Original Article

Cellular Automata Simulation of Osteoblast Growthon Microfibrous-Carbon-Based Scaffolds

Jarema S. Czarnecki, MS,1,2 Simon Jolivet, MS,1 Mary E. Blackmore, PhD,3,4

Khalid Lafdi, DSc, PhD,1,2 and Panagiotis A. Tsonis, PhD2,5

The objective of this study was to investigate the use of three fibrous carbon materials (T300, P25, and P120)for bone repair and develop and validate theoretical and computational methods in which bone tissue regen-eration and repair could be accurately predicted. T300 was prepared from polyacrylonitrile precursor while P25and P120 fibers were prepared from pitch, both common fiber precursors. Results showed that osteoblast growthon carbon scaffolds was enhanced with increased crystallinity, surface roughness, and material orientation. Forunidirectional scaffolds at 120 h, there was 33% difference in cell growth between T300 and P25 fibers and 64%difference between P25 and P120 fibers. Moreover, for multidirectional fibers at 120 h, there was 35% dif-ference in cell growth between T300 and P25 fibers and 43% difference between P25 and P120 fibers. Resultsshowed that material alignment was integral to promoting cell growth with multidirectional scaffolds having thecapacity for greater growth over unidirectional scaffolds. At 120 h there was 24% increase in cell growthbetween unidirectional alignment and multidirectional alignment on high-crystalline carbon fibers. Ultimately,data indicated that carbon scaffolds exhibited excellent bioactivity and may be tuned to stimulate uniquereactions. Additionally, numerical and computational simulations provided evidence that corroborated exper-imental data with simulations. Results illustrated the capability of cellular automata models for assessingosteoblast cell response to biomaterials.

Introduction

Currently, many researchers are working to developartificial tissues and organs for repair or replacement of

damaged or diseased tissue. Groups have explored the use ofbiomaterials as vehicles for tissue repair and regenerationbut results seem to present a variety of in vitro and in vivoresponses, indicative of high variability in material design.1–3

This underlines the challenges that are still present. Lim-ited availability of donor tissue, lack of feasible alternatives,and high potential for patient rejection are critical issues thatthe healthcare industry has faced in the past.4 Nevertheless,these challenges have served as a catalyst for innovativeresearch and continue to lead to new technologies, morerecently, for simple tissue types.2,3 However, to date, thereare many shortcomings.4 Additionally, the development ofmore complex structures that may mimic the properties ofnative tissues such as tendon or bone has been unsuccess-ful.5 Current limitations to understanding the relationshipbetween the biological environment (physical and chemical

response) and material properties impede success. Thestructure of the material, its physical and surface properties,and the biological response are all critical issues that governbiomaterial performance.

In the past two decades, many materials have been exploredas substrates for tissue repair and regeneration.6–11 Biode-gradable polymers are often limited to applications where theneed for high mechanical strength and rigidity is minimal.12,13

Studies have also shown that because polymer materials tendto degrade, they may yield a negative biological response.14

In some cases, degradation leads to implant loosening, whichthen increases the chance of catastrophic failure. Conversely,groups have shown that biodegradable materials may reducethe potential for scar tissue formation and inflammation. Re-searchers have attributed this behavior to contact durationbetween biomaterial and tissue.3,15,16 These results supportthe need for superior materials that enhance bioactivity,maximize cell integration, and support high loads.

Carbon-based materials may be ideal materials for bio-mechanical applications where high strength is required.

1Carbon Research Laboratory, UDRI Carbon Group, Department of Mechanical Engineering, University of Dayton, Dayton, Ohio.2Center for Tissue Regeneration and Engineering (TREND), University of Dayton, Dayton, Ohio.3Center for Tissue Innovation & Research, Dayton, Ohio.4Boonshoft School of Medicine, Wright State University, Dayton, Ohio.5Department of Biology, University of Dayton, Dayton, Ohio.

TISSUE ENGINEERING: Part AVolume 00, Number 00, 2014ª Mary Ann Liebert, Inc.DOI: 10.1089/ten.tea.2013.0387

1

Carbon-based materials, such as carbon fibers, carbon na-nofibers, and carbon nanotubes, are a subset of syntheticmaterials that have been incorporated into high-performancematerials, such as thermal barriers and structural compositeshells. The attractiveness of this material subset stems fromwide range of mechanical properties, the size and shape ofthe materials, and their processing feasibility.

Several groups have investigated the biocompatibility ofcarbon materials and have shown promising results. Re-searchers have explored carbon-based materials as biologi-cal implants, drug-delivery vehicles, and biosensors.17–26

Results from these studies illustrated the potential advan-tages of carbon materials. The most significant advantagesinclude the following: (i) high biocompatibility, (ii) repro-ducible properties, (iii) tunable geometric and surfacecharacteristics, (iv) availability, and (v) no communicabledisease transmission. Advanced processing techniques pro-vide tunability at the micro- and nanoscale. For example,carbon fiber tensile strength may be varied from low to hightensile strength (2.0–4.5 GPa) and stiffness may also bevaried from low to high elastic modulus (50–450 GPa).27

T300 carbon fibers are commonly prepared using polyacry-lonitrile (PAN) precursor materials. This is a high-strength,high-modulus fiber with increased interlaminar shear strength.P25 and P120 carbon fibers are prepared from pitch-basedprecursor. The steps to prepare fibers are common among allgroups.27 P25 fibers are low-strength and -modulus fiberswhereas P120 fibers are commonly heat treated to increasestrength and modulus. Research groups have also demon-strated that the diameter of the fibers seems to influence celladhesion; cells tended to attach better on fibers of smallerdiameter.28 Moreover, cell attachment and cell growthseemed to be inhibited by decreased crystallinity but en-hanced by higher grain and fiber orientation.29 It was alsoshown that porous and amorphous fibers performed well inmedical applications. These fibers enabled more effectivegrowth of cells and formation of connective tissues withinthe structure of a scaffold.29

As implant and scaffold constructs, carbon-based materialshave also been shown to support cell growth.30,31 Raw, un-modified carbon fibers have been explored as surgical implantsfor facial repairs in dogs32 and in cartilage lesions.33 Carbon-fiber-reinforced composites have also been explored as alter-native bone implants24,34 and intervertebral cages.35 Preliminarydata have indicated that there is a case for carbon-basedmaterials to be utilized as tissue substrates. Nonetheless, thedata from these studies did not describe an intimate interac-tion between material and tissue. Specifically, while showingthat carbon exhibited biocompatible properties and supportcell growth, investigations did not explore an in-depth ma-terial characterization.

An alternative benefit of carbon-based materials is thatproperties may be easily manipulated by tuning both pro-cessing and treatment techniques. Various heat treatmentprocesses may be performed to alter crystal structure.27,36

Carbon surface properties may be altered by gas or chemicaltreatment.37 These studies are critical because evidencesuggests that surface properties play an integral role in cellattachment and proliferation.38 It has been previously shownthat the surface topography directly influenced the attach-ment of bone-forming cells as well as their growth. Thisinfluence has been explored on titanium and some of its

alloys, such as Ti6Al4V, and results indicated that osteo-blasts seemed to prefer rougher surfaces; however, this wasnot investigated on carbon-based materials where resultsmay differ from reported data.39–41

Mathematical modeling has been a fundamental toolfor understanding behavior in a variety of applications.42,43

One of the most established math models is the popula-tion equation. It is a simplified version of what is generallyknown as the logistic equation.44 A significant factor of thismodel is that both a birth and a death occur within the sametime step. Additionally, similar to the logistic equation, thisdifferential equation models a population density but adds acarrying capacity or limiting factor, which controls themaximum density or population by capping how much it cangrow.45

An alternative model, the Malthusian model, is one of theoldest models developed to predict population growth. De-spite the model being quite simple, it has provided a solidfoundation for the development of several additional mod-eling techniques. However, the Malthusian model neglectsthe fact that after long periods of time, populations of bio-logical communities tend to reach a form of ‘‘steady state’’in which significant changes within the population no longeroccur, unless a major environmental change is encountered.On the other hand, a different approach to understandingpopulation theory is known as the Lotka–Volterra model.This model provides the ability to simulate how variousspecies interact.46

Lastly, a strong predictive technique that has been im-plemented in many biological applications is cellular auto-mata (CA) modeling. CA modeling is a dynamic systemthat consists of a set grid of ‘‘cells.’’ Each ‘‘cell’’ has a finitenumber of states that are discrete. The state of a ‘‘cell’’ attime, t, is dependent upon the states of the cells that sur-round it, also called the neighborhood.47 The rules of a CAprogram are analogous to initial conditions or boundaryconditions, in that they determine how each cell changes itsstate over time. Since its evolution, CA has been useful instudying various applications, including the behavior ofdifferent gases, the crystallization process, forest fire prop-agation, urban development, erosion, particle aggregation,and the Lattice–Boltzmann models for fluid dynamics. In allof these applications, the developed models strongly corre-lated to experimental data.48

This study investigated the use of three microfibrous-carbon-based materials (T300, P25, and P120) as substratesfor tissue growth. Additionally, it incorporated the devel-opment of tools that may support scaffold design. Specifi-cally, this study explored (i) the effects of varying materialproperties: crystallinity, orientation, and surface roughnessof fibrous carbon scaffolds on cell response, and (ii) theability to model the effects of varying the material proper-ties: crystallinity, orientation, and surface roughness, in or-der to develop an additional tool for understanding growthon carbon scaffolds.

Materials and Methods

Materials

Three types of carbon-based fibers were investigated:T300 (PAN-based carbon fibers; Textile Technologies In-dustries), P25, and P120 (pitch-based carbon fibers). The

2 CZARNECKI ET AL.

materials were heat treated at 200�C to remove the polymersizing and 100 mg of fibers was utilized for each well. Thefibers were cut into 25-mm lengths and oriented in twoconfigurations: unidirectional and multidirectional. Micro-fibers were oriented in respective configurations and fixedusing adhesive tape. The samples were then cut to shape.The samples were placed in six-well tissue culture plates(BD Falcon). The study was repeated three times with asample size of six wells per fiber type.

Material characterization

Environmental scanning electron microscopy (ESEM)was used to examine sample morphology. X-ray diffraction(XRD) technique was utilized to determine the crystallo-graphic structure of the carbon fiber scaffolds. An Ultima III(Rigaku) was used in wide-angle mode with Cu K alpharadiation to determine the interplanar spacing (d002) and theaverage crystallite size (Lc) of carbon. XRD spectra wereobtained to determine material crystallinity and crystal di-mensions (Fig. 3). The interlayer spacing d002 was calcu-lated using Bragg’s equation (1):

d¼ k2 sin (hc)

(1)

where 2hc = 26�, h being the scattering angle, and k theX-ray Cu radiation wavelength (0.154059 nm). The crys-tallite width La for the (100) plane and the crystallite heightLc for the (002) plane were calculated with the Scherrerequations (2) and (3)49:

Lc¼0:9k

C cos (hc)(2)

La¼1:84k

B cos (ha)(3)

Where hc and ha are the scattering angles (2hc = 26�,2ha = 44�), and C and B are the full-width half maximum(FWHM) (in radians) for each angle. These equations arecommonly used to evaluate material properties. Results arepresented in Table 1. Raman spectroscopy (RAMAN) hasbeen widely used as a tool for the analysis of material

structure: crystallite size and orientation. Crystallite size, La,was calculated using Knight’s empirical formula (4)50:

La¼4:35

LD=DG

(4)

with LD and LG representing the intensities of the disor-der peak D (1360 cm - 1) and graphite peak G (1580 cm - 1),respectively. Atomic force microscopy (AFM) was utilizedto determine the nanoscale surface topography of carbonfiber scaffolds. Multiple areas were scanned (at 4 and225mm2) and results were averaged to determine averagesurface roughness (Sa) of carbon materials.

Cell culture

Primary human osteoblasts hFOB 1.19 (ATCC 11372)were maintained in culture with Dulbecco’s modified Eagle’smedium with F12 (Sigma Aldrich) supplemented with 5%(v/v) fetal calf serum, 0.02 M of N-2-hydroxyethylpiperazine-n¢-2-ethanesulfonic acid (HEPES) buffer, 2 mM of glutamine,0.5 mM of sodium pyruvate (Atlanta Biologicals), 2.5 mM ofl-glutamine (Invitrogen), and 1% penicillin/streptomycin(100 U/100 mg/mL; Gibco BRL). Cells were incubated at37�C and 5% carbon dioxide (CO2) with 100% humidity.

Osteoblast viability

Approximately 20,000 cells were seeded on microfiberconstructs and maintained for a period of 24 h to supportadhesion. Cell viability was assessed at 24, 72, and 120 husing WST-1 assay (Roche Scientific). The tetrazolium salt2-(4-iodophenyl)-3-(4-nitrophenyl)-5-(2,4-disulfophenyl)-2H-tetrasolium, better known as WST-1, was used to quantifyviable osteoblasts in culture. WST-1 reagent was added to 24-well plates in a 1:10 dilution of WST-1 solution to media andwas incubated for 3 h. Photometric quantification of viablecells was performed by measuring absorbance at 450 and690 nm using a microplate reader. Cell proliferation wasmeasured as a function of absolute absorbance values (ab-sorbance at 450 nm - absorbance at 690 nm). Osteoblast growthin wells without scaffolds was used as a positive control forgrowth while scaffolds without seeded cells were used asbackground controls. Nonspecific absorbance from mediaand scaffold samples was subtracted from absorbance

Table 1. Environmental Scanning Electron Microscopy Data

of Carbon Fiber Diameters (D) Imaged at 10,000 ·

ESEM XRD RAMAN AFM

d (nm) d (A) Lc (nm) La (nm) FWHM Ratios (LD/LG) La (nm) Sa (nm)

T300 7.43 3.491 1.794 2.836 3.538 0.824 3.257 30.62P25 9.27 3.480 2.154 3.361 2.575 0.745 5.847 85.15P120 8.73 3.376 13.59 19.36 0.588 0.186 27.35 97.11

XRD data reporting interlayer spacing (d-spacing), crystallite size (Lc and La), and FWHM for T300, P25, and P120 fibrous carbonscaffolds. The theoretical minimum interlayer spacing (d) for pure graphite is equal to 3.35 A. RAMAN results reporting peak ratio, LD/LG,of the intensities of the disorder peak (LD) and the graphite peak (LG) and crystallite size, La, for T300, P25, and P120 fibrous carbonscaffolds. RAMAN can be used as a comparative tool to XRD. Raman spectroscopy may be used as a comparative tool to XRDspectroscopy. AFM analysis reporting average surface roughness, Sa, for T300, P25, and P120 fibrous carbon scaffolds.

AFM, atomic force microscopy; ESEM, environmental scanning electron microscopy; FWHM, full-width half maximum; RAMAN,Raman spectroscopy; XRD, X-ray diffraction.

CARBON SCAFFOLDS FOR TISSUE REPAIR AND RECONSTRUCTION 3

readings. Osteoblast density was correlated to absorbance bysequential serial dilutions of osteoblast cells and measuringabsorbance after 24 h. Absorbance values were comparedwith control values and related directly to cell viability.

Morphometric analysis of osteoblastgrowth on scaffolds

Osteoblast morphology was characterized after 120 h ofcell culture on scaffolds using fluorescent microscopy.Samples were rinsed twice with sterile phosphate-bufferedsaline (PBS) to remove debris. Cells were then fluorescentlylabeled with 20 mM rhodamine phalloidin to identify poly-merized actin (Invitrogen) and 20 mM DAPI nuclear coun-terstain (Invitrogen) to identify the cell nucleus. Scaffoldswere rinsed in PBS to remove excess stain. Cell fluorescenceand morphology were characterized at a magnification rangeof 10 · to 40 · .

Numerical modeling

The numerical model developed in this study is based on twodifferent modes of modeling. The first was based on a Lagrangepolynomial (5) and the second, an exponential function (6). Thenovelty in these models was that the model basis its response asa function of material properties. The coefficients of thesemodels were calculated based on experimental evaluation ofcell growth. The coefficients A1, B1, and C1 for model 1 andA2, B2, and C2 for model 2 were plotted as functions of thescaffold properties: the interlayer spacing d (crystallinity), theFWHM (orientation), and the average Sa (surface roughness).Each coefficient was based on which property exhibited thegreatest change in growth rate.

Model 1 : #cells1(t)¼A1(d)t2þB1(FWHM)tþC1(Sa) (5)

Model 2 : #cells2(t)¼ (B2þC2)(Sa)eA2(d)t (6)

with Xy(z)¼A¢yz2þB¢

yzþC¢y where X 2 (A, B, C), y 2 1, 2

and z¼fd if X 2 (A), Sa if X 2 (B, C)g

Computational modeling of osteoblastgrowth in two dimensions

The current model is based on CA principles of locationevents and specified rules to control response (Fig. 1). Themodel developed in this study uses traditional CA pro-

cesses utilized by other authors.51–55 However, the currentmodel also included the response due to material properties,porosity, architecture, and biological factors. The CA modelwas developed on a square lattice on the x–y plane. Thedistance between the lattice points was about 8mm, assumedto be the diameter of the carbon fiber as well as the ap-proximate diameter of an osteoblast.56 Each lattice site onlyoccupied one state at time t; thus, it can be empty, occupied,or blocked. Each cell in question has a local neighborhoodof eight other cells (s1–s8). After proliferation, another os-teoblast will occupy the daughter cell (snij) as shown in thebasic form of a CA set (Fig. 1).

Osteoblast growth on carbon scaffolds was modeled usingcharacterized parameters (crystallinity, orientation, androughness) as coefficient variables. These coefficients con-trolled the response of osteoblasts on biomaterials. The effectsof crystallinity, orientation, and roughness on cell growth weregraphed to determine a correlation between materials and cellresponse as well as growth kinetics. The response equations,with R2 values, for each effect were determined and were usedin the model response algorithm. Additionally, these equationswere then used as model parameters for determining the re-sponse coefficients (A1, B1, C1, and A2, B2) in both poly-nomial and exponential models, respectively. Following thisanalysis, cell growth parameters—cell splitting, maturation,and cell death—were combined with the current model anddata were compared with experimental results. Matlab� soft-ware package was used to develop all algorithms and runsimulations.

Statistical analysis

Statistical analyses were performed using SPSS Statistics19 Software Package from IBM. All experimental resultswere statistically evaluated using one-way analysis of var-iance, with p < 0.05 indicating significant differences amongexperimental groups. Post hoc, multiple-comparison analy-ses were also performed using the Tukey–Kramer test.

Results

Material properties

ESEM characterization (Fig. 2) suggested that all carbonfibers—T300, P25, and P120—were not statistically differ-ent, minimizing variability (Table 1). These materials werechosen to compare properties: crystallinity, orientation,roughness, and alignment. XRD analysis suggested that

FIG. 1. Cellular automata modeldescription with possible daughter-state positions. The distance be-tween the centers of each staterepresents the approximate diame-ter of the fiber material as well asthe diameter of an osteoblast. Srepresents the probability for adaughter cell to be located in eachproposed location. Color imagesavailable online at www.liebertpub.com/tea

4 CZARNECKI ET AL.

there was a distinct difference in crystallinity betweencarbon fibers. The P120 scaffolds displayed a sharp peakaround 26 degrees that is indicative of high crystallinity(Table 1 and Fig. 3). The interlayer d-spacing for P120 wascalculated to be 3.376 A (Table 1). The size of the crys-tallite, Lc and La, for P120 scaffolds was between eight andfive times larger than T300 and P25 fibers, respectively. P25fibers displayed higher crystallinity, compared with T300,with an interlayer d-spacing of 3.480 A and crystallite size,Lc and La, of 2.154 and 3.361 nm, respectively (Table 1).T300 fibers exhibited the lowest crystallinity, with d-spacingand crystallite size, La and Lc, values of 3.491 A, 1.794, and2.836 nm, respectively (Table 1). Data from RAMANspectra indicated a similar trend in crystallinity (Table 1).Graphical illustrations of RAMAN spectra in Figure 4 de-pict the D and G peaks. P120 displayed the largest crystallitesize, with a value of 27.35 nm. P120 was followed by P25and T300, where values of 5.847 and 3.257 nm were cal-culated, respectively. AFM was used to determine the na-noscale surface topography of fibrous materials (Fig. 5). TheAFM measurements of the fiber roughness revealed that P25and P120 displayed comparable surface topography andwere not statistically different from one another. AFM re-sults indicated that the surface roughness of P120, P25, andT300 was 97.11, 85.15, and 30.62 nm (Table 1 and Fig. 5).

Osteoblast attachment and proliferation

Cell viability studies, using WST-1 absorbance assay,were conducted to assess osteoblast attachment and prolif-

eration on fibrous carbon scaffolds. Two different configu-rations were assessed: unidirectional and multidirectional.All three fibrous carbon materials (T300, P25, and P120)displayed a strong capacity for attachment after 24 h and cellgrowth throughout 120 h (Fig. 6). Specifically, at 24 h, P120scaffolds displayed significantly higher absorbance ascompared with both T300 and P25 scaffolds, indicatinghigher osteoblast adhesion on P120 (Fig. 6). WST-1 assayresults also demonstrated marginal differences in osteoblastgrowth on both P25 and T300 scaffolds over 72 h (Fig. 6).T300 scaffolds displayed the lowest capacity for cell growththroughout 120 h (Fig. 6). Data were curve fit using bothpolynomial (Fig. 7) and exponential (Fig. 7) modes to de-termine growth rate kinetics. Results indicated that thepolynomial fit provided a more accurate determination, ascompared with the exponential mode, which would be ex-pected (Fig. 7). P120 scaffolds displayed the highest rate ofcell proliferation followed by P25 and T300 (Fig. 7). Celldensity correlations indicated that, at 120 h, on both unidi-rectional and multidirectional configurations, P120 scaffoldsdisplayed the greatest capacity for cell growth. Specifically,unidirectional configurations displayed 169% and 92% morecells compared with T300 and P25, respectively (Fig. 6).Additionally, multidirectional configurations displayed 120%and 54% more cells compared with T300 and P25, respec-tively (Fig. 6).

Osteoblast attachment and proliferation

Cell morphology analysis revealed concentrated growthon the carbon fiber axis and fiber junctions (Fig. 8), as is

FIG. 2. Environmental scanningelectron microscopy imaging ofcarbon fiber diameters imaged at10,000 · . (A) T300, (B) P25, and(C) P120.

FIG. 3. X-ray diffraction (XRD) analysis of fibrous car-bon scaffolds: T300, P25, and P120. Color images availableonline at www.liebertpub.com/tea

FIG. 4. RAMAN spectroscopy analysis of fibrous carbonscaffolds: T300, P25, and P120. Raman spectroscopy maybe used as a comparative tool to XRD spectroscopy. Colorimages available online at www.liebertpub.com/tea

CARBON SCAFFOLDS FOR TISSUE REPAIR AND RECONSTRUCTION 5

evident by the linear growth. Multidirectional scaffoldsexhibited a high concentration of cells around fiber junc-tions, suggesting that the availability of surface area pro-moted cell movement on scaffolds. Osteoblast migration onunidirectional configurations was predominately along thelength of the carbon fiber. Studies suggested that migrationfrom fiber to fiber was less common on unidirectional fiberscompared with multidirectional scaffolds (Fig. 8). Multi-directional configurations displayed greater areas of highcell density (Fig. 8).

Computational modeling of osteoblast growthusing two-dimensional CA simulations

The use of computational modeling was explored as a toolfor predicting cellular behavior and optimizing scaffolddesign. The ability to understand cell proliferation, move-ment, as well as the constituents of the tissue at any giventime may improve biological testing and expedite bioma-terial preparation. Additionally, by incorporating additionalparameters into the computational model, researchers maygain a more in-depth insight into the behavior of cellularsystems. Additional factors, such as growth factors, envi-ronmental stimuli, and material properties, will all influencetissue repair or regeneration—thus, evolving the presentunderstanding of cell–material interaction.

The experimental results of the cell number as a func-tion of time were approximated by two models: (5) apolynomial function of order two (Lagrange polynomial asthere are three time points) and (6) an exponential func-tion. Results from the curve fit data indicated that the R2

values for the exponential fit were lower in most cases ascompared with the polynomial results (Fig. 7). The coef-ficients A1, B1, and C1 for model 1 and A2, B2, and C2for model 2 were plotted as functions of the scaffoldproperties: the interlayer spacing d and FWHM, reflecting

the crystallinity and orientation of the structure and theaverage surface roughness. The roughness and orientationdid not have a greater effect on the cellular growth com-pared with crystallinity. Therefore, crystallinity was cho-sen for the dominant coefficients A1 and A2, in bothmodels. The crystallinity coefficient, A1, was assigned tox2 in the polynomial function and in the exponent, A2, inthe exponential component, as experimental results indi-cated that crystallinity seemed to have a greater impact oncell proliferation, noted by the variance in cell response.The second coefficients B1 and B2 were a function of theorientation, which correlated well with the crystallinity butto a lower degree. The last coefficients C1 and C2 weremodeled as a function of surface roughness.

The comparison between experimental results and nu-merical models showed that, at all three time points, valueswere comparable between scaffolds (Table 2); however, thepolynomial model tended to approximate values with agreater degree of accuracy. This was consistent betweenunidirectional and multidirectional scaffolds. The greatestdeviation between the polynomial model and the experi-mental results was 13.2% (Table 2). Additionally, for less-crystalline materials (T300), the polynomial model performedwith a higher degree of accuracy, compared with the ex-ponential model (Table 2). Conversely, within the expo-nential model, results were more accurate with highercrystalline scaffolds (Table 2). The exponential model wasless precise at predicting cell growth on all materials in bothunidirectional and multidirectional categories (Table 2). Theunidirectional scaffold model data tended to perform withless accuracy as compared with multidirectional model data.

Data sets from numerical modeling indicated that thepolynomial model data were more accurate. Therefore, thepolynomial model was used to develop the CA algorithm.An assumption of the CA model was that the first time pointrepresented generation ‘‘zero’’ and was therefore offset 24 h

FIG. 5. Atomic force microscopyanalysis of fibrous carbon scaf-folds: (A) T300, (B) P25, and (C)P120. Images display topographicsurfaces of carbon-based materials.Color images available online atwww.liebertpub.com/tea

FIG. 6. WST-1 cell viability assay results of osteoblast growth on fibrous carbon materials. (A) Osteoblast growth onunidirectional carbon scaffolds; (B) osteoblast growth on multidirectional carbon scaffolds. Absolute absorbance wasmeasured at 450 and 690 nm and background was subtracted from data. Data were normalized to cell number. Color imagesavailable online at www.liebertpub.com/tea

6 CZARNECKI ET AL.

to represent the seeding period. This assumption incorpo-rated a period of acclimation during seeding. The CA sim-ulation also incorporated several states for the cell. Thesestates were dependent on the surrounding space and the stateof that specific cell. The cells preferred to grow on materialswith greater crystallinity, orientation, and roughness. It wasnoted that osteoblast cells showed preferred growth oncarbon as opposed to the void space. However, additionalsituations included the ability of osteoblasts to attach at theintersections of the fibers or grow to a density where theywould be able to attach to local fibers and continue to fill thevoids. The algorithm process and the definitions of the CAprogram are illustrated in Figure 9 and Table 3.

The results from the CA simulation were comparable tothe results from the experimental data (Tables 4 and 5).The data set for both unidirectional and multidirectionalscaffolds displayed similar results compared with experi-mental data (Tables 4 and 5). Figures 10 and 11 illustratedtwo-dimensional CA simulations after growth. Results re-vealed that for the unidirectional models, the cells tended

FIG. 7. Growth rates of osteoblasts on multidirectionalfibrous carbon scaffolds: (A) T300, (B) P25, and (C) P120.Equations of polynomial (RED) and exponential (GREEN)models fitted to experimental (BLUE) data are reported withrepresentative R2 values. Color images available online atwww.liebertpub.com/tea

FIG. 8. Fluorescent imaging of osteoblast growth onT300 scaffolds. Images were recorded at 120 h after initialseeding. (A) 10 · magnification of osteoblast growth onunidirectional T300 scaffold; (B) 20 · magnification ofosteoblast growth on unidirectional T300 scaffold; (C) 10 ·magnification of osteoblast growth on multidirectional T300scaffold; (D) 20 · magnification of osteoblast growth onmultidirectional T300 scaffold. Morphology of osteoblastsgrown on scaffolds was comparable between all threescaffolds. T300 scaffolds are illustrated as a representativesample to display growth patterns on scaffolds. Osteoblastdensity was significantly lower on T300 scaffolds as com-pared with both P25 and P120 scaffolds. Growth pattern wasmore concentrated around the material junction points.Color images available online at www.liebertpub.com/tea

Table 2. Model Analysis of Unidirectional

and Multidirectional Scaffolds:

Percent Difference Between

the Polynomial/Exponential Model

and Experimental Data for both Unidirectional

and Multidirectional Scaffolds

Unidirectional scaffolds Multidirectional scaffolds

T300 P25 P120 T300 P25 P120

Percent differencebetween polynomial

model andexperimental data

Percent differencebetween polynomial

model andexperimental data

24 h 2.1 1.1 1.7 1.3 1.5 1.372 h 12.5 8.6 7.2 11.9 12.9 5.6120 h 13.2 9.2 2.3 10.1 7.1 4.4

Percent differencebetween exponential

model andexperimental data

Percent differencebetween exponential

model andexperimental data

24 h 22.9 18.8 10.1 18.4 25.5 8.572 h 29.4 31.8 17.3 35.6 42.5 22.8120 h 16.1 13.7 4.2 9.2 15.9 0.7

CARBON SCAFFOLDS FOR TISSUE REPAIR AND RECONSTRUCTION 7

FIG. 9. Numerical implementation for the algorithm proposed. The process is repeated iteratively and iteration represents1 h of in vitro activity.

Table 3. Description of Cellular Automata Rules Implemented into the Model

Rule No. Rule Result

1 Most actions occur in hours or days not weeks Each time step (one generation in simulation) = 1 h2 Osteoblasts attach to carbon (requires scaffold for

support)Initially, only cells attached to carbon survive and

proliferate3 Cells may attach in groups Not all cells will be separated from one another and

are able to attach to scaffold as a group of cells4 Cells mature in 24 h A cell can split after attaining the 24th generation5 The life of an osteoblast cell will last 300 h Apoptosis (cell death) occurs once 300 generations

are met for that cell or at random6 Mature osteoblasts will undergo mitosis (1) The cell divides into two daughter cells or (2) it

undergoes apoptosis7 Cell undergoes mitosis and divides Matrix is secreted and proteins are released to

mineralize previously secreted matrix and celldivides into two daughter cells

8 Cell undergoes apoptosis Osteoblast cell releases proteins9 Young osteoblast secretes matrix The osteoblast secretes matrix and follows a

maturation sequence10 The state of a cell can be empty, carbon, any

generation of an osteoblast cell, matrix ormineralization

If empty, then osteoblast may fill void. If osteoblastundergoes apoptosis and the previous state ofcell was carbon, then cell returns to previousstate. If matrix, then remains matrix. If miner-alized, then remains mineralized.

8 CZARNECKI ET AL.

to grow along the fiber axis. Following this stage, the cellscontinued to grow perpendicular to the fiber axis, which iscomparable to what was visualized in vitro. Conversely,multidirectional scaffolds followed a different growth pat-tern. Osteoblast cells tended to spread outward from fiberjunctions. The growth seemed to be heavily favorablearound the fiber junctions with clusters of growth on thescaffolds. These results were also comparable to what wasvisualized during morphological characterization (Fig. 8).These results were a representative characteristic on bothunidirectional and multidirectional scaffolds (Fig. 8). There-fore, it may be suggested that model rules produced similarbehaviors to what is happening throughout the in vitro culturestudies.

Discussion

The work presented in this study incorporated the use offibrous-carbon-based materials for biological applications.A numerical and CA model was developed to simulate thebehavior of osteoblast cells, including maturation and death.Published research has shown that fibrous carbon materi-als support cell attachment and growth, which has also beenconfirmed by our group.30,33,57–60 However, this study at-tempts to expand upon just material observations and hopesto present several properties that influence cell response.

This type of approach is extremely encouraging for the areaof artificial tissue development.

In this study, the investigation of T300, P25, and P120fibers has indicated that cell response may be influenced bychanges in material properties. It is also indicative of theversatile nature of carbon-based materials. Modification ofmaterial by altering chemistry and processing techniques aretwo of the most advantageous characteristics of syntheticmaterials. This is not feasible with natural polymers sinceany additional processing steps diminish material integrity.

This study is one of a few that attempts to model osteo-blast response on biomaterials. Moreover, it is also the first toincorporate the use of carbon materials with specific materialproperties: crystallinity, orientation, and surface roughness.Upon understanding the behavior of osteoblast cells on car-bon fibers, the response was directly translated into simula-tion by incorporating theoretical and experimental data.Results suggested that increasing crystallinity, orientation,and roughness had a positive effect on cell attachment andcell proliferation. These three factors were introduced into thecomputational model in order to control cell proliferation andmigration. Morphological analysis suggested that cells pre-ferred to adhere to fiber axis and migrate along the fiber axis.Following this, osteoblasts tended to elongate along the fiberor grow perpendicular to the fiber axis and migrate from fiberto fiber. On multidirectional patterned scaffold, osteoblaststended to grow more abundantly around the junction of thefibers and migrate outward.

Additionally, cell growth increased around areas wherecarbon fibers crossed, suggesting that localized surface areamay provide avenues for cell migration and proliferation.An increase in surface roughness provided several advan-tageous characteristics. One of the most obvious was theincrease in surface area, which would provide more materialarea and volume for cell proliferation. Cell viability studiesconfirmed that increasing surface roughness improved at-tachment and growth. Increasing roughness on carbon ma-terials increases surface energy. This feature is a factor ofavailable edges and disorder, both in and between grapheneplanes.27,36 Surface area also increases with an increase inthe number of dislocations and free edges. This study hasshown that there may be a correlation between surfaceroughness and surface energy, something that has also beenconfirmed by other groups.41

Table 5. Simulation Analysis of Unidirectional

and Multidirectional Scaffolds:

Percent Difference Between the Cellular

Automata Simulation Data and Experimental

Data for both Unidirectional

and Multidirectional Scaffolds

Unidirectional scaffolds Multidirectional scaffolds

T300 P25 P120 T300 P25 P120

Percent differencebetween cellular

automata simulationand experimental

Percent differencebetween cellular

automata simulationand experimental

24 h 0.9 1.3 1.1 0.5 0.9 1.272 h 10.1 9.2 4.8 7.9 8.1 4.2120 h 10.9 10.7 1.1 11.7 6.9 2.3

Table 4. Comparison of Cell Counts Between Experimental Data, Model Results, and Cellular

Automata Simulation for Unidirectional and Multidirectional Carbon Fiber Scaffolds

T300 P25 P120

TimeExperimentalcell No. (SD)

Polynomialmodel

cell No.

Cellularautomatasimulation

cell No.Experimentalcell No. (SD)

Polynomialmodel

cell No.

Cellularautomatasimulation

cell No.Experimentalcell No. (SD)

Polynomialmodel

cell No.

Cellularautomatasimulation

cell No.

Unidirectional carbon fiber scaffolds24 h 2729 (578) 2786 2975 2940 (190) 2972 2978 3339 (210) 3396 337572 h 3142 (435) 2749 2674 3740 (650) 3418 3396 7288 (764) 6763 6938120 h 6981 (460) 6060 6150 9788 (499) 8888 8740 18,789 (399) 18,357 18,582

Multidirectional carbon fiber scaffolds24 h 3311 (736) 3354 3327 3136 (270) 3183 3164 3897 (245) 3948 394472 h 3416 (450) 3044 3146 3329 (740) 2890 3059 7164 (982) 6763 6863120 h 10,968 (523) 9860 9684 15,563 (472) 14458 14,489 24,112 (491) 23,051 23,557

CARBON SCAFFOLDS FOR TISSUE REPAIR AND RECONSTRUCTION 9

Carbon materials may be prepared in various forms andthe flexibility of carbon-based materials is one of its mostadvantageous qualities. These properties enable researchersto form curved surfaces that would be advantageous in bonerepair. However, attachment is the first sign of assimilation,

as the construct serves as an initial support system and, inmost cases, it must be designed to maximize growth andminimize integration time.

The results of this study place emphasis on which pa-rameters may be used to maximize the biological response

FIG. 11. Illustration of two-dimensional model simulation: os-teoblast growth on multidirectionalcarbon scaffolds. (A) Growth ofosteoblasts on multidirectional T300carbon scaffolds at 24 h; (B) growthof osteoblasts on multidirectionalT300 carbon scaffolds at 72 h; (C)growth of osteoblasts on multidi-rectional T300 carbon scaffolds at120 h; (D) growth of osteoblasts onmultidirectional P25 carbon scaf-folds at 24 h; (E) growth of osteo-blasts on multidirectional P25carbon scaffolds at 72 h; (F) growthof osteoblasts on multidirectionalP25 carbon scaffolds at 120 h; (G)growth of osteoblasts on multidi-rectional P120 carbon scaffolds at24 h; (H) growth of osteoblasts onmultidirectional P120 carbon scaf-folds at 72 h; (I) growth of osteo-blasts on multidirectional P120carbon scaffolds at 120 h. Cell den-sity on multidirectional scaffoldsseems to be concentrated aroundmaterial junctions, which is similarto what is visualized in fluorescentimaging. Color images availableonline at www.liebertpub.com/tea

FIG. 10. Illustration of two-dimensional simulation: osteoblastgrowth on unidirectional carbonscaffolds. (A) Growth of osteoblastson unidirectional T300 carbonscaffolds at 24 h; (B) growth ofosteoblasts on unidirectional T300carbon scaffolds at 72 h; (C) growthof osteoblasts on unidirectionalT300 carbon scaffolds at 120 h; (D)growth of osteoblasts on unidirec-tional P25 carbon scaffolds at 24 h;(E) growth of osteoblasts on unidi-rectional P25 carbon scaffolds at72 h; (F) growth of osteoblasts onunidirectional P25 carbon scaffoldsat 120 h; (G) growth of osteoblastson unidirectional P120 carbon scaf-folds at 24 h; (H) growth of osteo-blasts on unidirectional P120 carbonscaffolds at 72 h; (I) growth ofosteoblasts on unidirectional P120carbon scaffolds at 120 h. Cell den-sity on unidirectional scaffoldsseems to be concentrated aroundfibers with growth perpendicular tothe fiber axis, which is similar towhat is visualized in fluorescentimaging. Color images availableonline at www.liebertpub.com/tea

10 CZARNECKI ET AL.

and increase the capacity for attachment and proliferation onmicroscale carbon materials. Thus, while cell attachmentand proliferation may depend on several factors, the bio-logical assays suggested that crystallinity, orientation, andsurface roughness promoted osteoblast adhesion on the fi-ber. However, results suggested that crystallinity and ori-entation tended to have a greater impact compared withsurface roughness. Differences in cell response at the 120-htime point may further support the idea that that crystallinityand orientation facilitated the growth of cells on the scaffoldsurface. This is supported by evidence that there is a pro-gressive increase in healthy cells.

Many applications have incorporated modeling as a tool forpredicting response and troubleshooting behavior. The use ofcomputational software has previously provided accurate dataand may be easily adapted to design changes of biomaterials.One of the goals of this study was to develop a comparativetool to current biochemical assays. It may help researchersunderstand cellular activity without the use of expensive bi-ological assays. It would be very advantageous for researchersto predict response as a factor of input variables, throughsimulations. Several models have already been developed inan attempt to explain biological response.61 The logistic andMalthusian laws attempt to describe the growth of a givenpopulation.45 However, most of the current models that im-plement these methods are based on two major factors—timeand cell population—and do not consider boundary condi-tions, states of surrounding conditions, architecture, materialproperties, and additional environmental stimulators, such asproteins and growth factors. Additionally, current efforts havenot attempted to predict the tissue–biomaterial interaction,which is critical in scaffold design.

On the other hand, CA has been commonly used as pre-dictive technique. CA has the ability to incorporate a greaternumber of factors and may offer a more accurate repre-sentation of the cellular environment. There are many ad-vantages of CA. (i) CA is a discrete and computationallyefficient model and (ii) CA may incorporate a large subsetof variables and transformation states. Literature has shownthat researchers have had success in simulating biologicalenvironments with CA.62 Many biological systems havebeen investigated, such as stem cells, fibroblasts, osteo-blasts, tumor cells, and bacterial cultures. These examplesdemonstrate the versatility of CA.

The majority of biological CA simulations have im-plemented rules based on either theoretical models, such asrandom-walk theory, or experimental data. These studieshave attempted to predict cell migration, proliferation,scale, and cell distributions. A model developed by Mary E.Kundrat, incorporated CA-based principles, combined bothlogistic and Malthusian laws.55 The Kundrat model alsolinked the role of proteins, growth factors, white bloodcells, and mineralization, which was based on publishedstudies that produced both theoretical and biological data.55

However, the Kundrat model was primarily focused onwound healing around blood vessels and not on carbon-based materials. Kundrat’s model was used to predict thegrowth rate and overall cell population of osteoblasts but didnot focus specifically on the tissue–biomaterial interaction.While results show promise in investigating tissue response,more variables may need to be included to understand howcells respond to specific materials.

The current CA model was the first to explore the role ofcarbon-based properties on osteoblast behavior. Moreover,there is limited data on the response of human osteoblaststo fibrous-carbon-based materials. To explore the capabilitiesto model this response, it was necessary to compare data toexperimental cell culture studies. The empirical model de-veloped in this study was based on timed sequence of events,several carbon-based material parameters, and the orientationof scaffolds. Specifically, the CA model incorporated materialcrystallinity, orientation, and surface roughness. Resultssuggested that the simulations paralleled those obtained within vitro characterization. Overall, no statistically significantdifferences were found in the cell growth capacity predictedcomputationally and those measured by in vitro experiments.The polynomial model displayed a greater degree of accu-racy, as the relative deviation was < 13% throughout all timepoints (Table 2). Conversely, there was greater deviation inthe exponential model, especially for materials with lowercrystallinity. While each model exhibited slight deviationsfrom experimental data, initial results indicated promisingoutput. Additionally, results from the present model sug-gested that the model was capable of quantitatively reprod-ucing the osteoblast distribution on a scaffold. When analyzingboth unidirectional and multidirectional scaffold data, it isclear that there was a strong correlation between experimentaldata and simulation results. The computational simulationaccurately depicted the response on both unidirectional andmultidirectional areas of a scaffold. However, while the de-veloped model compared carbon properties to cell growthrather precisely, future models may need to incorporate agreater library of properties in order to more accurately gaugecell response.

To minimize computational time, the model was simplifiedby limiting it to two dimensions. The advantages from sim-plifying the model included decreased processing time andvariation. While results showed comparable data to experi-mental data, it is unclear whether data would correlate inthree dimensions. Therefore, model development may need tobe extended to understand how cells migrate, proliferate, andmature in a three-dimensional construct as this may moreaccurately represent a tissue scaffold material. Moreover, in-creasing sample size may improve model accuracy. It wouldprovide a more detailed view of the response between thecurrent time points. Also, the study incorporated only threetypes of fibrous carbon scaffolds. While this does provide abroad range of crystallinity properties and surface roughness,the model may benefit from including several more datapoints. Ultimately, this will broaden the functional scope ofthe model, increase its accuracy, and may be used as a globaltool for carbon-based materials.

In conclusion, this study demonstrated that carbon scaf-folds support cell growth. The experiments performed in thisstudy have provided evidence that modified fibrous carbonmaterials offer valuable biological properties and may reg-ulate cellular response.

1. Unidirectional scaffolds at 120 h: results illustrated33% difference in cell growth between T300 and P25fibers and 64% difference between P25 and P120 fibers.

2. Multidirectional scaffolds at 120 h: results displayed35% difference in cell growth between T300 and P25fibers and 43% difference between P25 and P120 fibers.

CARBON SCAFFOLDS FOR TISSUE REPAIR AND RECONSTRUCTION 11

3. Material alignment was integral in promoting cellgrowth with multidirectional scaffolds having the ca-pacity for greater growth over unidirectional scaffolds.At 120 h there was 24% increase in cell growth be-tween unidirectional alignment and multidirectionalalignment on high-crystalline carbon fibers.

4. Increased crystallinity, orientation, localized surfacearea, and surface roughness enhanced cell growth.

5. Computational modeling of biomaterial–cell responsedemonstrated similarities between experimental andcomputational simulations with differences between0% and 15%.

This study presented an opportunity to understand osteo-blast behavior on carbon materials and develop tools thatcould be utilized in future characterization protocols. How-ever, additional explorations into the in vivo response andmodel sensitivity may be required to develop superior ma-terials and models with greater accuracy.

Disclosure Statement

No competing financial interests exist.

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Address correspondence to:Jarema S. Czarnecki, MS

Carbon Research LaboratoryUDRI Carbon Group

Department of Mechanical EngineeringUniversity of Dayton

300 College ParkDayton, OH 45469

E-mail: jczarnecki1@udayton.edu

Received: August 8, 2013Accepted: May 28, 2014

Online Publication Date: August 29, 2014

CARBON SCAFFOLDS FOR TISSUE REPAIR AND RECONSTRUCTION 13