1

3

4

5

6

7 Q1

8

910

1 2

1314151617

181920212223 Q224

2 5

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

Acta Biomaterialia xxx (2014) xxx–xxx

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

Contents lists available at ScienceDirect

Acta Biomaterialia

journal homepage: www.elsevier .com/locate /actabiomat

Pore size distribution of bioresorbable films using a 3-D diffusion NMRmethod

http://dx.doi.org/10.1016/j.actbio.2014.02.0141742-7061/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +972 36407542.E-mail address: danbenj@gmail.com (U. Nevo).

Please cite this article in press as: Benjamini D et al. Pore size distribution of bioresorbable films using a 3-D diffusion NMR method. Acta Biomaterhttp://dx.doi.org/10.1016/j.actbio.2014.02.014

Dan Benjamini, Jonathan J. Elsner, Meital Zilberman, Uri Nevo ⇑Department of Biomedical Engineering, The Iby and Aladar Fleischman Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel

a r t i c l e i n f o

262728293031323334353637

Article history:Received 16 September 2013Received in revised form 21 January 2014Accepted 5 February 2014Available online xxxx

Keywords:PorosityMicrostructurePore size distributionSEM (scanning electron microscopy)Polyglycolic acid

3839404142

a b s t r a c t

Pore size distribution (PSD) within porous biomaterials is an important microstructural feature forassessing their biocompatibility, longevity and drug release kinetics. Scanning electron microscopy(SEM) is the most common method used to obtain the PSD of soft biomaterials. The method is highlyinvasive and user dependent, since it requires fracturing of the sample and then considers only the smallportion that the user had acquired in the image. In the current study we present a novel nuclear magneticresonance (NMR) method as an alternative method for estimation of PSD in soft porous materials. Thisnoninvasive 3-D diffusion NMR method considers the entire volume of the specimen and eliminatesthe user’s need to choose a specific field of view. Moreover, NMR does not involve exposure to ionizingradiation and can potentially have preclinical and clinical uses. The method was applied on four porous50/50 poly(DL-lactic-co-glycolic acid) bioresorbable films with different porosities, which were createdusing the freeze-drying of inverted emulsions technique. We show that the proposed NMR method is ableto address the main limitations associated with SEM-based PSD estimations by being non-destructive,depicting the full volume of the specimens and not being dependent on the magnification factor. Uponcomparison, both methods yielded a similar PSD in the smaller pore size range (1–25 lm), while theNMR-based method provided additional information on the larger pores (25–50 lm).

� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

43

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

1. Introduction

Porosity and the distribution of pore sizes play an importantrole in the characterization of materials – in particular, biomateri-als. These characteristics have been shown to affect the biocompat-ibility of biomaterials [1] and their longevity [2], and govern thecontrolled release of drugs and other bioactive agents from them[3]. Since many biomaterials undergo structural changes in thebody, by degradation or by biological response, such as tissue infil-tration, there is a clear need to develop a method to track thesechanges in vivo. Thus, the use of noninvasive and nondestructivenuclear magnetic resonance (NMR) holds clear advantages in thebiomedical field, where the ongoing surveillance of changes to abiomaterial or the biological reaction to it necessitates noninvasivemonitoring over time.

Depending on the length scale of the pores, different methodscan be used to gather microstructural information from porousmaterials. Mercury porosimetry is often used to estimate the poresize distribution (PSD) in porous media, and is sensitive to a widerange of pore sizes (3 nm–500 lm) [4]. In this method, mercury is

84

85

86

injected into the sample and its volume/mass is measured as afunction of the applied pressure [5]. One of the key limitations ofthis method is that it measures the size of the entrance to the porerather than its actual inner volume [5]. It therefore cannot be usedto analyze materials which contain closed pores, as the mercuryhas no way of entering them. Another limitation of this methodis the use of high pressure, which may be unsuitable for soft mate-rials. Lastly, mercury porosimetry is invasive, and can only be ap-plied on dry samples. It is therefore not suited for theinvestigation of biomaterials in their natural environment.

Microcomputed tomography (micro-CT) is a noninvasive X-rayimaging method that provides a 3-D image of the internal architec-ture of a sample. 2-D images are acquired, each representing aslice, and then stacked together to form the 3-D structure. Micro-CT can be used to image porous polymers and scaffolds [6–8]. Thismethod is primarily efficient when the materials are dry, and isbased on a 3-D image-processing algorithm to provide the neces-sary structural features [9]. The ionizing radiation level plays a sig-nificant role when considering clinical applications, such asstructural characterization of polymer implants in humans. Theimpact of X-ray exposure on tissue has been widely investigatedand results in direct damage to nearby molecules, specificallyDNA [9]. In micro-CT, the X-ray radiation exposure to the subject

(2014),

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

2 D. Benjamini et al. / Acta Biomaterialia xxx (2014) xxx–xxx

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

increases with the fourth power of the voxel side dimension [9].While acceptable in preclinical studies on small animals, ultra-high-resolution micro-CT radiation levels make it impossible forclinical use.

The most common way to obtain local microstructural featuresof biomaterials is by using scanning electron microscopy (SEM)images [10]. While it can provide a very high spatial resolution,this method is highly invasive and requires fracturing of the sam-ple to expose a cross-section of its inner bulk, and in certain mate-rials an electrically conducting coating is also needed.

The microstructural information from both micro-CT and SEM isobtained directly from an image. As opposed to spectroscopicmethods such as NMR, the acquired image has a finite spatial res-olution. In addition, before applying an image-processing algo-rithm to obtain the structural information, a field of view (FOV)must be chosen by the user. This choice, as will be demonstratedlater on, predetermines the extracted geometrical properties ofthe sample. Furthermore, the automated image-processing algo-rithm can introduce additional error to the estimation.

In NMR, nuclear spins in a magnetic field are put under reso-nance (using radio-frequency pulses that induce precession). Theprecession of such an ensemble of spins is detected as an electro-magnetic induction, which is the NMR signal. Diffusion-weightedNMR (DW-NMR) is a sub-technique of NMR in which manipulationof the phase of precession of the precessing spins quantifies thedisplacement of the molecules holding the spins. DW-NMR is anoninvasive method that is sensitive to the displacement of mole-cules. Typical DW-NMR experiments operate in the following way:an ensemble of spins of water hydrogen that precess synchro-nously and coherently (with the same phase) is assumed. Applica-tion of a momentary spatial perturbation in the magnetic field (e.g.applying a magnetic field gradient) induces a momentary deviationof the precession frequency. This deviation is ‘‘preserved’’ evenafter the momentary perturbation (gradient) has gone, as a resid-ual difference in the accumulated phase of precession. Applicationof an opposite perturbation after a finite time (D) will ‘‘erase’’ thisresidual phase. However, spins that diffuse during the time D willencounter canceling perturbations, and will have a residual non-zero phase. The higher the diffusion of molecules in the ensemble,the higher their displacement in time D and the variance of theresidual phase. Thus, experimentally, the degree of diffusion canbe quantified by the phase variance that is detected, or as an atten-uation of the superposed signal of the entire ensemble. A typicalDW-NMR experiment consists of a series of experiments, as de-scribed above, in each of which a pulsed gradient of different valueis applied.

However, molecular diffusion in porous media is not free, asmolecules of the dispersed phase (usually water) interact withthe boundaries of the continuous phase. When the environmentfor molecular displacement is not a free medium, the displacementis tightly linked to the specific microstructural barriers and hinder-ing obstacles that surround the molecules. The detected displace-ment thus reflects the interactions of the moving molecules withthe boundaries. The statistics of displacement of water in a spher-ical pore can be characterized analytically. Thus, if a material iscomposed of identical equal sized pores, the result of a DW-NMRexperiment can be easily fitted, and the size of the pores can befound. Estimation of microstructural properties with diffusionweighted NMR-based techniques presents many benefits, the mostimportant of which are its non-invasiveness and its ability to col-lect information from the entire volume of the sample. DW-NMRhas been applied on many porous materials, and specifically on tis-sues [11]. The qualitative characterization of microstructures hasalready been demonstrated in many types of experimental models,ranging from biological tissues [12,13] to dairy products [14] andsandstone [15,16]. However, in samples that are composed of

Please cite this article in press as: Benjamini D et al. Pore size distribution of biohttp://dx.doi.org/10.1016/j.actbio.2014.02.014

polydisperse pores, an exact quantitative NMR-based estimationof the PSD is a challenging task, since it involves the solution of amathematically ill-posed problem (i.e. small noise in the datamay cause large changes in the reconstructed pore size distribu-tion). Despite this challenge, estimation of an emulsion’s PSD usingdiffusion weighted NMR has been demonstrated [17]. Recently,this method was extended to include a second dimension in theparameter space [18], by applying a second magnetic gradient pairimmediately after the first one. By doing so, the two dimensions inthe parametric space are the gradient amplitude and the relativeangle, u, between the two gradient pairs. The method for recon-struction of the pore size distribution is applied as follows (for amathematical description, see the Supplementary Information):(1) a series of DW-NMR experiments is performed, with varianceof these two experimental values (gradient amplitude and relativedirection). (2) The spectrum of possible pore sizes is discretized(binned) with values chosen between Rmin and Rmax. (3) The theo-retical signal attenuation is calculated analytically for each of thesediscrete radii and for each set of experimental values. This processresults in a library (a matrix) of known basis values calculated foreach experimental set. (4) The observations are assumed to resultfrom the superposition of contributions of signals from multiplepores with different radii, each weighted by its relative fraction(defined by the PSD). (5) A numeric fitting process is appliedwhereby iterations include trials with different PSDs. The solutionis the PSD that gives the best fit to the experimental observationsdescribed in (1). The 2-D method was shown to improve the stabil-ity and reliability of the estimated PSD. It was further tested exper-imentally on calibrated microcapillary PSD phantoms, resulting inaccurate size distribution estimation [19].

In the current study we present a novel noninvasive methodof estimation of PSD in soft porous materials that considers theentire sample volume, and serves as an alternative to the tradi-tional SEM method. The above-mentioned 2-D NMR method isfurther extended here to a 3-D parametric space (see the Sup-plementary Information for further details). Based on previouswork [18], this extension is predicted to significantly improvethe stability and reliability of the PSD estimation. The 3-Dmethod was applied on four porous 50/50 poly(DL-lactic-co-gly-colic acid) (PDLGA) bioresorbable films with different porosities,which were created using the freeze-drying of inverted emul-sions technique. The microstructure of such films, specificallythe overall pore volume, pore size and interconnection of pores,has been shown to greatly affect the release pattern of bioactiveagents from such films in wound dressings, stents and bonescaffold applications [3,20]. The relevant size range of poreswithin these bioresorbable films is 1–50 lm, which is applicableto and representative of many other polymer biomaterials.

2. Materials and methods

2.1. Preparation of porous structure

50/50 PDLGA films were prepared utilizing the freeze-dryingof inverted emulsions technique [3]. The aqueous phase of theinverted emulsion consisted of double-distilled water with 1%(w/v) bovine serum albumin as surfactant. The organic phaseof the inverted emulsion consisted of 15% (w/v) of 50/50 PDLGA,which was dissolved in chloroform. Freshly prepared invertedemulsions were prepared by homogenization of the organicand aqueous phases (O:A ratio = 6:1) at four different stir rates(2500, 5000, 7500 and 10,000 rpm). The emulsions were thenpoured into an aluminum plate and immediately frozen in a li-quid nitrogen bath before placing them in a pre-cooled(�105 �C) freeze-dryer. Freeze-drying the samples overnight to

resorbable films using a 3-D diffusion NMR method. Acta Biomater (2014),

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256 Q3

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306Q4

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

D. Benjamini et al. / Acta Biomaterialia xxx (2014) xxx–xxx 3

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

remove the solvents preserved the microstructure of the emul-sion-based structures in the solid state. The different homogeni-zation rates of the emulsion were expected to result in differentpore size distributions, as previously described [21]. Each poly-mer sample was cut into an 8 mm diameter disc, 1.5 mm wide.

2.2. NMR sample preparation

In order to obtain an NMR signal the pores must be filled withan NMR-visible material, which in this case was water. The airfrom within the pores should thus be exchanged with water, whichdiffuses through the polymer bulk. To achieve this exchange, thesample was immersed in distilled water for a period of 3 days priorto each experiment, during which it was put in sub-pressure con-ditions (0.4 bar) for a period of 1 h to insure the departure of airbubbles. The 3 day period was selected in accordance with the typ-ical release profile of antibiotics from PDLGA structures (for exam-ple, it was previously reported [3] that 95% of a drug that was heldinside such pores was released into the medium within 3 days).

After this period the polymer was put in a 10 mm NMR tube(New Era, NJ, USA) filled with Fluorinert (3 M, MN, USA). Owingto its high density and the fact that its molecules are non-polar,the Fluorinent kept most extracellular water (i.e. water outsidethe pores) in the upper part of the NMR tube. This part of the tubewas located outside the radio-frequency coils, thus minimizing thefree water content of the sample.

2.3. NMR experimental design

An unshielded Bruker 8.4 T NMR spectrometer (Karlsruhe,Germany) equipped with a Micro5 probe capable of producingnominal pulsed gradients of up to 1900 mT m�1 in each directionwas used.

A stimulated bipolar double-pulsed field gradient sequence[22,23] (Fig. S1) was applied to all samples, resulting in a typicallinewidth of 200 Hz. The experimental parameters were varied inthe three following dimensions: (i) the angle u between the firstand second diffusion gradient blocks. The direction of the first gra-dient, G1, was fixed in the x direction throughout the experiment,while the direction of a second gradient, G2, was varied in thex–y plane. The angles were taken to be linearly spaced, with 13increments varying from 0� to 360�. (ii) Eight different diffusiongradient amplitudes were taken (where |G1| = |G2|), withGmax = 460 mT m�1. (iii) Two diffusion periods, D1 = D2 = 300 and500 ms. Other parameters were fixed throughout the experiment,namely, d = 3 ms, tm = 0 and TR = 5 s. The overall time of the 3-Dexperiment was a little less than 2.5 h.

2.4. SEM acquisition and processing

SEM images of two representative polymers, the 5000 and10,000 rpm samples, were acquired using a JEOL JSM76300 scan-ning electron microscope at an accelerating voltage of 5 kV. Thecryogenically fractured surfaces were Au-sputtered prior to obser-vation. The magnification factors used were: �200, �250, �500,�750, �1000, �2000 and �2500. SEM-based PSD estimation ofthe 5000 and 10,000 rpm polymers was obtained by using ImageJ(NIH, MD, USA), with several different magnification factors andregions of interest.

3. Results and discussion

3.1. SEM-based PSD estimation

The structural information within a single SEM image is verylimited since, for example, with an �1000 magnification, the

Please cite this article in press as: Benjamini D et al. Pore size distribution of biohttp://dx.doi.org/10.1016/j.actbio.2014.02.014

inspected volume is of a typical volume of 120 lm � 85 lm� 10 lm � 0.0001 mm3. It is worth noting that the average volumeof each polymer sample was 75 mm3, which is 750,000 times morethan the inspected volume in a typical SEM image. This intrinsiclimitation of SEM-based image analysis gives rise to at least twosources of errors and inaccuracies.

The first source of error is the choice of FOV by the user, whichin itself predetermines the extracted geometrical properties of thesample. Since each FOV presents about 0.0001% of the sample’svolume, significantly different microstructural properties can befound in different locations. Fig. 1 provides an example of this lim-itation, where two cross-section cryo-fractographs, both takenfrom the 5000 rpm polymer sample using the same magnificationfactor (�500), are presented. Below them are the independentlyderived SEM-based PSDs. While most of the volume in Fig. 1C isof 5–10 lm pores, the majority of the volume in Fig. 1D consistsof 20–25 lm pores. These drastic differences within the same poly-mer specimen emphasize the biases created by the choice of theFOV.

A second source of errors is the chosen magnification factor. If ahigh magnification factor is used, it is possible to detect small ob-jects and consequently small pores. However, such use of a highmagnification factor leads to two problems: (i) the higher the mag-nification factor, the smaller the FOV and the weight of the abovedescribed limitation increases (since the fraction of this FOV fromthe entire sample is now even smaller). (ii) Larger pores cannot bedetected under high magnification. The ‘‘filtering-out’’ of small-pores significantly biases the results. On the other hand, a rela-tively low magnification factor will bias the results in the oppositedirection (more sensitive to bigger pores). An example that illus-trates this point is presented in Fig. 2. Two cross-section cryo-fractographs, both taken from the 10,000 rpm polymer sampleusing different magnifications factors (�2500 and �250), areshown, respectively, in Fig. 2A and B. Below are the independentlyderived SEM-based PSDs. Note that in Fig. 2C the PSD is narrow andrevolves around 2 lm, while in Fig. 2D a new and larger size pop-ulation appears around 7.5 lm, and the small sizes disappear.

When measuring the volumetric fraction of each pore size, oneshould bear in mind the non-linear nature of the relation betweenthem. If Ni and Vi are the numeric and volumetric fractions of apore with size Ri, then Vi / Ni � R3

i . For example, adding 1 poreof R1 = 40 lm radius to a population of 99 pores of R2 = 5 lm re-sults in N1 = 0.01 and N2 = 0.99, while V1 = 0.84 and V2 = 0.16. Thisrelation illustrates the great impact that a small number of largepores have on the estimated volumetric PSD. As previously dis-cussed, the SEM-based image analysis leads to a filtering of the lar-ger pores; therefore it can result in a significantly biased PSDestimation.

3.2. NMR-based PSD estimation

The partial volumetric fraction vector, f, obtained from solvingEq. (S3), is in fact the PSD (see the Supplementary Informationfor further details). The NMR signal, which is three-dimensionalin the parameter space, was separately fitted for each of the fourpolymer samples. The squared 2-norm of the residual was0.0035, 0.013, 0.0065 and 0.016, for the 2500, 5000, 7500 and10,000 rpm polymers, respectively. Two representative 3-D signalattenuation curves (of the 2500 and 5000 rpm polymers) and theirtheoretical fit are presented in Fig. 3. In order to include all threeparameter dimensions in the plot (i.e. the angle u, the diffusiongradient amplitude G and the diffusion period, D; for further de-tails see the Supplementary Information), the angular dependencyof the signal is presented for different gradient amplitudes, G (sep-arated by a dashed vertical line). Each color in the plot indicates a

resorbable films using a 3-D diffusion NMR method. Acta Biomater (2014),

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

Radius [µm]

Vol

umet

ric fr

actio

n

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

Radius [µm]

Vol

umet

ric fr

actio

n

(A) (B)

(C) (D)

Fig. 1. Two cross-section cryo-fractographs (A) and (B), taken from the same polymer (5000 rpm) sample using the same magnification factor (�500). The independently SEMimage-based PSDs from (A) and (B) are presented, respectively, in (C) and (D). This example illustrates why the choice of field of view by the user predetermines the extractedgeometrical properties of the sample.

(A) (B)

(C) (D)

1 2 3 4 5 6 7 8 9 100

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Radius [µm]

Vol

umet

ric fr

actio

n

0 1 2 3 4 5 6 7 8 9 100

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Radius [µm]

Vol

umet

ric fr

actio

n

Fig. 2. Two cross-section cryo-fractographs, (A) and (B), taken from the same polymer (10,000 rpm) sample using different magnifications factors (�2500 and �250,respectively). The independently SEM image based PSDs from (A) and (B) are presented, respectively, in (C) and (D). Note the addition of a size population around 7.5 lm in(D). This example illustrates how the choice of magnification factor affects the extracted geometrical properties of the sample.

4 D. Benjamini et al. / Acta Biomaterialia xxx (2014) xxx–xxx

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

Please cite this article in press as: Benjamini D et al. Pore size distribution of bioresorbable films using a 3-D diffusion NMR method. Acta Biomater (2014),http://dx.doi.org/10.1016/j.actbio.2014.02.014

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

D. Benjamini et al. / Acta Biomaterialia xxx (2014) xxx–xxx 5

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

different experimentally defined diffusion period, D, while circlesindicate experimental data and solid lines show the theoretical fit.

The volumetric PSD of each of the polymer samples are shownin Fig. 4. In two cases, the 5000 and 10,000 rpm polymers, an SEM-based PSD is presented on top of the NMR PSD (colored in blue). Asthe homogenization rate of the emulsion is increased, the averagepore size is expected to become smaller [21]. Indeed, the obtainedaverage radii from the NMR-based estimation are 25.6, 20.7, 13.8and 11.8 lm for the 2500, 5000, 7500 and 10,000 rpm polymers,respectively. Apart from the average size, a PSD may provide dee-per insight into the microstructural properties of the material.Upon examination of the different PSDs, one can roughly divideeach of them into four size ranges, namely, R < 5 lm,5 lm < R < 15 lm, 15 lm < R < 30 lm and R > 30 lm. The total vol-ume of pores within these four size ranges can provide more de-tailed information on the relation between the homogenizationrate of the emulsion and the resulting microstructure. Such infor-mation has never been available before. The volumetric fractionof different size ranges within different samples is provided inTable 1.

When comparing the SEM- and NMR-based PSD estimations(Fig. 4B and D), a clear advantage of the NMR-based method canbe seen. The difference between the two PSDs is evident in the lar-ger pore population, where, in the cases of the 5000 and10,000 rpm polymers, an entire population of larger pore sizes,which is overlooked by the SEM-based method, is detected bythe NMR-based method. As discussed in the previous sections,the SEM-based PSD estimation tends to filter-out the larger pores.In addition, in Fig. 4B it is evident that, while the NMR-based PSDreports a significant population around 5 lm, the SEM-based PSDdoes not. Smaller differences can be spotted in the case ofFig. 4D. The NMR-based PSD estimation does not exclude or under-estimate any pore size population, since it is based on information

Fig. 3. The 3-D signal attenuation curves (circles) and their theoretical fit (solid lines) froperiod, D. The gradient amplitude, G, of each angular dependency sub-curve is indicate2-norm of the residual is 0.0035 and 0.013 for (A) and (B), respectively.

Please cite this article in press as: Benjamini D et al. Pore size distribution of biohttp://dx.doi.org/10.1016/j.actbio.2014.02.014

from the entire volume of the sample (rather than from 0.0001% ofit, in the case of a �1000 magnification SEM image). Such an anal-ysis from the entire bulk of the biopolymer sample cannot be ob-tained from SEM image analysis.

Other than the differences mentioned, the agreement betweenthe SEM- and NMR-based methods is fairly good. To illustrate thispoint, if the biggest pore size population is excluded from theNMR-based PSD, it leads to an average pore size, for the 5000and 10,000 rpm polymers, respectively, of 5.9 and 13.7 lm, com-pared to 5.0 and 14.1 lm from the SEM.

Preliminary NMR scans in all three directions (x, y and z) wereperformed on each of the polymers in order to determine if thepores indeed exhibit ensemble isotropy. These scans resulted invery similar signal attenuation curves in all three directions forall samples; therefore, they are macroscopically isotropic (see theSupplementary Information for further details and figures).

Both the NMR- and SEM-based analysis share the fundamentalassumption of the spherical geometry of the pores. If the shape ofthe pore is an imperfect sphere, then the analysis should not yield asignificant error. However, as the pore shape becomes more arbi-trary, the underlying assumptions lose their validity. Althoughthe emulsion-based preparation of the porous structure should re-sult in the distribution of spheres, the estimation error increaseswith the deviation from a spherical structure. In the case of non-spherical pores, if the underlying geometry can be described as acombination of parallel plates, cylinders and spheres, then the pro-posed MR method may be applied. In the case where the geometryis arbitrary and undefined, with no specific resemblance to any ba-sic shapes, then the analysis is yet to be derived.

Moreover, pore interconnections were not modeled in the cur-rent method. Like in SEM, interconnections result in fluid exchangebetween pores, which violates the underlying geometry assump-tion. This deviation further contributes to the overall estimation

m the (A) 2500 and (B) 5000 rpm polymers. Each color indicates a different diffusiond in the plot (for further details see the Supplementary Information). The squared

resorbable films using a 3-D diffusion NMR method. Acta Biomater (2014),

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

Radius [µm]

Vol

umet

ric fr

actio

n

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

Radius [µm]

Vol

umet

ric fr

actio

n

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

Radius [µm]

Vol

umet

ric fr

actio

n

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

Radius [µm]

Vol

umet

ric fr

actio

n

NMR−basedSEM−based

NMR−basedSEM−based

(A) (B)

(C) (D)

Fig. 4. The volumetric NMR-based PSD of the (A) 2500, (B) 5000, (C) 7500, and (D) 10,000 rpm polymers, with an average radius of 25.6, 20.7, 13.8 and 11.8 lm, respectively.In the cases of the 5000 and 10,000 rpm polymers, an SEM-based PSD is presented on top of the NMR PSD (colored in blue). Information regarding the volumetric fractions isdetailed in Table 1.

6 D. Benjamini et al. / Acta Biomaterialia xxx (2014) xxx–xxx

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

error. Future analysis could include an average isotropic exchangewith a given rate to model such interconnection. Such an approachwould add to the complexity of the problem by introducing the ex-change rate as a variable, but should prove feasible.

Detectable NMR signal arises from the fluid or gas that fills thepores – which in this study was water. Complete loading of waterinto the pores is difficult to accomplish, so partial water filling maypresent an additional source of error in the suggested NMR meth-od. Although the water-filling phase was conducted with greatcare, this possibility exists.

Another aspect that limits the use of the current method is thedetectable pore size range. The maximal detectable pore size, Rmax,is established and limited by the diffusion period, D, since, in thistype of experiment, the water molecules serve as the detectingprobes, and Rmax would be their largest displacement within thediffusion period. This length can be written as Rmax �

ffiffiffiffiffiffiffiffiffiffi

2DDp

(whereD is the diffusion coefficient). However, the diffusion period cannotbe extended indefinitely. The longer it is, the lower the signal-to-noise ratio (SNR). In this study, the SNR allowed an Rmax of about50–60 ls. For future applications, the limiting pore size could beextended by improving the SNR. This can be achieved by the useof an NMR scanner with a stronger magnetic field, or with an in-creased number of averages in each scan. On the other side of

447

448

449

450Table 1The volumetric fraction of different size ranges within different samples.

Polymer Radius [lm]

R < 5 5 < R < 15 15 < R < 30 R > 30

2500 rpm 0.12 0.17 0.49 0.225000 rpm 0.18 0.29 0.32 0.217500 rpm 0.24 0.37 0.39 010,000 rpm 0.36 0.32 0.32 0

Please cite this article in press as: Benjamini D et al. Pore size distribution of biohttp://dx.doi.org/10.1016/j.actbio.2014.02.014

the distribution, the minimal detectable size, Rmin, is determinedby the diffusion gradient pulse duration, d, in the same mannerðRmin �

ffiffiffiffiffiffiffiffiffi

2Ddp

Þ. In this case, too, the duration of the pulse cannotbe shortened indefinitely. To maintain the same encoding effect,shortening the pulse would result in the application of strongergradient amplitudes, which could impose a hardware limitation.

PSD estimation using NMR is mathematically ill-conditioned(i.e. small noise in the data may cause large changes in the recon-structed pore size distribution). The spatial resolution of the PSDdetermines the number of coefficients (i.e. the different volumetricfraction of each pore size; see the Supplementary Information formore details) found in the estimation process. In general, as theresolution is higher, more coefficients have to be found, and moreNMR scans with different parameters (G and u) should be acquiredto prevent reduced stability in the estimation. The PSD’s resolutionin this study was chosen according to the number of acquisitions,and it is essentially limited by the overall experiment duration.Although the method presented improves the stability and reliabil-ity of the estimated PSD, its solution may still be affected by thislimitation.

Further investigation of the polymer’s degradation kinetics andtheir influence on the microstructure can provide valuable infor-mation. This can be achieved by scanning a sample soaked in waterfor different time periods and following the changes in the result-ing PSD. The influence of other synthesis-related parameters, suchas the organic–aqueous phase ratio, on the PSD can also bedemonstrated.

451

452

453

454

4. Conclusion

This study presents an alternative to the traditional method ofestimation of PSD by SEM in soft porous materials, which has thebenefits of performing the estimation in a non-invasive manner

resorbable films using a 3-D diffusion NMR method. Acta Biomater (2014),

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470 Q5

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486487

488489490491492493494495496497498499500501502503504505506507508509510Q6511512513514515516517518

D. Benjamini et al. / Acta Biomaterialia xxx (2014) xxx–xxx 7

ACTBIO 3113 No. of Pages 7, Model 5G

25 February 2014

while considering the entire sample volume. This multi-dimensional NMR method has already been validated on a well-calibrated and controlled porous phantom [19], thus its stabilityand robustness are established.

Upon comparison between the SEM- and NMR-based methods,both yielded a similar PSD in the smaller pore size range(1–25 lm), while the NMR-based method provided additionalinformation on larger pores (25–50 lm).

The presented multi-dimensional NMR method holds threemajor advantages over the existing SEM-based analysis: (i) it iscompletely noninvasive and nondestructive, and thus has the po-tential for clinical use (e.g. in vivo drug eluting polymer implantsstructural characterization in humans). (ii) It provides informationfrom the entire volume of the sample, thus eliminating the user’sneed to choose specific FOVs, and removes bias. (iii) It is equallysensitive to all pore sizes, and does not depend on parameters asthe magnification factor.

Acknowledgements

This study was supported by the Marie Curie IRG grant (MMD-TIAN) and by the Israel Science Foundation (ISF). U.N. is supportedby a Colton family scholarship.

519520521522523524525526527

Appendix A. Figures with essential colour discrimination

Certain figures in this article, particularly Figs. 1–4, are difficultto interpret in black and white. The full colour images can be foundin the on-line version, at http://dx.doi.org/10.1016/j.actbio.2014.02.014.

528529530531532533534535536537538539540541

Appendix B. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.actbio.2014.02.014.

References

[1] Malmberg P, Nygren H. A method for evaluating the influence of porosity onthe early reactions of blood with materials. Biomaterials 2002;23:247–53.

542

Please cite this article in press as: Benjamini D et al. Pore size distribution of biohttp://dx.doi.org/10.1016/j.actbio.2014.02.014

[2] Dunne NJ, Orr JF, Mushipe MT, Eveleigh RJ. The relationship between porosityand fatigue characteristics of bone cements. Biomaterials 2003;24:239–45.

[3] Elsner JJ, Zilberman M. Antibiotic-eluting bioresorbable composite fibers forwound healing applications: microstructure, drug delivery and mechanicalproperties. Acta Biomater 2009;5:2872–83.

[4] Conner WC, Cevallos-Candau JF, Weist EL, Pajares J, Mendioroz S, Cortes A.Characterization of pore structure: porosimetry and sorption. Langmuir1986;2:151–4.

[5] Giesche H. Mercury porosimetry: a general (practical) overview. ParticleParticle Syst Charact 2006;23:9–19.

[6] Alberich-Bayarri A, Moratal D, Ivirico JLE, Hernández JCR, Vallés-Lluch A,Martí-Bonmatí L, et al. Microcomputed tomography and microfinite elementmodeling for evaluating polymer scaffolds architecture and their mechanicalproperties. J Biomed Mater Res B Appl Biomater 2009;91B(1):191–202.

[7] Lin ASP, Barrows TH, Cartmell SH, Guldberg RE. Microarchitectural andmechanical characterization of oriented porous polymer scaffolds.Biomaterials 2003;24(3):481–9.

[8] Ho ST, Hutmacher DW. A comparison of micro CT with other techniques usedin the characterization of scaffolds. Biomaterials 2006;27(8):1362–76.

[9] Ritman EL. Current status of developments and applications of micro-CT. AnnRev Biomed Eng 2011;13:531–52.

[10] Hoffman AS, Schoen FJ, Lemons JE. Biomaterials science: an introduction tomaterials in medicine; 2012. Epub 3.

[11] Johansen-Berg H, Behrens TEJ. Diffusion MRI. London: Academic Press; 2009.[12] Basser PJ, Mattiello J, LeBihan D. MR diffusion tensor spectroscopy and

imaging. Biophys J 1994;66(1):259–67.[13] Komlosh ME, Özarslan E, Lizak MJ, Horkayne-Szakaly I, Freidlin RZ, Horkay F,

et al. Mapping average axon diameters in porcine spinal cord white matter andrat corpus callosum using d-PFG MRI. NeuroImage 2013;78:210–6.

[14] Callaghan PT, Jolley KW. Diffusion of fat and water in cheese as studied bypulsed field gradient nuclear magnetic resonance. J Colloid Interface Sci1983;93(2):521–9.

[15] Mitra PP, Sen PN, Schwartz LM, Le Doussal P. Diffusion propagator as a probe ofthe structure of porous media. Phys Rev Lett 1992;68(24):3555–8.

[16] Pape H, Tillich JE, Holz M. Pore geometry of sandstone derived from pulsedfield gradient NMR. J Appl Geophys 2006;58(3):232–52.

[17] Hollingsworth KG, Johns ML. Measurement of emulsion droplet sizes usingPFG NMR and regularization methods. J Colloid Interface Sci 2003;258:383–9.

[18] Benjamini D, Katz Y, Nevo U. A proposed 2D framework for estimation of poresize distribution by double pulsed field gradient NMR. J Chem Phys2012;137:224201.

[19] Benjamini D, Nevo U. Estimation of pore size distribution using concentricdouble pulsed-field gradient NMR. J Magn Reson 2013;230:198–204.

[20] Grinberg O, Binderman I, Bahar H, Zilberman M. Highly porous bioresorbablescaffolds with controlled release of bioactive agents for tissue-regenerationapplications. Acta Biomater 2010;6:1278–87.

[21] Kraitzer A, Zilberman M. Paclitaxel-loaded composite fibers: microstructureand emulsion stability. J Biomed Mater Res A 2007;81A(2):427–36.

[22] Shemesh N, Cohen Y. Overcoming apparent susceptibility-induced anisotropy(aSIA) by bipolar double-pulsed-field-gradient NMR. J Magn Reson2011;212:362–9.

[23] Zheng G, Price WS. Suppression of background gradients in (B0 gradient-based) NMR diffusion experiments. Concepts Magn Reson A2007;30A:261–77.

resorbable films using a 3-D diffusion NMR method. Acta Biomater (2014),