Biomaterials 23 (2002) 1369–1373

Comparison of corneal epithelial cellular growthon synthetic cornea materials

Andrew George, William G. Pitt*

Department of Chemical Engineering, Brigham Young University, 350 Clyde Building, Provo, UT 84602, USA

Received 20 December 2000; accepted 13 June 2001

Abstract

The application of artificial corneas for severely wounded ocular surfaces has always encountered the problem of biocompatibilitywith corneal epithelial cells (CECs). For the eye to stay healthy, it must continually have a complete sheet of CECs across theartificial corneal surface. Various surface modifications of different polymeric materials have been examined to determine whichhave the best cellular growth rates. A mathematical model of corneal cell growth profiles on synthetic materials was formulated

based upon a linear mitotic growth rate. Experimental data reported for the CEC growth on modified poly(vinyl alcohol), siliconerubber, polystyrene, and polycarbonate was analyzed using the model to estimate the linear mitotic rate constant (k). The modelproved to be useful in comparing data from different investigators. Plasma-induced graft copolymerized poly(hydroxyethyl

methacrylate) (pHEMA) on silicone rubber provided the best growth rate from this particular set of data. r 2002 Elsevier ScienceLtd. All rights reserved.

Keywords: Keratoprosthesis; Corneal epithelial cell; Cell growth; Polymer; Mathematical model

1. Introduction

Following corneal wounding, epithelium migratesover the exposed corneal surface to close the wound.If the injury is severe enough, as in a cornealperforation, penetration, or progressive ulceration, therequirement for corneal epithelial cells (CECs) is toogreat for the eye to provide. A laminar patch allografthas usually been used to restore ocular integrity in thiscase [1]. Transplant corneal tissue, however, is difficultto obtain because its main source is cadavers. Thus,there is a need for biocompatible materials forkeratoprosthetics (artificial corneas).One of the major challenges to the success of

keratoprosthetics is maintaining an epithelial coverageon the transparent optic. The absence of this epithelialsheet allows bacteria to enter, inhibits the spreading ofan even tear film, and permits epithelial downgrowth [2].Also important is the exposure of the underlying stromaat the joint between the ocular rim and cornea when the

CEC sheet is interrupted. Ulceration of the stromaoccurs when proteinases, the tear film, and inflamma-tory cells are allowed to enter it [3]. A complete CECsheet requires three steps to succeed: the migration ofthe CECs from the remaining cornea onto the newmaterial, the attachment of the CECs onto the surface,and proliferation via mitosis of the CECs to restorenormal cell density across the ocular surface.The maintenance of complete CEC coverage is only

one of the issues required for the success of an artificialcornea. Also vital is the suppression of CEC down-growth when the implant is maintained in the livingcornea for a long period of time, and the tight fixture ofthe implant on the host cornea for complete woundhealing. These factors give import to the hydrophilicity/hydrophobicity (wettability), softness/hardness, tensilestrength, and biocompatibilty of the surface [4].As one can see, it is a complicated, difficult science to

design keratoprosthetics. The use of ‘‘hybrid’’ artificialcorneas, consisting of natural corneal tissue bound to apolymer has been suggested as possibly the only solutionto long term visual recovery and stability [3]. This paperis an attempt to assist in the selection of topography andmaterial composition of artificial corneas by providing a

*Corresponding author. Tel.: +1-801-378-2589; fax: +1-801-378-

7799.

E-mail address: pitt@byu.edu (W.G. Pitt).

0142-9612/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 4 2 - 9 6 1 2 ( 0 1 ) 0 0 2 5 7 - 5

method of comparing the growth rate of the CECs oncandidate materials. Surface growth of the CECs wasmathematically modeled and fitted to experimental datafrom the literature for materials of various compositionsand pore diameters, thus providing a direct comparisonof the growth rate constants of the CECs grown indifferent labs.

2. Mathematical model

A mathematical model was prepared to predict theCEC amounts on the polymer surface as a function oftime. This model was based on a logistic equation,commonly used in studies of cell population growthkinetics [5]:

qnqt

¼ kn 1�n

nN

� �; ð1Þ

in which n is the cell population, t is the time, k is thelinear mitotic growth rate constant, and nN representsthe cell density in an unwounded cornea, when a steady-state balance exists between cell growth and death. Thefollowing equation has the form of a Bernoulli equationwith a non-linear, polynomial relation of mth order [6]:

qnqt

þ PðtÞn ¼ QðtÞnm: ð2Þ

The autonomous character of the functions PðtÞ andQðtÞ; as well as the second degree nature of thepolynomial characterize the following equation as aparticular type of Bernoulli equation called the Ricattiequation. A Ricatti equation can be solved to give arational function of exponentials [6]. By separation ofvariables, Eq. (2) was solved to yield

ln nj j � ln nN � nj j ¼ ktþ C; ð3Þ

where C is a constant of integration. An initialboundary condition was defined as n ¼ ni at time zero.This allowed evaluation of the constant, C:

C ¼ lnni

nN � ni

� �: ð4Þ

Values of cell concentration vs. time allowed linearregression of k from Eq. (3).The profile of nðtÞ can be evaluated by rearrangement

of terms:

n ¼nNC0ekt

1þ C0ekt; ð5Þ

where the constant C0 is defined as

C0 ¼ni

nN � ni: ð6Þ

3. Experimental data set

The two polymer characteristics commonly evaluatedin the CEC growth studies are material composition andpore diameter. These topics have been the subject ofrecent experimentation [1–4,7–9]. In particular, forkeratoprosthetic applications, experimentation has beenfocused on plasma-induced modification of polymersurfaces and track-etched porosity by laser ablation ofpolycarbonate (PC). The experimental variables con-sidered in this study were polymer surface chemistry andthe pore size. The initial number of the CECs (ni) wasalso different in the various experiments. The area of thetest surface was usually 1 cm2. After attachment of someCECs onto the surface, the excess cells were removedand the amount of cell proliferation was measured atspecified time increments. The data obtained fromreports of these experiments were fitted to Eq. (3) andthe growth parameter k was regressed for each data set.This allowed examination of the response in cell growthrate due to differences in surface topography andcomposition. Details of the five analyzed experimentsare as follows.

3.1. PVA: plasmas

Poly(vinyl alcohol) (PVA) copolymer hydrogels wereplasma-treated separately with ammonia, a mixture ofacetone and oxygen, and Ar gas at two pressures [2].Only Ar-plasma-treated surfaces allowed cell prolifera-tion after seven days. Cells became confluent on Ar-plasma-treated surfaces processed under both reactionpressures.

3.2. SR: plasma, phospholipid-grafts

Cell growth experiments were carried out with acontrol silicone rubber (SR) membrane, an Ar-plasma-treated SR membrane, and the SR membranes graftedwith three different amounts of poly(2-methacryloylox-yethyl phosphorylcholine) (pMPC), measured by aphosphorous to carbon ratio (P1s=C1s) from X-ray

Nomenclature

CEC corneal epithelial cellt timen corneal epithelial cell density

nN unwounded cell densityni initial (post-seeding) cell densityk linear mitotic growth rate constantC;C0 constants of integrationd nominal pore diameter

A. George, W.G. Pitt / Biomaterials 23 (2002) 1369–13731370

photoelectron spectroscopy [7]. The phospholipids weregrafted onto the SR via Ar-plasma-induced polymeriza-tion.

3.3. SR: plasma, pHEMA-grafts

Cell culture was performed on unmodified SR(control), Ar-plasma-treated SR, a poly(hydroxyethylmethacrylate) hydrogel (pHEMA), and the SR graftedwith different amounts of the pHEMA (55, 75, 280, 570,1250, and 1650 mg cm�2) [4]. The pHEMA graftamounts in the 55–150 mg cm�2 range worked best forattachment and growth of the CECs. Larger amounts(500–1650 mg cm�2) seemed to actually inhibit growth.Subsequent in vivo tests confirmed that the SRmembranes grafted with the pHEMA were completelycovered with the CEC, three weeks after implantationinto host corneas.

3.4. PS: plasma, hydrophilic-grafts

Two hydrophilic surfaces, tissue culture polystyrene(TCPS) and Primaria, a gas-plasma-modified polystyr-ene (PS) surface with nitrogen- and oxygen-containingsurface chemistry, and one relatively hydrophobic sur-face (unmodified PS), were tested to determine the effectof wettability upon cell growth and attachment [8]. Also,experiments were conducted in the absence of fibronec-tin and vitronectin (proteins responsible for cell attach-ment on the ocular surface), causing the cells to employan alternate method of attachment and an intact systemof microtubules. Cell growth was very similar for allthree surfaces.

3.5. PC: track-etched

The PC membranes were made porous by columnartrack-etching in nominal pore diameters of 0, 0.1, 0.4,0.8, 1.0, 2.0, and 3.0 mm [9]. Materials with porediameters of 0.1–0.8 mm were reported to support muchmore CEC growth than when the pore diameters were1.0 mm or larger. Cytoplasmic processes and some cellspenetrated the larger pores, reducing the number of cellson the surface.

4. Results and data analysis

The cell cycle time, or the inverse of k; for epithelialcells has been shown to lie somewhere in the broadrange of 20–500 h [10]. In modeling cell growth on thehuman eye, the cell cycle time for the CECs wasreported to be 25 h (k ¼ 0:04 h�1), indicating that theCECs have a relatively short cycle time. One wouldexpect that healthy cells growing on a keratoprosthesiswould have a shorter cell cycle time approaching that

reported for in vivo growth. It should be noted that theexperimental data reported in this paper were basedupon growth data of rabbit and bovine CECs, ratherthan human cells.The experimental data from the literature cited above

were fitted to Eq. (3), and the regressed estimates of k(and standard deviations) are given in Table 1. Anumber of observations can be made from this data. Asone can see, the highest values of k occurred on plasma-induced pHEMA grafts on the SR, especially on thesurface grafted with 55–75 mg cm�2 (k ¼0.026–0.032 h�1). These values are similar to those reportedfor normal human CEC growth. Also showing a highrate are low pressure Ar-plasma treatments, phospho-lipid grafts of P1s=C1s=0.00189, TCPS, Primaria,unmodified PS, and PC with pore diameters of 0.1–0.8 mm.Negative values of k imply negative growth rates and

indicate that the cells are not growing or perhaps aredying. Examination of the graphical data showed thatthose data sets yielding negative slopes were nearlyhorizontal lines (slope of zero), showing no CEC growthon those surfaces. For example, Fig. 1 illustrates thelinear fit of two of the data sets for the SR: plasma,pHEMA-grafts experiments, corresponding to the Ar-plasma-treated SR (at 200mTorr) and the Ar-treatedSR grafted with 75 mg cm�2 of the pHEMA. The fit ofthe former data set is an example of a negative growthparameter, while the latter set yielded the highest growthparameter of all fitted data.In general, the data shows the following trends. On

the PVA, ammonia and acetone/O2 plasma treatmentproduces no significant cell growth. Cell growth on theAr-treated PVA surfaces does seem to slightly improveas the pressure is increased.Growth rate decreases on the SR as the amount of the

pMPC grafted onto the surface increases. Any amountof the pHEMA grafted on the SR greater thanB100 mg cm�2 leads to a decreased k value.On the PS surfaces, all cell growth rates are high.

Non-porous PC, or the PC with pores of any diameterless than 1.0 mm sustains good cellular growth.The precision of this data-modeling system was

measured by the standard deviations in k for each dataset (see Table 1). Low standard deviations show that thefits were best for the PC: track-etched experiments. Ingeneral, the standard deviation decreases as theregressed value of k decreases. Those data sets with anegative value for k or k close to zero have a standarddeviation of the same magnitude as the growthparameter. Therefore, surfaces with little or nogrowth capability could not be fitted to Eq. (3) withprecision.Another measure of precision and of consistency of

the data set is a comparison of the two common entries.The Ar-plasma treatment of the SR was reported in

A. George, W.G. Pitt / Biomaterials 23 (2002) 1369–1373 1371

separate publications, and neither surface producedmuch growth. The k values for a pressure of200mTorr are not significantly different ( p ¼ 0:40).The TCPS was used as a control by two groups, and theregressed k values are very similar (k ¼ 0:00644 and0:00541).

There are several sources of error which should beconsidered in evaluating this data, including randomerror in experimentation within a laboratory, slightlydifferent procedures in different laboratories, and errorintroduced with the assumptions made in the mathema-tical model. Cell migration, attachment rates, andseeding are probably not as uniform as assumed in themathematical model. Also, the experimental literatureare sometimes unclear in reporting actual cell concen-trations values, as they were usually intended more forqualitative comparisons. Better data reports on nðtÞ; aswell as additional research to determine nN (theunwounded concentration of cells on the cornea) wouldenhance the reliability of these comparisons.From the standard deviations, as well as the match

success of the fits, this modeling method was determinedto be efficacious in predicting growth rate vs. timeprofiles for any of the materials and topographies withsustainable growth capability. It establishes a way tohomogeneously quantify, standardize, and compareexperimental data across laboratories. It also may beof use in developing future relationships, such asfunctions for the growth rate at any pore diameter, orany phosphorus concentration, etc. Future models that

Table 1

k and cell cycle time results for all fits

Polymer Cells Characteristic k7SD (h�1) Cell cycle time (h) Ref.

PVA Rabbit Argon-1 (P ¼ 50mTorr) 0.0051870.00008 193.06 [2]

Argon-2 (P ¼ 80mTorr) 0.0060270.00008 166.14

Ammonia-1 (P ¼ 50mTorr) �0.0007170.00016 N/Aa

Ammonia-2 (P ¼ 80mTorr) �0.0035970.00015 N/A

Acetone/O2-1 (P ¼ 35mTorr) �0.0027270.00016 N/A

Acetone/O2-2 (P ¼ 45mTorr) �0.0030570.00013 N/A

SR Rabbit Control SR �0.0000470.00087 N/A [7]

P1s=C1s ¼ 0:00189 0.0053770.00081 186.24

P1s=C1s ¼ 0:00709 0.0004070.00088 2494.73

P1s=C1s ¼ 0:0154 0.0001170.00088 9107.45

Argon (P ¼ 200mTorr) 0.0002070.00086 4906.70

SR Rabbit Argon (P ¼ 200mTorr) �0.0000770.00027 N/A [4]

pHEMA=55mg cm�2 0.0261570.00009 38.24

pHEMA=75mg cm�2 0.0315570.00005 31.69

pHEMA=280mg cm�2 0.0064770.00019 154.57

pHEMA=570mg cm�2 0.0007270.00024 1396.25

PS Bovine TCPS 0.0064470.00017 155.31 [8]

Primaria 0.0070870.00017 141.23

PS (unmodified) 0.0046070.00013 217.30

PC Bovine PC, non-porous 0.0043270.00001 231.59 [9]

PC, d ¼ 0:1mm 0.0046270.00001 216.55

PC, d ¼ 0:4mm 0.0047370.00001 211.30

PC, d ¼ 0:8mm 0.0040770.00001 246.00

PC, d ¼ 1:0mm 0.0019970.00002 502.56

PC, d ¼ 2:0mm 0.0002470.00002 4134.34

TCPS 0.0054170.00001 184.80

aNot applicable.

Fig. 1. Example of data regression for the CEC growth on surface-

modified silicone rubber. m, growth on the 200mTorr Ar-treated SR;

K, growth on the SR grafted with 75mg cm�2 pHEMA. Lines are

least-squares linear fit to the experimental data.

A. George, W.G. Pitt / Biomaterials 23 (2002) 1369–13731372

include CEC migration and attachment mechanismsmay also be useful.

5. Conclusions

The CEC cell growth was determined to be greateston the plasma-induced pHEMA grafts on the SR,especially for a grafting density of 55–75 mg cm�2

(k ¼0.026–0.032 h�1). Other potentially useful surfacesare low pressure Ar-plasma treatments, phospholipidgrafts with a P1s=C1s ratio of 0.00189, TCPS, Primaria,unmodified PS, and PC with pore diameters of 0.1–0.8 mm. The precision of this data-modeling system wasevidenced by the low standard deviations within a dataset, and the correlation of common values from differentdata sets. This technique establishes a way to homo-geneously quantify, standardize, and compare experi-mental data from different laboratories. Surfaces withlittle or no growth capability could not be fitted withprecision to Eq. (3). Better data reports on nðtÞ; as wellas additional research to determine nN (the unwoundedconcentration of cells on the prosthetic cornea) arenecessary before this model may be improved upon.

Acknowledgements

The authors would like to express appreciation to Dr.Scott Glasgow and Jon Ward for their assistance inunderstanding the mathematical model. Their collectiveassistance was necessary in the completion of this paper.

Partial funding was provided by the National Institutesof Health grant HL 59923.

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