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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Biomech Eng. Author manuscript; available in PMC 2010 October 1.
Published in final edited form as:
PMCID: PMC2830731



Aligned nanofibrous scaffolds hold tremendous potential for the engineering of dense connective tissues. These biomimetic micro-patterns direct organized, cell-mediated matrix deposition, and can be tuned to possess nonlinear and anisotropic mechanical properties. For these scaffolds to function in vivo, however, they must either recapitulate the full dynamic mechanical range of the native tissue upon implantation, or must foster cell infiltration and matrix deposition so as to enable construct maturation to meet these criteria. In our recent studies, we noted that cell infiltration into dense aligned structures is limited, but could be expedited via the inclusion of a distinct, rapidly eroding sacrificial component. In the present study, we sought to further the fabrication of dynamic nanofibrous constructs by combining multiple fiber populations, each with distinct mechanical characteristics, into a single composite nanofibrous scaffold. Towards this goal, we developed a novel method for the generation of aligned electrospun composites containing rapidly eroding (PEO), moderately degradable (PLGA and PCL/PLGA), and slowly degrading (PCL) fiber populations. We evaluated the mechanical properties of these composites upon formation and with degradation in a physiologic environment. Further, we employed a hyperelastic constrained mixture model to capture the nonlinear and time-dependent properties of these scaffolds when formed as single-fiber populations or in multi-polymer composites. After validating this model, we demonstrated that by carefully selecting fiber populations with differing mechanical properties, and altering the relative fraction of each, a wide range of mechanical properties (and degradation characteristics) can be achieved. This advance allows for the rational design of nanofibrous scaffolds to match native tissue properties, and will significantly enhance our ability to fabricate replacements for load bearing tissues of the musculoskeletal system.

Keywords: Electrospinning, fibrous tissue engineering, composite scaffolds, constitutive modeling, temporal properties, mechanical properties


Fibrous tissues are collagen-rich structures present throughout the musculoskeletal system that serve a variety of vital load-bearing roles. The organization of these tissues is paramount to their mechanical function, and is to a great extent dictated by the mechanical environments in which they operate. For example, those tissues that function under cyclic, near-uniaxial tension (such as flexor tendons) are comprised of collagen fibers organized in a single, predominant direction [1]. On the other hand, tissues that function in more complex, multi-axial loading environments, such as the knee meniscus [24] and the annulus fibrosus of the intervertebral disc, reveal more complex hierarchical collagen organization [5]. Despite the refined characteristics that function has imparted on the form of these tissues, traumatic injury and degeneration are common occurrences and can interrupt normal mechanical function. As a result, there remains unmet clinical need for engineered replacements for damaged or diseased native fibrous tissues.

When engineering fibrous tissue replacements, the demanding physical environment in which they will perform must be taken into consideration. Tissue engineered constructs should at minimum recapitulate the sub-failure stress-strain response of the tissue [6]. Because success in such endeavors has been limited to date, the most common clinical solution for fibrous tissue damage remains the autologous or allogeneic transfer of tissue to the defect site (for example, meniscus transplantation and bone-patella-bone autografts). However, low availability of suitable grafting tissues and high failure rates engender a need for tissue engineered solutions. To specifically address the hierarchical and structural organization of fibrous tissues, many tissue engineering strategies have focused on collagen gel-based constructs. Organization in such constructs is mediated by the traction forces that cells within the collagen gel exert against a fixed boundary, and can promote pronounced anisotropy in the forming construct [7, 8]. However, these collagen gel-based constructs remain very soft, even after long culture durations, in comparison to native fibrous tissue [9, 10]. In other work, hierarchical structure has been imparted through the use of macro-scale polymer fibers (including biodegradable polyesters and silk) to engineer fiber-reinforced constructs [1113]. These scaffolds better recapitulate the native tissue mechanical response, and have moved toward clinical implementation.

An alternative strategy that has recently become more prevalent for engineering such tissues is based on the process of electrospinning [14]. This is an old technology, first patented in the 1930s [15], and has been extensively investigated for applications such as textile and filter manufacturing [16]. Within the last decade, this process has found renewed interest for the engineering of a number of different tissues. Compared to macrofibrous construction methods, electrospinning generates nano- and micron-scale fibers, thereby providing a ready means to recapitulate the organizational features and length-scales of many collagenous tissues [17]. In its most basic form, electrospinning involves the application of a high voltage potential and resulting gradient to draw a polymer solution into thin fibers which can then be collected en masse. Numerous processing variables can be varied to fine tune the electrospinning process, and both biologic and synthetic polymers can be processed in this fashion [18, 19]. Moreover, multiple polymers can be combined in the same fiber (intra-fibrillar) [18, 20], or separate jets can be used to deliver multiple polymers to the same collecting surface [2123] to modulate the as-formed mechanical properties.

More recently, numerous groups have begun to examine the role of fiber alignment in nanofibrous scaffolds, and its potential application for fiber-reinforced tissue engineering. Aligned fibers can be formed by simply focusing deposition onto a rapidly moving surface [24]. We and others have shown that these aligned arrays mimic the structure of numerous fiber-reinforced and anisotropic tissues [17, 2528]. In our previous studies, we used electrospun scaffolds composed of poly(ε-caprolactone) (PCL), and demonstrated that multiple cell types adhere to and organize themselves into aligned communities when cultured on aligned scaffolds. Importantly, with time in culture, the organization of the cell-generated extracellular matrix (ECM) paralleled the governing fiber direction defined by the nanofibrous array [28]. However, we also observed a significant limitation in these scaffolds; surface-seeded cells have difficulty infiltrating through the small pore-sizes that result from the dense packing of aligned fibers. This slow infiltration rate results in inhomogeneous ECM deposition and incomplete cell colonization even in relatively thin scaffolds (~1mm thick) and over long culture durations (>10 weeks).

To address this issue, we developed a dual-polymer electrospinning process that enables the interspersion of a sacrificial fiber population within a dual-component nanofibrous scaffold [23]. These sacrificial fibers, comprised of water-soluble poly(ethylene-oxide) (PEO), serve as space-holders during the formation of the scaffold, and their subsequent removal provides the necessary increase in pore size to accelerate cellular ingress. Unfortunately, while removal of a sufficient fraction of sacrificial fibers enhanced infiltration, it also resulted in an overall loss in scaffold structural integrity as cell-mediated traction forces compacted the construct. Thus, to maintain scaffold integrity while still implementing pore-forming sacrificial fibers, the present work focuses on the inclusion of a more slowly eroding third fiber population. This fiber population would serve to maintain scaffold integrity initially, and then gradually erode to augment pore size and porosity as the composite evolves. Inclusion of this third fiber population would provide time-dependent characteristics in the composite scaffold, and could also be used to further refine the mechanical properties.

In addition to experimental characterization of scaffold mechanics and porosity as described above,, constitutive modeling of these structures can also provide additional insight by permitting investigations that, experimentally, may be laborious or even impossible. Constitutive models of electrospun scaffolds have varied widely in their complexity, from simple geometrically motivated linear models [17, 27, 29] to hyperelastic continuum models [26, 30, 31]. Hyperelastic models have the additional advantage of describing materials with nonlinear mechanical behaviors over large deformations. Because nonlinearity and finite deformations are functional hallmarks of many fiber-reinforced soft tissues, hyperelastic models are of great utility not only for characterizing acellular scaffolds and engineered constructs, but also for yielding comparisons of these materials with native tissue benchmarks [27, 31]. In previous work, we used a fiber-reinforced hyperelastic model to characterize the mechanics of acellular electrospun scaffolds with a single population of PCL nanofibers, and used this model to quantify the functional evolution of cell-seeded scaffolds over 8 weeks as ECM was deposited and the constructs matured in vitro. The model was validated as a predictive tool for that system, and is expanded in the present work to account for the combined behavior of multiple constituent fiber populations.

To carry out this study, we designed and fabricated a novel multi-jet electrospinning device for the production of aligned composite nanofibrous scaffolds with multiple and distinct fiber populations. Using this device, we formed a composite scaffold containing slow, medium, and fast-eroding elements, and evaluated its mechanical properties (as well as those of its constituent fiber populations). To better understand the mechanical response of these novel composites, we used a hyperelastic model to assess the full nonlinear and anisotropic response of these meshes and developed numerical descriptions of how these properties change over the time course of component degradation. We utilized data from scaffolds containing a single fiber population, coupled with a constrained mixture approach, to predict the time-dependent nonlinear tensile behavior of the evolving composite. Finally, we used this validated model to predict the mechanical response of any combination of fiber populations. This new fabrication method and modeling approach provides a means by which rational and directed design can be used to manufacture tissue-specific nanofibrous scaffolds for the engineering of dense connective tissues.

Materials and Methods

Two separate studies were performed: Study I included device and methodology development to enable fabrication and testing of multi-component scaffolds; Study II analyzed and modeled dynamic multi-component scaffolds over a nine week time course.

Scaffold Fabrication

In Study I, solutions of PCL, PLGA, and PEO were electrospun either individually or simultaneously to generate scaffolds with a single fiber population or with multiple fiber populations (Composite) , respectively. All polymers were dissolved by stirring over 18 hours at 40°C. PEO (10% w/v, 200kDa, Polysciences, Warrington, PA) was prepared in 90% ethanol while PLGA (50:50 lactic acid:glycolic acid, 22.2% w/v, 100kDa, Durect, Pelham, AL) and PCL (14.3% w/v, 80kDa, Sigma, St. Louis, MO) were each dissolved in equal parts dimethylformamide and tetrahydrofuran (DMF:THF, Sigma). Due to the undesirable mechanical characteristics of electrospun PLGA (see Results), the PLGA solution was replaced with a mixture of PCL and PLGA (termed Blend) in Study II. In study II, PCL and PEO solutions were prepared as described above, and PCL (7.2% w/v) and PLGA (11.1% w/v) were dissolved together in DMF:THF to produce the blended polymer solution (Table 1).

Table 1
Scaffold Fabrication

Electrospinning was performed using a custom device designed to focus three electrospun polymer jets from separate spinnerets towards a common, centralized rotating mandrel (Fig 1). Each solution was driven through the spinnerets via syringe pump (KDS100, KD Scientific, Holliston, MA) at 1ml/h (Study I) or 2.5ml/h (Study II) from an 18G needle that was translated (with custom fanning devices) over a 5cm distance along the vertical mandrel (which rotated at a linear surface velocity of ~10m/s). All three spinnerets were charged to +13kV and placed 15cm from the mandrel surface, which was itself charged to −2kV to enhance fiber collection. Additionally, aluminum plates were positioned at the vertices of this setup and charged to either +9kV (Study I) or +8kV (Study II) to focus the electrospun cloud so as to further aid in efficient fiber capture. In both studies, each polymer solution was electrospun individually to generate a mesh containing a single fiber population, then, all three polymers were co-electrospun onto the same mandrel simultaneously to generate multi-fiber composites.

Figure 1
Composite nanofibrous scaffolds containing three distinct fiber populations were fabricated with a custom electrospinning device


In additional studies, polymer solutions were fluorescently doped and electrospun to confirm the presence and interspersion of the three distinct fiber populations. Cell Tracker Red, 7-dimethylaminocoumarin-4-acetic acid (Invitrogen, Carlsbad, CA), and fluorescein (Sigma) were added at 0.2% w/v to solutions of PCL, PEO, and blended PCL/PLGA, respectively. Fluorescently labeled solutions were then co-electrospun for 15s onto glass cover slips affixed to the rotating mandrel. Fibers were imaged at 20× magnification using a Nikon T30 inverted fluorescent microscope equipped with a CCD camera and the NIS Elements software (Nikon Instruments, Inc., Melville, NY). Additionally, PCL, Blend, and Composite scaffolds were examined by scanning electron microscopy at each time point. Samples were AuPd sputter coated and imaged with a JEOL 6400 scanning electron microscope operating at an accelerating voltage of 10kV (Penn School of Medicine Microscopy Core Center).

Mechanical Testing

From each mat, 30mm by 5mm strips were excised in the prevailing fiber direction (Fiber) or perpendicular to this direction (Transverse). For Study 1, all testing was performed on as-formed, dry samples. In Study 2, acellular scaffolds were rehydrated and maintained in a standard culture environment (37°C, 5% CO2) for nine weeks in order to measure degradation-dependent behavior. After determining the initial dry mass, samples were UV sterilized, rehydrated in diminishing fractions of ethanol (100, 70, 50, 30%), and incubated in DMEM containing 1× PSF at 37°C until testing. For samples from both studies, four measurements of the cross-sectional area were acquired with a custom LVDT/laser system. The strips were airbrushed with black enamel to generate texture before mounting in an Instron 5848 Microtester (Instron, Canton, MA). After a nominal preload of 0.1N, t he samples were allowed 1min to equilibrate. Following this, the strips were extended beyond their yield point at a rate of 0.1% of the gauge length per second. Images of the central third of each specimen were captured at 0.5Hz for subsequent texture-correlation analysis via Vic2D to determine two-dimensional Lagrangian strain (E) (Correlation Solutions, Columbia, SC). Modulus was determined from the linear region of the stress-strain plot. Linear regressions were performed iteratively over ranges of 0.6% strain and the yield strain was demarcated when the R2 transitioned below 0.996. This strain range and R2 threshold was chosen as a conservative and reproducible method for defining the end of the linear portion of the stress-strain curve, and was maintained for analysis throughout the entire study. After tensile testing, samples were dried and reweighed to determine mass loss at each time point.

Determination of Fiber Fractions

Day 0 samples from Study II were enzymatically digested to estimate starting fiber fractions of Composite scaffolds. PCL, Blend, and Composite scaffolds were digested with 10U/ml of Pseudomonas sp. lipase (Type XIII, Sigma) in phosphate buffered saline and incubated at 37°C for 48h with agitation. After lipase-mediated digestion of the PCL component of each scaffold, samples were washed twice in distilled water before being dried and reweighed.

Constitutive Modeling of Composites

A hyperelastic fiber-reinforced constitutive model was employed to describe the tensile behavior of hydrated composite nanofibrous scaffolds in Study II. We first determined the constitutive laws for scaffolds composed of single fiber populations of Blend or PCL. These were then applied, using a constrained mixture approach, to predict the time-varying behavior of the two-component composite scaffold (after removal of PEO). Upon validation, the model was used to simulate time and composition dependent mechanics.

The composite and single component scaffolds were modeled using the constitutive theory of highly anisotropic solids as described by Spencer, in which the strain energy density function is decomposed into the sum of ‘fiber’ and ‘matrix’ functions [32].

Single Component Constitutive Laws

For each Blend and PCL scaffold, the matrix phase was described as a compressible Neo-Hookean material, while the fibers were described with an exponential law [31, 33, 34]. As detailed in Nerurkar et. al., the resulting constitutive law is given by


Where the superscript i = B, C for Blend and PCL, respectively; T is the Cauchy stress tensor, μi and υi=βi1+2βi are the two matrix parameters that characterize matrix modulus and material compressibility; γi and ξi are fiber parameters representing the fiber stiffness and the degree of their stress-strain nonlinearity; I3 = det(C) is the third invariant of the Right Cauchy Green Tensor C = FTF, where F is the deformation gradient tensor [35]; the scalar I4 is an invariant defined as I4 = a · Ca, where a is a unit vector along the fiber direction [32]. Fiber contributions were restricted to tensile stresses only (I4 = 1 for I4 < 1) [36].

Therefore, each single fiber population scaffold, Blend or PCL, was described by four scalar material parameters: μi and νi to describe the matrix phase, and γi and ξi to represent the fiber phase. The implementation of this model for single-component electrospun scaffolds was performed as described previously [31]. In brief, a least squares curve fit of the model to the transverse stress-strain data was performed at each time point to yield matrix material parameters, μi and νi. The average of the resulting values was used to fit the fiber direction stress-strain curves in order to determine the time-matched values of fiber parameters, γi and ξi. Accordingly, the four material parameter values were obtained for each component (Blend and PCL) at each time point (days 0, 7, 21, 42, 63).

Composite Constitutive Law

To model the composite scaffold mechanics, it was assumed that the composite properties were determined entirely by the constituent material parameters and the relative amounts of each constituent present, or:


where Tt is the total stress of the composite and ϕi is the mass fraction of each component. Specifically, a constrained-mixture approach was used, whereby each constituent deforms identically, according to the overall deformation of the composite, or in other words F = Fi for i = Blend, PCL. Additionally, the composite stress is the sum of constituent stresses scaled to their current mass fraction:


Conventionally, it is required that the sum of mass fractions always be unity. Although this constraint was enforced at Day 0, it was relieved at subsequent time points in order to account for the loss of intact, load-bearing fibers with degradation; mass fractions were computed at each time point as the current constituent mass normalized to the initial total mass. At Day 0, it was assumed that ϕB = ϕC = 0.5 , based upon experiments using lipase to remove the PCL component from both Blend and Composite scaffolds. From Days 7 to 63, mass fractions were approximated by assuming all mass loss of the composite (measured experimentally) was due to loss of the Blend component, while ϕC = 0.5 was maintained for all time points (see Results). The contention that PCL mass does not degrade significantly over 63 days was supported by the experimental results. The model was then validated by predicting the fiber direction stress-strain behavior of the composite scaffold at each time point using time-matched material parameters and mass fractions. For each sample, the experimentally measured 2-D deformations were input into the model and the resulting model-computed stresses were compared with experimentally measured stress. Agreement of the model predicted stress with the corresponding experimental stress was assessed to indicate the suitability of the proposed model as a full quantitative description of the nanofibrous composite scaffold [31].

Model Simulation

Upon validation, the model was used to simulate the time-varying mechanical behavior of composite nanofibrous scaffolds for a range of initial compositions. In order to approximate the time dependence of the material parameters, each parameter was assumed to vary linearly with time and linear regression were utilized. This assumption proved reasonably accurate for all time-varying parameters (see Results). The moduli of simulated composites were determined by fitting a tenth order polynomial to the model-generated stress-strain curve, and evaluating the derivative of the polynomial at E=0.05.

Statistical Analyses

For experimental data, ANOVA with Bonferroni post-hoc tests was used to make comparisons between groups. Data is presented as the mean ± standard deviation from a minimum of 5 samples for each condition and time point. The quality of model fits are reported by R2 values as well as the Bland-Altman limits of agreement (B-A, bias ± standard deviation), reported in MPa [37].



A custom multi-jet electrospinning device was successfully constructed and employed to generate single fiber population and multiple fiber population composite aligned nanofibrous scaffolds (Fig 1). Fluorescently labeled fibers demonstrated successful interspersion of discrete fibers throughout the composite scaffold. In Study I, PCL, PLGA, and PEO scaffolds were formed and tested in uniaxial tension in the fiber direction. Stress-strain profiles for each single fiber population scaffold were distinct (Fig 2A). PEO and PCL scaffolds had comparable tensile moduli while the modulus of PLGA scaffolds was ~20 times higher (Fig 2B). While PCL scaffolds exhibited a significant toe region and yielded at a higher strain (E=0.100), both PEO and PLGA scaffolds lacked toe regions and were significantly less extensible, yielding at E=0.012 and E=0.014, respectively (Fig 2C). When all three polymers were co-electrospun into a composite scaffold, the resulting mesh displayed characteristics of its constituents (Fig 2A). Composite scaffolds had a modulus intermediate to PCL and PLGA (Fig 2B) and a toe region was observed, though composite scaffolds still yielded at low strains (E=0.026) relative to pure PCL scaffolds (Fig 2C). Of note, these scaffolds were all taken from the same location on the rotating mandrel. However, when composite strips were excised from different locations along the length of the mandrel we observed a gradient in the deposition of PCL and PLGA fibers (Fig 2D). Where PLGA fibers were dominant, stress-strain profiles revealed a linear behavior with a higher modulus. Conversely, increases in the PCL fiber fraction resulted in a more pronounced toe region but a lower modulus. This suggests that care must be taken in ensuring full interspersion of composite fibers, particularly when one component has markedly higher mechanical properties than the others. We also noted that, upon hydration, both PLGA and Composite scaffolds contracted in length by ~70% and ~60%, respectively (data not shown). Due to this behavior, as well as the low yield strains of PLGA fibers, the PLGA solution was replaced with a blend of PCL and PLGA in Study II.

Figure 2
Study I: Electrospun PCL, PLGA, and PEO scaffolds have unique stress-strain profiles. When all three elements are combined, the Composite scaffold stress-strain behavior shares characteristics of each constituent

In Study II, scaffolds comprised of a single fiber population of Blend PCL/PLGA fibers could be hydrated without noticeable decreases in scaffold length or fiber morphology in SEM images (not shown). This allowed for evaluation of scaffold mechanical behavior over a time course of degradation, without the influence of complicating factors such as gross scaffold distortion. For this study, composite scaffolds were hydrated before mechanical analysis. As expected, upon hydration, PEO scaffolds dissolved completely, and so are excluded from further analysis of mechanics or mass loss. On day 0 (immediately after hydration), PCL and Blend scaffolds tested in the fiber direction demonstrated distinct stress-strain profiles (Fig 3A). As in Study I, PCL revealed a significant toe region with yield strains of E=0.115 (Fig 3B). Blend scaffolds were linear and lacked a toe region, but were extensible to higher strains (E=0.080) before yield (compared to yield at ~1% for pure PLGA scaffolds evaluated in study I). Similar to Study I, composites comprised of PCL and Blend fibers showed characteristics of the two remaining constituents (recall that PEO is removed upon hydration). Initially, composite scaffolds had moduli intermediate to PCL and Blend (Fig 3C), but lower strains at yield than both of its constituents (Fig 2B). Testing performed on transverse samples revealed the high degree of anisotropy in all three types of scaffolds as evidenced by the significantly lower moduli in the transverse direction (Fig 3D).

Figure 3
Study II: Single- and multiple-fiber population scaffold tensile behavior is modulated by composition and degradation time

After the initial day 0 hydration and testing, scaffolds were incubated in DMEM+PSF at 37°C and fiber and transverse properties as well as changes in mass were assessed on days 7, 21, 42, and 63. As observed in previous studies, the mass of pure PCL scaffolds did not diminish up to 63 days (Fig 3E, p=1.0). Paralleling the lack of mass loss, the mechanical behavior of PCL scaffolds did not change appreciably, with moduli in both the fiber and transverse directions remaining constant for the entire course of the study (Fig 3C,D, p=1.0). Interestingly, the yield strain of PCL increased with time, and was significantly higher than starting values by day 42 (Fig 3B). Contrasting the immutability of PCL scaffolds, Blend scaffolds began degrading from the outset, as indicated by the significant mass loss by day 7. Additional decreases in mass were observed at all remaining time points, cumulating to a ~40% mass loss by day 63 (Fig 3E). Degradation of these Blend fibers resulted in decreases in both fiber and transverse moduli in the scaffolds (Fig 3C,D, p<0.001). Additionally, yield strains of Blend scaffolds extended in the fiber direction increased with degradation time (Fig 3B, p<0.001).

Composite scaffolds showed time dependent characteristics as well. These scaffolds lost ~22% of their original mass upon hydration as a result of the immediate dissolution of the PEO fiber population (Fig 3E). Lipase digestion after PEO removal showed that Blend fibers made up 54.3% of the remaining Composite scaffold, while pure PCL fibers made up 45.7%. Due to the presence of Blend fibers, Composites continually lost mass for the duration of the study resulting in an additional 18% decrease in mass by day 63. As observed in Blend scaffolds, Composite scaffolds showed temporal changes in mechanical properties, with both fiber and transverse moduli decreasing in a time-dependent manner (Fig 3C,D, p<0.001). Contrasting Blend behavior, the fiber-direction modulus of Composites decreased dramatically by day 7 to levels well below PCL and Blend values (p<0.001), then appeared to stabilize towards later time points. As with PCL and Blend scaffolds, Composite yield strains increased with time (p<0.001) approaching E=0.122 by day 63.


The constitutive model was successfully fit to transverse PCL and Blend constructs at all time points to yield matrix constants μi and νi (Fig 4B,C and Table 2), with average R2=0.986 and B-A −0.002±0.004 MPa. As an example, model fits to experimental data of day 0 samples tested in the transverse direction are shown in Fig 4A. The Blend matrix parameter μB decreased linearly with time by up to 2.5-fold on day 63. No significant changes were observed in μC, νC or νB with time. The constitutive model also successfully fit Blend and PCL samples along the fiber direction to yield fiber parameters γi and ξi with average R2=0.988 and B-A −0.018±0.055 MPa (Fig 4E,F). Model fits to fiber direction experimental data of day 0 samples are shown in Fig 4D. The fiber modulus parameter γi decreased approximately 2-fold with time for Blend samples, but did not change with time for PCL. ξC increased slightly by Day 63, and ξB was zero at all time points.

Figure 4
Characterization of single-fiber population (PCL and Blend) scaffold tensile behavior with a hyperelastic fiber-reinforced constitutive model
Table 2
Model Validation

Having determined the time-varying material parameters for each single fiber population scaffold, we next used this information to predict the behavior of the composite scaffold. Accurate prediction of the composite scaffold mechanics would indicate that the model is valid for this application. The model was successfully validated at each time point, using only the deformation, the relative amount of Blend to PCL fibers remaining, and the material parameters from each time point to predict the Composite scaffold stress under uniaxial extension in the fiber direction (Fig 5, average R2=0.997 and B-A −0.013±0.053 MPa, Table 2). Although at Day 0 the model under-predicted stresses, it provided strikingly close predictions of experimental stress-strain curves at each subsequent time point (Table 2).

Figure 5
Material parameters from single-component scaffolds successfully predict Composite scaffold behavior

Using the validated model, we next predicted the modulus and curvature of theoretical scaffolds consisting of any combination of PCL and Blend at any time point. The model simulation demonstrated that the composite scaffold modulus can be tuned between 20 and 45 MPa, simply by varying the initial content of Blend or PCL (Fig. 6). Additionally, the composite mechanics are increasingly sensitive to degradation with time as the Blend content is increased. Finally, by varying the balance between Blend and PCL fiber populations, the model demonstrated that the magnitude and the nonlinearity of the composite stress-strain behavior can both be modulated.

Figure 6
Simulation of Composite scaffolds of any formulation


Electrospun nanofibrous scaffolds hold great promise for the tissue engineering of fibrous elements of the musculoskeletal system. The electrospinning process is inexpensive, straightforward, and easily modified to produce scaffolds with a range of mechanical and degradation characteristics [18, 38]. Furthermore, the alignment of nanometer- to micron-scale fibers engenders structural and mechanical anisotropy in scaffolds comparable to that of many soft tissues [17, 27, 28, 39]. However, the mechanical behavior of native tissues is complex, with most showing not only pronounced anisotropy but also non-linear stress-strain profiles [40]. Both ‘toe’ and ‘linear’ properties are critical for normal tissue response; ‘toe’ region properties are essential for flexibility, while ‘linear’ region properties resist extreme deformations at high loads. These non-linear properties are dependent on the complex interplay of numerous tissue constituents, including fibers (e.g., collagens), matrix (e.g., proteoglycans and water), and fiber-matrix interactions (e.g., cross linking molecules) [41, 42].

While the target tissues are complex, most electrospinning efforts to date have relied upon the use of a single polymeric fiber population for scaffold formation. The number of polymers that can be electrospun is increasing at a rapid rate and these fibers show a diverse array of mechanical properties, including some with non-linear behaviors. However, it is somewhat unreasonable to suppose that a single fiber population can recapitulate the intricate mechanical behavior of native tissues. This would therefore limit scaffold applications to non-load bearing situations, or rely on cell-mediated ECM deposition to provide tissue specific functionality. We have shown that, with extended periods of in vitro pre-culture, cells seeded onto aligned scaffold can improve functional properties and impart increasing non-linearity [31, 43]. An ideal scaffold would, however, match the native tissue properties over the entire time course of maturation. We hypothesized that such complex features might be achieved by combining multiple fiber populations, each with distinct mechanical characteristics, into a single composite nanofibrous scaffold.

The particular polymer set chosen for this work are commercially available, widely applied, and are generally considered to be biocompatible upon implantation. Previous work from our group identified PCL as a suitable electrospun polymer as it is distensible to high strains before yield, exhibits a toe region akin to that of fibrous tissues, and is stable in culture for long durations [38, 43]. However, due to the dense packing of nanofibers in aligned PCL scaffolds, pore size is limited and thus cell infiltration and matrix deposition is slow and inhomogeneous [28, 31]. To increase porosity of these scaffolds, we developed methods for the incorporation of sacrificial, pore-forming fibers [23]. In that study, it was observed that removal of increasing fractions of sacrificial fibers correlated linearly with decreases in scaffold properties. Since cell infiltration was enhanced only at >50% sacrificial fiber content, a 50% decline in initial scaffold properties would be required to hasten colonization. Furthermore, because dissolution of the sacrificial PEO fibers is ‘all-or-none’, these mechanical changes occur very rapidly, and so cell-mediated contraction can result in distortion of the scaffold shape.

To specifically address this issue, we sought to include a stiffer, slower degrading fiber population in these composite structures. Based on previous reports in the literature, PLGA was chosen for its high stiffness and moderate degradation rate. In Study I, PLGA was successfully electrospun and incorporated into composite scaffolds. Single fiber population PLGA scaffolds were very stiff (~20-fold higher than PCL), however, two significant limitations were observed. First, consistent with previous reports [38], pure PLGA scaffolds could only be deformed by ~1% before succumbing to permanent deformation and/or failure. Thus when PLGA was electrospun into the Composite scaffold, the resulting yield strain was reduced by a factor of four, to E=0.025. As most fibrous tissues experience deformations on the order of 5–10%, we considered this attribute to be a serious deterrent to using pure PLGA fibers. Additionally, and through a mechanism not yet fully understood, PLGA scaffolds underwent severe contraction and thickening immediately upon hydration, precluding a longitudinal study of mechanical properties with degradation.

Previous work b y Barnes and co-workers had demonstrated that inelastic polymers (such as PLGA) could be made more elastic with the inclusion of PCL [18]. Thus, in Study II, we utilized a blended solution of PLGA and PCL to introduce temporal characteristics to the composite. The modulus of pure Blend scaffolds was significantly lower than that of pure PLGA, though its yield strain (~8%) was markedly higher. These changes are possibly due to alterations in crystallinity within each fiber strand, though this was not assessed in the current study. Blend scaffolds could be hydrated without the gross distortion, as had been observed for pure PLGA fibers. Interestingly, removal of the PCL component of Blend fibers on day 0 (via lipase digestion) caused the remaining PLGA portion to contract, confirming a secondary role of PCL as an intra-fibrillar stabilizer (not shown). With this Blend component, we evaluated the temporal characteristics of composite scaffolds. Instantaneous removal of PEO from the composite resulted in ~22% mass loss upon hydration. Conversely, Blend fibers (formed into single component scaffolds) degraded slowly over nine weeks, with corresponding decreases in mechanical properties. Composite scaffolds containing Blend populations showed similar time-dependent decreases in mechanical properties, while pure PCL scaffolds did not change, suggesting that these dynamic characteristics arise from the degrading Blend component. The mechanism by which Blend scaffolds (or fibers) degrade was not assessed. While the idealized mechanism shown in Fig 1B suggests degradation resulting in complete fiber removal, Blend fibers may undergo scission and complete removal or may experience internal changes that leave the fiber present but in a weakened state. SEM imaging over the time course did not reveal obvious structural changes, although this may be an inherent limitation of the 2D imaging modality. The specific mode of degradation of the Blend fiber population, and its influence on scaffold porosity, will be important to characterize in future studies.

To better understand and predict the complex behaviors of nanofibrous scaffolds, which are further compounded when multiple fiber populations are combined, a hyperelastic constitutive model was employed. The model fit single fiber population Blend and PCL data well, despite the distinct stress-strain profiles of each. As evident from experimental results, PCL was nonlinear along the fiber direction, while Blend was mostly linear. The model reflected this, with a significant difference found between ξC and ξB. Without applying any constraints, fits to Blend along the fiber direction invariably resulted in ξB = 0, suggesting that the parameter values obtained were unique results of the curve-fits, and thus the physical interpretation of these parameters were preserved. The model also described time-varying mechanics of the PCL and Blend scaffolds, accounting for degradation through changes in the material parameters. Degradation of Blend scaffolds was mirrored functionally by a significant decline in both the matrix (μB) and fiber (γB) terms. However, PCL, which demonstrated negligible mass loss and did not change in modulus, did not show changes in either μC or γC. The nonlinearity parameter, ξC, increased slightly with time.

We next validated the model by combining the constituent polymer parameters into a mixture model for the Composite scaffold. Despite slightly underestimating stresses at the initial time point, the model provided very good approximations of the stress-strain behavior of Composite scaffolds at all subsequent stages of degradation. The poor prediction at day 0 may suggest that, initially, the Composite does not behave as a true mixture. This may be due to transient, complex behaviors such as fiber-fiber welding or sliding, which diminish with degradation. Although homotypic fiber-fiber interactions are represented by the matrix phase, heterotypic fiber-fiber interactions, like those present in the composite, are not accounted for in the model. The experimental data may underscore this point, in that the fiber to transverse modulus ratio for PCL was 10:1, while for the Blend it was only 3:1. It has previously been shown that small changes in solvent or environmental conditions can alter the degree of fiber-fiber welding that occurs with fiber deposition, changing tensile properties by as much as 4-fold [44]. Nevertheless, the excellent prediction of composite behavior for day 7 through 63 of incubation demonstrates that the model not only fits curves, but that it represents a true biophysical description of static and time-varying mechanics of the composite material.

With the validated model, the complete range of possible Blend and PCL combinations was simulated. This simulation demonstrated that the magnitude and time-dependence of Composite scaffold mechanics can be modulated in a predictable fashion by altering the initial composition. Simulations also showed that it is possible to tune not only linear region modulus (Fig 6A), but also the profile of the stress-strain curve. For instance, introducing an increasing fraction of PCL fibers to the Composite reduces the modulus, while conferring nonlinearity to the overall material behavior. This model result is consistent with experimental observations of Study I and II (Fig 2D). Because many fiber reinforced soft tissues are subject to physiologic deformations below the transition strain, it is important to implement a method for scaffold design that incorporates full material nonlinearity, and not only linear region metrics such as a single modulus value [6].

Taken together, this work represents a significant advance in the formulation of nanofibrous scaffolds for load bearing applications, and sets the stage for further advance. For example, it will be of great value to characterize the full elastic behavior of a wide collection of polymers. Model parameters from each would be integrated into a “functional library” that, coupled with the specific metrics taken from a tissue of interest, could be used to determine the exact composition and combination of fiber populations that would most closely reproduce the desired stress-strain profile. Such techniques can also define polymers that are not suitable for certain applications. For example, the polymer set employed here is not likely to be useful when rigorous load bearing is required at the time of implantation. The linear modulus of the Composites generated in this study cannot exceed 45MPa, a value far below that of many fiber-reinforced tissues. A stiffer, more slowly degrading element would be ideal as it could withstand physiologic loading and at the same time provide structural support to the construct, as other more rapidly eroding elements vacated the scaffold (in order to foster cell infiltration and matrix elaboration). We have recently made progress towards this goal with the electrospinning of select elements of a degradable poly(β-amino ester) library spanning a wide range of mechanical and degradation profiles [45], and new elastomeric and hydrolytically degradable polymers [46]. Combining these new polymers with rigorous mechanical testing and validated predictive models may result in improved scaffolds for implantation. This approach represents a novel direction in the rational design and fabrication of nanofibrous scaffolds for the repair or replacement of dense connective tissues.


This work was funded in part by the Aircast Foundation, a pilot grant from the Penn Center for Musculoskeletal Disorders (RLM, NIH AR050950), the National Institutes of Health (RLM and DME, NIH EB02425), and a Graduate Research Fellowship from the National Science Foundation (BMB). The authors also gratefully acknowledge Ms. Giana Montero for her superb technical assistance.


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