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Tissue Engineering. Part A
Tissue Eng Part A. 2008 September; 14(9): 1507–1515.
PMCID: PMC2748927

A Neural Network Model for Cell Classification Based on Single-Cell Biomechanical Properties


The potential success of tissue engineering or other cell-based therapies is dependent on factors such as the purity and homogeneity of the source cell populations. The ability to enrich cell harvests for specific phenotypes can have significant effects on the overall success of such therapies. While most techniques for cell sorting or enrichment have relied on cell surface markers, recent studies have shown that single-cell mechanical properties can serve as identifying markers of phenotype. In this study, a neural network modeling approach was developed to classify mesenchymal-derived primary and stem cells based on their biomechanical properties. Cell sorting was simulated using previously published data characterizing the mechanical properties of several different cell types as measured by atomic force microscopy. Neural networks were trained using combined data sets, with the resultant groupings analyzed for their purity, efficiency, and enrichment. Heterogeneous populations of zonal chondrocytes, chondrosarcoma cells, and mesenchymal-lineage cells, respectively, could all be classified into enriched subpopulations. Additionally, adult stem cells (adipose-derived or bone marrow–derived) separated disproportionately into nodes associated with the three primary mesenchymal lineages examined. These findings suggest that mathematical approaches such as neural network modeling, in combination with novel measures of cell properties, may provide a means of classifying and eventually sorting mixed populations of cells that are otherwise difficult to identify using more established techniques. In this respect, the identification of biomechanically based cell properties that increase the percentage of stem cells capable of differentiating into predictable lineages may improve the overall success of cell-based therapies.


The ability to purify or enrich cell populations may significantly influence the overall success of cell-based therapies such as tissue engineering. Enrichment of cell populations is usually achieved by either removing unwanted cells or isolating target cells from a heterogeneous population.1 Current approaches for cell enrichment include fluorescence-activated cell sorting (FACS), microfluidics, osmotic selection, antibiotic selection, laser capture dissection, micropipette aspiration, and optical traps.29 The vast majority of sorting procedures is based on fluorescence detection of cell surface markers or intracellular enzymes that have been associated with a specific stem cell population. However, such biochemical approaches have had limited success when sorting cell types of mesenchymal origin for applications in tissue engineering.10,11

Recent studies comparing the single-cell mechanical properties for a variety of mesenchymal-derived primary and stem cells have shown that different cell types exhibit distinct biomechanical characteristics,12 which may represent a potential set of phenotypic measures that could be used as a basis for cell sorting. Biomechanical properties such as elastic modulus, equilibrium modulus, and apparent viscosity, or structural properties such as cell size, might help distinguish among cell types or even indicate a preferred differentiation lineage for adult stem cells.12 However, the relationship between mechanical biomarkers and cell lineage could be difficult to identify given a large number of measured parameters. In this respect, artificial neural networks provide a potential means of sorting and classifying large collections of properties, since they excel at discerning patterns within complex problems.13

A benefit to using neural networks is that large, high-dimensioned data sets can be easily analyzed for distinct groupings of similar cases. No limit on the number of input properties exists, so it is not necessary to determine a priori which parameters should be included in an analysis. Relative weightings of the individual properties are determined from the neural network, giving an alternative approach to identifying the most influential properties for a given population. One type of neural network, Kohonen's self-organizing feature maps, gives additional information on how neighboring groups, or nodes, are related to each other.14,15 The current study utilizes this approach to virtually sort populations of cells using past experimental data.

The goal of this study was to determine whether a neural network analysis of cell properties could provide a means of classifying heterogeneous cell populations into identifiable groups based solely on physical properties measured via atomic force microscopy. We hypothesized that cells of various origins—that is, zonal chondrocytes, multiple chondrosarcoma cell lines, and mesenchymal-derived primary and stem cells—possessed distinct biomechanical signatures that could be classified using self-organizing feature maps. Neural networks were trained using previously recorded data sets, and then simulated with subsets of the data corresponding to specific cell types. The overall effectiveness of the virtual sorting procedure was analyzed by comparing the average properties associated with each grouping.

Materials and Methods

Cell biomechanical properties

A neural network classification technique was evaluated using single-cell, biomechanical properties measured in several prior studies.12,16,17 The first study focused on differences between superficial and middle/deep zone articular chondrocytes.17 The second showed that previously characterized chondrosarcoma cell lines (JJ012, FS090, and 105KC) with varying degrees of malignancy (JJ012>FS090>105KC)18 exhibited significantly different viscoelastic properties, which were associated with degree of malignancy.16 The third study examined the mechanical properties of individual adipose-derived stem cells (ASCs) and bone marrow–derived stem cells (MSCs) in comparison with a number of primary mesenchymal-derived cell types.12

In all studies, cell biomechanical properties were measured in the same manner using an atomic force microscope (MFP-3D; Asylum Research, Santa Barbara, CA) via elastic and viscoelastic tests as described previously.16 Spherically tipped, AFM cantilevers (k = ~0.05 N/m; Novascan Technologies, Ames, IA) were used to reduce local strains at the site of indentation. The elastic modulus, Eelastic, was extracted from force versus indentation data using an appropriate Hertz model, while the equilibrium modulus, Eequil, was calculated using force and indentation data at the end of a 60-s stress relaxation test. Probe–cell contact was identified with contact point extrapolation, a method that uses the indentation portion of the approach curve to determine where probe–cell contact begins.12 The relaxed modulus (ER), instantaneous modulus (E0), and apparent viscosity (μ) were determined using a previously derived stress relaxation model of a viscoelastic solid.16

Neural network design

Virtual sorting was accomplished by a custom program that utilized the self-organizing feature map function in Matlab's Neural Network Toolbox (The MathWorks, Natick, MA). Neural networks were used to determine how best to separate heterogeneous cell populations into similar groups (Fig. 1). This approach could handle a large number of input characteristics (i.e., Eelastic, ER, E0, μ, Eequil, Height, etc.), iteratively assess the optimal property groupings based on the distribution of data throughout an n-dimensional space, and match a set of future inputs to nodes possessing the most similar characteristics. Self-organizing maps were advantageous because the numerical designation of the nodes revealed additional information about how closely neighboring groups were related.19,20 For example, in a 10-node system, nodes 1 and 10 would be the least similar based on the parameters considered.

FIG. 1.
Neural network schematic. A theoretical distribution of properties is shown with the initial placement of nodes. Iterative analysis of the relationship between properties in n-dimensions allowed the neural network to optimally place the nodes within identifiable ...

Each set of cellular properties was analyzed using the same neural network program. In general, the network was initially trained with the mechanical properties measured for the known cell types. For example, in the zonal chondrocyte study this included Eelastic, Eequil, ER, E0, and μ for superficial and middle/deep zone chondrocytes. For the chondrosarcoma study, this included the same properties for cells from JJ012, FS090, and 105KC cell lines. For the mesenchymal-lineage study, the network was trained using these properties, as well as Height (cell height) for spherical and spread osteoblasts, chondrocytes, and adipocytes. The adult stem cells (ASCs and MSCs) were not included in the training segment as they were not considered to be a differentiated cell type. The training process iteratively assessed the relationships among the input properties for each mixed population, resulting in optimal groupings of cells around a set number of nodes defined by the user. For the current study, this number was chosen so that statistical significance existed among all nodes for a majority of the measured properties.

Once the neural network was trained, it could be queried using sets of mechanical biomarkers for individual cells. The new inputs could be defined groups, such as superficial zone chondrocytes or JJ012 chondrosarcoma cells, or unknown populations, such as ASCs or MSCs. By simulating the trained networks with known groups, a distribution across the nodes was achieved. Simulating with unknown populations (i.e., stem cells) identified the mechanical phenotypes with which they most closely associated. Property weighting was defined as the difference between maximum and minimum input weights for all nodes, effectively indicating how delineated the data were for each property.

Neural network evaluation

The biomechanical properties of grouped subpopulations were investigated by analyzing nodal characteristics. Mean and standard deviation were used as the primary comparison among nodes. Input weightings provided information on which mechanical property played the largest role in how cells were distributed among nodes. The types of cells within each node were recorded, with special attention being paid to the purity of nodes containing large proportions of a single cell type. In addition to nodal characteristics, the entire classification procedure was evaluated for enrichment and efficiency with respect to initial, heterogeneous populations. For example, if a network was trained using a population containing 4/10 type A cells, then a sorted group containing 3/5 type A cells would have a purity of 60% (3/5), efficiency of 75% (3/4), and enrichment of 150% (60/40).

Statistical analysis

Single-factor ANOVA with Fisher LSD post hoc analysis was conducted to determine whether significant differences in biomechanical properties existed (α = 0.05) among nodes. Results were compiled separately for each experimental study (zonal chondrocyte, chondrosarcoma, and mesenchymal lineage). Because properties were not normally distributed, data were log-transformed for statistical analyses. Graphs are depicted as mean ± standard deviation.


Neural network effectiveness

Analysis of mechanical biomarker data sets using neural networks revealed information about likely groupings within the mixed populations. Nodes associated with the various subpopulations were reported by average property values, with standard deviations indicating the variability among cells present within a node (Fig. 2F). Scatterplots illustrated how each property related to the other inputs from a single dimensional aspect (Fig. 2A–E). Certain measures of effectiveness for the classification procedure depended on the composition of the initial population. In general, cell subpopulations were equally proportioned for each analysis, but practically, this might not be the case (i.e., superficial zone chondrocytes are overrepresented compared to a typical chondrocyte harvest). Further, greater enrichment could be virtually achieved in some cases by cell types comprising a smaller proportion of the initial population.

FIG. 2.
Mechanical property scatterplots. Two dimensions of the n-dimensional space considered in the neural network analysis are shown here (spread, mesenchymal-lineage cells). Eelastic was plotted against the other properties to illustrate the distribution ...

Zonal chondrocytes

Mechanical biomarkers associated with spherically shaped, superficial and middle/deep zone chondrocytes were sufficient for identification of both cell types using a neural network containing three nodes. Simulating the network with data sets containing only superficial or middle/deep cells revealed a clear distribution across the nodes (Fig. 3A). Generally, more middle/deep cells grouped in node 1, whereas more superficial cells were grouped in node 3. The classification procedure enriched superficial cells to a greater extent than middle/deep cells, although this is likely an artifact due to the lower numbers of superficial cells in the initial, heterogeneous group (Table 1). The consequence of enrichment, however, was an effective decrease in cell numbers since only 26 out of 49 superficial cells allocated to node 3.

FIG. 3.
Cell distributions for zonal chondrocytes (A) and chondrosarcoma cells (B). Superficial and middle/deep zone chondrocytes were grouped into three nodes characterized by five mechanical properties as inputs. Distinct separation existed for the two zonal ...
Table 1.
Classification Effectiveness Using Neural Networks

Biomechanical properties showed clear differences after the classification procedure. Average moduli were significantly different among all nodes (p < 0.0001). A trend existed from node 1 to 3, with node 1 (middle/deep cells) being less stiff than node 3 (superficial cells) (Table 2). Input weightings were similar for all moduli properties (Eelastic, Eequil, ER, and E0), while apparent viscosity (μ) was slightly lower. This indicated no predominant mechanical property played a role in grouping the cells.

Table 2.
Node Mechanical Properties

Chondrosarcoma cell lines

A neural network containing four nodes successfully distributed chondrosarcoma cells from three different cell lines into virtual subpopulations (Fig. 3B). Simulating the network with known data sets (105KC, FS090, and JJ012) resulted in node/mechanical property relationships similar to the zonal chondrocyte results. A trend in increasing moduli was apparent from node 1 to node 4. JJ012 cells were allocated primarily to node 1 due to their low moduli. 105KC and FS090 cells were distributed fairly evenly across all nodes, although FS090 cells had the highest purity in node 4. The classification procedure resulted in enrichment of all cell types: 191% for JJ012 cells (node 1), 248% for FS090 cells (node 4), and 165% for 105KC cells (node 3). Table 1 shows the respective purity of each node and efficiency at separating cell types from a hypothetical, mixed population into separate groups. Property weightings were similar to zonal chondrocyte results with no single property being more influential in the classification procedure (Table 2).

Mesenchymal-lineage cells

Primary cell classification

A neural network approach successfully identified subpopulations present within a hypothetical, heterogeneous population of mesenchymal-lineage cells (Fig. 4A, B). Osteoblasts (O), chondrocytes (C), and adipocytes (A), exhibiting either spherical or spread morphologies, were analyzed using a network containing four nodes; results showed good enrichment for spherical cell populations and excellent enrichment for spread cell populations (Table 1). For both morphologies, elastic moduli monotonically decreased from node 1 to node 4, whereas height generally increased across the same nodes (Table 2). The property weightings indicated that for spherical cells, Height was the most influential classification factor. Eelastic was the second most heavily weighted property, followed closely by E0 (Table 2). Spread cell properties had slightly different weightings, with Eelastic, E0, and Height being more influential.

FIG. 4.
Mesenchymal-lineage cell distribution. Osteoblasts, chondrocytes, and adipocytes were distributed among four nodes based on their mechanical properties. Individual stem cells were then simulated on the previously trained neural network to determine which ...

Both morphologies allowed for significant enrichment via classification by mechanical biomarkers. Spherical, primary cells separated into distinct nodes that were over 60% pure for specified cell types. Osteoblasts were the presiding cell type in node 1, chondrocytes in node 2, and adipocytes in nodes 3 and 4 (Fig. 4A). Good enrichment was achieved for all cell types (O, 205%; C, 180%; A, 285%). Spread primary cells showed an even greater potential for enrichment (O, 305%; C, 269%; A, 294%) (Fig. 4B).

Stem cell association

Adult stem cell populations contained disproportionate numbers of individual cells with mechanical biomarkers similar to osteoblasts, chondrocytes, and adipocytes. This distribution was obtained by sorting the stem cell populations using the neural networks previously trained with primary, mesenchymal-lineage cell data. Cell lineages were assigned to the four nodes using results from the previous analyses. Spherical ASCs showed a 38-60-2 (O-C-A) percentage split, indicating which primary cell types their mechanical properties most closely matched (Fig. 4A). Spherical MSCs exhibited a 45-45-10 split, indicating a slightly higher proportion of osteoblast- and adipocyte-like cells (and lower proportion of chondrocyte-like cells) than for ASCs. Spread adult stem cells exhibited a similarly even split among the osteoblast/chondrocyte lineages, although no adipocyte-like cells were identified due to the heavy weighting of Height associated with primary adipocytes (Fig. 4B). Consequently, ASCs showed a 58-42-0 split, and MSCs showed a 60-40-0 split, indicating generally more osteoblast-like stem cells were in the sample populations than chondrocyte-like stem cells.


The potential success of tissue engineering or other cell-based therapies is dependent on factors such as the purity and homogeneity of the source cell populations. Our findings suggest that a neural network approach may provide a novel means of sorting heterogeneous cell populations into similar groups using single-cell mechanical properties. Self-organizing maps are particularly intriguing since the relationship among nodes can also reveal relationships among the samples populating those nodes.19 For example, the nodal arrangement in the current study indicates that osteoblasts possess mechanical characteristics more similar to chondrocytes than adipocytes. This relationship is confirmed when comparing the average values associated with each node. By including other biological parameters, a clearer picture of the relationships among cell types could also be revealed.

Results showed that cell populations can be classified and virtually enriched to varying degrees based on their mechanical properties. Superficial zone chondrocytes, which make up only a small fraction of the total cells in a typical cartilage harvest (~5% purity),21 possessed mechanical properties that were sufficiently different from middle/deep zone chondrocytes to group into a significantly more pure (~80%) subpopulation. If directly translated to a bulk tissue harvest, this would result in an enrichment of 1600%. Recent work has suggested that the superficial zone population within articular cartilage may contain stem/progenitor cells,22,23 so an enrichment procedure targeting this subpopulation could be beneficial for future cell therapies. Chondrocytes within articular cartilage experience mechanical and biochemical environments that vary with depth, which could explain why zonal differences exist among cells.24 The higher moduli observed for superficial zone cells could be attributed to a larger F-actin content within this subpopulation,25 since past studies have shown that mechanical properties are dependent on the F-actin structure within the cell.2628

Similarly, chondrosarcoma cells from different cell lines could also be grouped using a panel of mechanical properties. JJ012 cells, which were described as having a high degree of metastasis, grouped predominantly into a single node that was characterized as having lower cell moduli. Past studies have investigated the relationship between mechanics and cancer cell migration, differentiation, and transformation16,2931 (reviewed by Suresh32). In general, cancer cells were less stiff than their normal counterparts, and cells with increased metastatic potential were even softer. This change in mechanical properties has been hypothesized to be due to cytoskeletal disorganization.30 In this respect, the identification of otherwise indistinguishable, malignant cells may provide novel means of assessing the stage of cancer in a tumor.33

Primary cells of mesenchymal origin also separated into distinct nodes based on their characteristic mechanical properties. Adipocytes comprised a clearly defined population that exhibited uniformly larger cell sizes. Chondrocytes and osteoblasts were sized similarly, so grouping was based more heavily on the biomechanical parameters. The differences in mechanical properties were more distinct for the spread morphology than spherical, which was reflected by the more uniform groupings among nodes (Fig. 4). Upon simulation, the adult stem cells allocated to several different nodes, indicating a heterogeneous makeup. However, it is possible that stem cells in the process of differentiating along specific lineages will associate with nodes populated heavily by primary cells of that lineage. Past studies have shown that the mechanical properties of stem cells alter during differentiation,34,35 which could be exploitable when isolating specific lineages. Whether partially differentiated stem cells are present or not, primary cells still contaminate adult stem cell harvests and could be separated using the described methodology once their mechanical properties have been identified. Increasing the proportion of true stem cells would have a positive effect on cell-based therapies since a larger percentage of cells would respond as expected to a given stimulus.

While neural networks can be applied to a variety of problems, their ultimate effectiveness is dependent on the nature and quality of the data being analyzed. Ideally, inputs are totally unrelated to each other, providing independent parameters that the network can use to determine optimal groupings.14 In this regard, the current study is limited by the high correlations present between properties. For example, cells with large elastic moduli typically have large relaxed moduli (Fig. 2B, C, and E). Since these properties are related, the distinctiveness of groupings is lessened. This effect was especially apparent in the zonal chondrocyte and chondrosarcoma classification results, where property weightings were generally equivalent. Theoretically, only a single property would be necessary to achieve the same results as sorting on all the similarly weighted properties. Future studies using this sorting method will incorporate additional input parameters, such as cell surface markers. Due to the nature of neural networks, however, no limits need to be placed on the number of input parameters used, and highly correlated parameters do not necessarily need to be omitted.

FACS, which relies on fluorescent labeling of specific cell surface markers, has been the preferred method for obtaining targeted cell subpopulations quickly and efficiently.4,36 However, for many cell types, specific cell surface markers have yet to be identified. Thus, the inclusion of additional classes of parameters, such as mechanical biomarkers, may provide sufficient information to properly identify cells with complex phenotypes, such as adult stem cells. Further, recent studies have shown that populations of stem/progenitor cells may contain a spectrum of differentiation capacities from unipotent to pluripotent.1,37,38 Even in clonogenic studies, only a fraction of clones have the potential to differentiate along one or more lineages (i.e., osteogenic, chondrocytic, and adipocytic).3943 The ability to sort such subpopulations of stem cells into what may be preferred lineages would provide cell sources appropriate for numerous applications. For FACS, assessment of possible subpopulations is typically accomplished through manual cluster visualization.44 This technique is effective for a limited number of parameters, but including additional factors such as mechanical properties adds another layer of complexity, especially if the relative importance of the input parameters is not known. In this regard, neural networks simplify the process by iteratively identifying similar groupings through comparison of all parameters with adaptable weightings.

Our findings suggest that a neural network approach may provide a means of sorting and enriching mixed cell populations, based on cell mechanical properties as the primary inputs. Results showed that mixed cell populations could be theoretically enriched to a great extent using neural networks and mechanical biomarkers. If applied, this approach could improve tissue regeneration therapies by separating heterogeneous stem cell populations into tissue-specific subpopulations. Further, cell types that are difficult to distinguish, such as malignant versus benign cancer cells, might be successfully classified via mechanical biomarkers. While such measurements are currently made on single cells, the development of novel methods for high-throughput testing of cell mechanical properties will increase the feasibility of such techniques.29 The inclusion of additional characteristics, such as geometric properties, cell surface markers, or other biological properties, will help refine the sorting process. Additionally, combining the current technique with other sorting methodologies, such as flow cytometry, may further enhance specificity in cell separation.


This work was supported in part by NIH grants AR53448, AR54673, AG15768, AR50245, AR48182, and AR48852; the Coulter Foundation; and the Duke Translational Research Institute (RR024128). The authors would also like to thank Dr. Dana Nettles for her contributions, and Stefan Zauscher, Joel Block, Matthew Topel, and T. Parker Vail for their contributions to previous studies on the measurement of cell properties.


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