, and J. P. 616 Desai, “Atomic force microscopy-based single-cell indentation: Experi- 617 mentation and finite element simulation,” inProc. IEEE Int. Conf. Robots 618 Intell. Syst., St. Louis, MO, Oct. 11–15 2009. 619 [20] A. Pillarisetti, H. Ladjal, C. Keefer, A. Ferreira, and J. P. Desai, “Mechan- 620 ical characterization of mouse embryonic stem cells,” inProc. 31st Ann. 621 Int. IEEE EMBS Conf., Minnesota, MN, Sep. 2–6 2009. 622 [21] A. Pillarisetti, C. Keefer, and J. P. Desai, “Mechanical response of embry- 623 onic stem cells using haptics-enabled atomic force microscopy,” inProc. 624 Int. Symp. Exp. Robot., Athens, Greece, 2008. 625 [22] V. V. Lulevich, D. Andrienko, and O. I. Vinogradova, “Elasticity of poly- 626 electrolyte multilayer microcapsules,” J. Chem. Phys., vol. 120, no. 8, 627

pp. 3822–3826, 2004. 628

[23] W. Vogl, K.-L.-Ma. Bernice, and M. Sitti, “Augmented reality user inter- 629 face for an atomic force microscope-based nanorobotic system,” IEEE 630 Trans. Nanotechnol., vol. 5, no. 4, pp. 397–406, Jul. 2006. 631 [24] R. Adams, M. Moreyra, and B. Hannaford, “Stability and performance of 632 haptic displays: Theory and experiments,” inProc. ASME Winter Annu. 633

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[27] H. Ladjal, J.-L. Hanus, A. Pillarisetti, C. Keefer, A. Ferreira, and J. P. De- 639 sai, “Realistic visual and haptic feedback simulator for real-time cell 640 indentation,” inProc. IEEE Int. Conf. Robots Intell. Syst., Taipei, Taiwan, 641

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[28] Y. Cao, D. Yang, and W. Soboyejoy, “Nanoindentation method for de- 643 termining the initial contact and adhesion characteristics of soft poly- 644 dimethylsiloxane,”J. Mat. Res., vol. 20, no. 8, pp. 2004–2011, 2005. 645 [29] M. Girot, M. Boukallel, and S. R´egnier, “Modeling soft contact mech- 646 anism of biological cells using an atomic bio-microscope,” inProc. Int. 647 Conf. Intell. Robots Syst., Beijing, China, 2006, pp. 1831–1836. 648 [30] E. U. Azeloglu and K. D. Costa, “Dynamic AFM elastography reveals 649 phase dependent mechanical heterogeneity of beating cardiac myocyte,” 650 inProc. IEEE Conf. Eng. Med. Biol. Soc., 2009, pp. 7180–7183. 651 [31] C. L. Kao, L. K. Tai, S. H. Chiou, Y. J. Chen, K. H. Lee, S. J. Chou, 652 Y. L. Chang, C. M. Chang, S. J. Chen, H. H. Ku, and H. Y. Li, “Resveratrol 653

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robot,” IEEE/ASME Trans. Mechatronics, vol. 14, no. 4, pp. 434–445, 666

Aug. 2009.

667

Hamid Ladjalreceived the Engineer degree in elec- 668

tronics and computing from Houari Boumedi`ene Uni- 669

versity of Science and Technology, Algeria, in 2000, 670

the Master’s degree in virtual reality and complex 671

systems from Evry-Val d’Essone University, Evry, 672

France, and the Ph.D. degree in robotics from the 673

University of Orl´eans, Orl´eans, France, in 2010.

Q9 674

He is currently an Associate Professor in 675

the Institut PRISME, Ecole Nationale Sup´erieure 676

d’Ing´enieurs de Bourges, Bourges, France. His re- 677

search interests include modeling and finite-element 678

simulation, visual and haptic feedback, reality-based soft-tissue modeling for 679

real-time simulation, image processing, control and micromanipulation, biolog- 680

ical cell characterization, and cell biomechanics.

681 682

Jean-Luc Hanusreceived the M.S. degree from the 683

National Aerospace and Mechanical Enginneering 684

School, France, in 1993, and the Ph.D. degree in me- 685

chanical engineering from the University of Poitiers, 686

Poitiers, France, in 1999.

687

He is currently an Assistant Professor of mechan- 688

ical engineering at the Bourges National Engineering 689

School, Bourges, France. His research interests in- 690

clude the area of nonlinear mechanical models and 691

efficient numerical methods in dynamic analysis of 692

biological cell responses.

693 694

Anand Pillarisettireceived the Undergraduate de- 695

gree from the National Institute of Technology, 696

Warangal, India, in 2002, the M.S. degree in mechan- 697

ical engineering and mechanics from Drexel Univer- 698

sity, Philadelphia, PA, in 2006, and the Ph.D. degree 699

in mechanical engineering from University of Mary- 700

land, College Park, MD, in 2008.

Q10701

He is currently a Postdoctoral Researcher in the 702

Department of Mechanical Engineering and Applied 703

Mechanics, University of Pennsylvania, Philadel- 704

phia. His research interests include sensors, micro- 705

electromechanical systems, atomic force microscopy, and nanotechnology.

706 707

Prof. Keefer is a member of the Editorial Board ofCellular Reprogramming 720 (formerlyCloning and Stem Cells). She is an active member of the Society 721 for the Study of Reproduction (SSR). She was President of the International 722

Embryo Transfer Society (IETS). 723

724

Antoine Ferreira (M’04) received the M.S. and 725 Ph.D. degrees in electrical and electronics engineer- 726 ing from the University of Franche-Comt´e, Besancon, 727 France, in 1993 and 1996, respectively. 728 In 1997, he was a Visiting Researcher in the 729 ElectroTechnical Laboratory, Tsukuba, Japan. He 730 is currently a Professor of robotics engineering at 731 the Institut PRISME, Ecole Nationale Sup´erieure 732 d’Ing´enieurs de Bourges, Bourges, France. He is an 733 author of three books on micro- and nanorobotics 734 and more than 100 journal and conference papers 735 and book contributions. His research interests include the design, modeling, 736 and control of micro and nanorobotic systems using active materials, micro- 737 nanomanipulation systems, biological nanosystems, and bionanorobotics. 738 Dr. Ferreira was the Guest Editor for different special issues of the 739 IEEE/ASME TRANSACTIONS ONMECHATRONICSin 2009,International Jour- 740 nal of Robotics Researchin 2009, and theIEEE Nanotechnology Magazinein 741

2008. 742

743

Jaydev P. Desai(SM’07) received the B.Tech. degree 744 from the Indian Institute of Technology, Bombay, 745 India, in 1993, and the M.A. degree in mathemat- 746 ics in 1997, and the M.S. and Ph.D. degrees in me- 747 chanical engineering and applied mechanics, in 1995 748 and 1998, respectively, all from the University of 749

Pennsylvania, Philadelphia, PA. 750

He is currently an Associate Professor in the De- 751 partment of Mechanical Engineering, University of 752 Maryland, College Park, MD, where he is also the Di- 753 rector of the Robotics, Automation, and Medical Sys- 754 tems Laboratory. His research interests include image-guided surgical robotics, 755 haptics, reality-based soft-tissue modeling for surgical simulation, model-based 756 teleoperation in robot-assisted surgery, and cellular manipulation. 757 Prof. Desai was the recipient of an NSF CAREER Award, a Lead Inventor 758 on the “Outstanding Invention of 2007 in Physical Science Category” at the 759 University of Maryland, and the Ralph R. Teetor Educational Award. He is 760 currently a member of the Haptics Symposium Committee, the Co-Chair of 761 the Surgical Robotics Technical Committee of the IEEE Robotics and Automa- 762 tion Society, and a member of the Editorial Board of the IEEE TRANSACTIONS 763 ONBIOMEDICALENGINEERING,ASME Journal of Medical Devices, and IEEE 764 TRANSACTIONS ONINFORMATIONTECHNOLOGY INBIOMEDICINE. He is also a 765 member of the American Society of Mechanical Engineers. 766 767

IEEE Proof

Q11. Author: Please provide the title (B.Sc., M.Sc., Ph.D., etc.) and university names from which C. Keefer received these degrees.

781