Acta Biomaterialia 10 (2014) 2762–2768

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Acta Biomaterialia

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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).

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

Article history:Received 16 September 2013Received in revised form 21 January 2014Accepted 5 February 2014Available online 15 February 2014

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

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.

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 tissueinfiltration, 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

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 softmaterials. Lastly, mercury porosimetry is invasive, and can onlybe applied on dry samples. It is therefore not suited for the inves-tigation 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 asignificant 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

D. Benjamini et al. / Acta Biomaterialia 10 (2014) 2762–2768 2763

increases with the fourth power of the voxel size dimension [9].While acceptable in preclinical studies on small animals,ultrahigh-resolution micro-CT radiation levels make it impossiblefor clinical 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 thesample to expose a cross-section of its inner bulk, and in certainmaterials 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 spatialresolution. 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-processingalgorithm 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 the precessing spins quantifies the displacement ofthe molecules holding the spins. DW-NMR is a noninvasive methodthat is sensitive to the displacement of molecules. Typical DW-NMRexperiments operate in the following way: an ensemble of spins ofwater hydrogen that precess synchronously and coherently (withthe same phase) is assumed. Application of a momentary spatialperturbation in the magnetic field (e.g. applying a magnetic fieldgradient) induces a momentary deviation of the precession fre-quency. This deviation is ‘‘preserved’’ even after the momentaryperturbation (gradient) has gone, as a residual difference in theaccumulated phase of precession. Application of an opposite per-turbation after a finite time (D) will ‘‘erase’’ this residual phase.However, spins that diffuse during the time D will encounter can-celing perturbations, and will have a residual non-zero phase. Thehigher the diffusion of molecules in the ensemble, the higher theirdisplacement in time D and the variance of the residual phase.Thus, experimentally, the degree of diffusion can be quantified bythe phase variance that is detected, or as an attenuation of thesuperposed signal of the entire ensemble. A typical DW-NMRexperiment consists of a series of experiments, as described above,in each of which a pulsed gradient of different value is 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 ontissues [11]. The qualitative characterization of microstructureshas already been demonstrated in many types of experimentalmodels, ranging from biological tissues [12,13] to dairy products[14] and sandstone [15,16]. However, in samples that arecomposed of polydisperse pores, an exact quantitative NMR-based

estimation of the PSD is a challenging task, since it involves thesolution of a mathematically ill-posed problem (i.e. small noisein the data may cause large changes in the reconstructed pore sizedistribution). Despite this challenge, estimation of an emulsion’sPSD using diffusion weighted NMR has been demonstrated [17].Recently, this method was extended to include a second dimensionin the parameter space [18], by applying a second magnetic gradi-ent pair immediately after the first one. By doing so, the twodimensions in the parametric space are the gradient amplitudeand the relative angle, u, between the two gradient pairs. Themethod for reconstruction of the pore size distribution is appliedas follows (for a mathematical description, see the SupplementaryInformation): (1) a series of DW-NMR experiments is performed,with variance of these two experimental values (gradient ampli-tude and relative direction). (2) The spectrum of possible pore sizesis discretized (binned) with values chosen between Rmin and Rmax.(3) The theoretical signal attenuation is calculated analytically foreach of these discrete radii and for each set of experimental values.This process results in a library (a matrix) of known basis valuescalculated for each experimental set. (4) The observations areassumed to result from the superposition of contributions ofsignals from multiple pores with different radii, each weightedby its relative fraction (defined by the PSD). (5) A numeric fittingprocess is applied whereby iterations include trials with differentPSDs. The solution is the PSD that gives the best fit to the experi-mental observations described in (1). The 2-D method was shownto improve the stability and reliability of the estimated PSD. It wasfurther tested experimentally on calibrated microcapillary PSDphantoms, resulting in accurate size distribution estimation [19].

In the current study we present a novel noninvasive method ofestimation of PSD in soft porous materials that considers the entiresample volume, and serves as an alternative to the traditional SEMmethod. The above-mentioned 2-D NMR method is furtherextended here to a 3-D parametric space (see the SupplementaryInformation for further details). Based on previous work [18], thisextension is predicted to significantly improve the stability and reli-ability of the PSD estimation. The 3-D method was applied on fourporous 50/50 poly(DL-lactic-co-glycolic acid) (PDLGA) bioresorbablefilms with different porosities, which were created using the freeze-drying of inverted emulsions technique. The microstructure of suchfilms, specifically the overall pore volume, pore size and intercon-nection of pores, has been shown to greatly affect the release patternof bioactive agents from such films in wound dressings, stents andbone scaffold 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-drying ofinverted 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 phase ofthe 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 organic andaqueous phases (O:A ratio = 6:1) at four different stir rates (2500,5000, 7500 and 10,000 rpm). The emulsions were then poured intoan aluminum plate and immediately frozen in a liquid nitrogenbath before placing them in a pre-cooled (�105 �C) freeze-dryer.Freeze-drying the samples overnight to remove the solventspreserved the microstructure of the emulsion-based structures inthe solid state. The different homogenization rates of the emulsion

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were expected to result in different pore size distributions, as pre-viously described [21]. Each polymer sample was cut into an 8 mmdiameter 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, the diffusion gradient duration, d = 3 ms, the mixing time,tm = 0, and the repetition time, 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 JSM76300scanning electron microscope at an accelerating voltage of 5 kV.The cryogenically fractured surfaces were Au-sputtered prior toobservation. The magnification factors used were: �200, �250,�500, �750, �1000, �2000 and �2500. SEM-based PSD estimationof the 5000 and 10,000 rpm polymers was obtained by usingImageJ (NIH, MD, USA), with several different magnification factorsand regions 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 inspected volume is typically 120 lm � 85 lm � 10 lm� 0.0001 mm3. It is worth noting that the average volume of eachpolymer sample was 75 mm3, which is 750,000 times more thanthe inspected volume in a typical SEM image. This intrinsic limita-tion of SEM-based image analysis gives rise to at least two sourcesof 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 represents 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. At the bottom of the figures are theindependently derived SEM-based PSDs. While most of the volumein Fig. 1C is of 5–10 lm pores, the majority of the volume in Fig. 1Dconsists of 20–25 lm pores. These drastic differences within thesame polymer specimen emphasize the biases created by thechoice of the FOV.

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 thatillustrates this point is presented in Fig. 2. Two cross-sectioncryo-fractographs, both taken from the 10,000 rpm polymer sam-ple using different magnifications factors (�2500 and �250), areshown, respectively, in Fig. 2A and B. Underneath each cross-sec-tion is the corresponding independently derived SEM-based PSD.Note that in Fig. 2C the PSD is narrow and revolves around 2 lm,while in Fig. 2D a new and larger size population appears around7.5 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 volumetric PSD. As previously discussed, theSEM-based image analysis leads to a filtering of the larger pores;therefore it can result in a significantly biased PSD estimation.

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 furtherdetails see the Supplementary Information), the angulardependency of the signal is presented for different gradient ampli-tudes, G (separated by a dashed vertical line). Each color in the plotindicates a different experimentally defined diffusion period, D,

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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.

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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.

D. Benjamini et al. / Acta Biomaterialia 10 (2014) 2762–2768 2765

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while circles indicate experimental data and solid lines show thetheoretical 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 totalvolume of pores within these four size ranges can provide moredetailed 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 thelarger 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 indicatednorm of the residual is 0.0035 and 0.013 for (A) and (B), respectively.

from the entire volume of the sample (rather than from 0.0001% ofit, in the case of a �1000 magnification SEM image). Such ananalysis from the entire bulk of the biopolymer sample cannot beobtained 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,compared 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 anybasic shapes, then the analysis is yet to be derived.

Moreover, pore interconnections were not modeled in thecurrent method. Like in SEM, interconnections result in fluidexchange between pores, which violates the underlying geometryassumption. This deviation further contributes to the overall

m the (A) 2500 and (B) 5000 rpm polymers. Each color indicates a different diffusionin the plot (for further details see the Supplementary Information). The squared 2-

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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.

D. Benjamini et al. / Acta Biomaterialia 10 (2014) 2762–2768 2767

estimation error. Future analysis could include an average isotropicexchange with a given rate to model such interconnection. Such anapproach would add to the complexity of the problem by introduc-ing the exchange 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 NMRmethod. Although the water-filling phase was conducted withgreat care, 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 anincreased number of averages in each scan. On the other side of

Table 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

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,u and D) should beacquired to prevent reduced stability in the estimation. The PSD’sresolution in this study was chosen according to the number ofacquisitions, and it is essentially limited by the overall experimentduration. Although the presented method improves the stabilityand reliability of the estimated PSD, its solution may still beaffected by this limitation.

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.

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

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while considering the entire sample volume. This multi-dimensionalNMR method has already been validated on a well-calibrated andcontrolled porous phantom [19], thus its stability and robustnessare 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 thepotential for clinical use (e.g., in vivo drug eluting polymerimplants structural characterization in humans). (ii) It providesinformation from the entire volume of the sample, thus eliminatingthe user’s need to choose specific FOVs, and removes bias. (iii) It isequally sensitive to all pore sizes within the sample, and does notdepend on parameters such as the 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.

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.

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.

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