A diagnostic approach is developed and implemented that provides clear feature definition in atomic force microscopy (AFM) images of neural cells on nanofibrillar tissue scaffolds. Because the cellular edges and processes are on the same order as the background nanofibers, this imaging situation presents a feature definition problem. The diagnostic approach is based on analysis of discrete Fourier transforms of standard AFM section measurements. The diagnostic conclusion that the combination of dynamic range enhancement with low-frequency component suppression enhances feature definition is shown to be correct and to lead to clear-featured images that could change previously held assumptions about the cell-cell interactions present. Clear feature definition of cells on scaffolds extends the usefulness of AFM imaging for use in regenerative medicine.
The use of atomic force microscopy (AFM) in biomedical investigation has grown rapidly, with recent exciting applications in diverse fields including regenerative medicine (tissue engineering) (Fan et al., 2007; Tiryaki et al., 2010) , drug delivery (Sitterberg et al., 2010) , protein folding (Wang et al., 2011) , and clinical medicine (Kreplak et al., 2007) . Even so, AFM remains an underutilized technique within the biomedical research community and more importantly an underdeveloped enabler of significant new nanoscale biomedical discoveries due to a general problem with inconsistent feature definition. When a feature definition problem is encountered, the standard approach is to use instrument-supplied hardware or software capabilities to resolve it. Deflection imaging (contact mode) or phase imaging (tapping mode) can improve feature definition when changes in cantilever deflection or RMS cantilever oscillation are greatest at boundaries. Alternatively, image processing can be used to extract information that actually exists in an AFM image but is inaccessible prior to processing. Useful filters are a standard component of commercial image processing packages for AFMs, and low-pass filtering for noise reduction is a known and popular approach. However, for either hardware or software approaches to be successful, it is key to diagnose and accurately identify the nature of the feature definition problem involved. As will be shown, low-pass filtering can be the wrong approach to improve feature definition. There has been comparatively little systematic methodology developed for image diagnosis, other than user experience. This can make the AFM learning curve a lengthy one for new biomedical researchers, especially for certain classes of biomedical problems that have feature definition issues.
In the present work, a severe problem with feature definition of astrocyte neural cells on a promising prosthetic nanofibrillar scaffold for brain and spinal cord injury repair (Meiners et al., 2007; Meiners et al., 2009) is first diagnosed and then resolved. Recent studies indicate that cells grown on nanofibrillar surfaces that approximate their native extracellular matrix (ECM) environments behave differently, and in seemingly more biomimetic ways (Georges et al., 2006; Delgado-Rivera et al., 2009) . Many details of the cell-cell and cell-scaffold interactions that may induce the biomimetic response are not presently well known. This is therefore a research area in which the nanoscale resolution capability of AFM could offer significant biomedical insights. The difficulty with AFM investigation is that cells on nanofibrillar surfaces interact with these surfaces via nanoscale edges and processes that are not distinguishable from the nanofibrillar background by height, deflection, or phase imaging. This is because the cellular edges and processes are approximately the same order in height as the background nanofibers, ∼100 to 200 nm. We demonstrate that this problem can be resolved by filtering and present a novel diagnostic approach based on standard AFM section measurements to enable knowledgeable filter selection and design. The requirements for successful image processing were identified as a combination of low-frequency component suppression with dynamic range enhancement. This design was implemented to filter the harmonic components present in the images in such a way that the cellular edges and processes became distinguishable from the nanofibrillar backgrounds. We demonstrate that the new information revealed in the filtered AFM images would change the biomedical interpretations drawn about the cell-cell interactions present, especially when compared with a more typical analysis of fluorescent microscopy images.
Neural Cell Culture
Rat cerebral cortical astrocytes were prepared from postnatal day 1 (P1) Sprague Dawley rats and grown to confluence in astrocyte medium in 75-cm 2 tissue culture flasks as previously described (Delgado-Rivera et al., 2009) . The astrocyte culture medium was comprised of Dulbecco’s Modified Eagle’s Medium (Invitrogen, Carlsbad, CA) +10% calf serum (Invitrogen). After reaching confluence (∼8-10 days), flasks were shaken overnight on a rotary shaker at 37 • C to remove any loosely adherent oligodendrocytes, neurons, or macrophages. Astrocytes were then subcultured in astrocyte medium (0.5 ml) at a density of 50,000 cells/well onto 12-mm coverslips coated with nanofibers in 24-well trays. The astrocytes were maintained for 24 h. The astrocytes were then fixed with paraformaldehyde (4%) and stained with phalloidin (Schindler et al., 2005) for fluorescent microscopy investigation. Staining did not affect the AFM imaging.
Nanofibrillar Culture Surface
Randomly oriented polyamide nanofibers (median diameter ∼180 nm) were electrospun from a blend (Chung et al., 2004; Schindler et al., 2005) MN) . Crosslinking of nanofibers was done in the presence of an acid catalyst. The resulting nonwoven polymeric nanofibrillar matrix was approximately 2.0-μm thick when measured on edge by optical microscopy, with no direct openings to the coverslip surface (Grafe and Graham, 2002; Ahmed et al., 2006) .
Epi-fluorescence microscopy images of astrocyte neural cell cultures at 24 h were captured using a Zeiss Axioplan microscope (Carl Zeiss Microimaging GmbH, Jena, Germany). Fluorescence optical microscopy is the most widely utilized technique for cell culture analysis.
Atomic Force Microscopy (Afm)
AFM images of astrocyte neural cell cultures at 24 h were captured using a Nanoscope IIIA (Bruker AXS Inc, Madison WI, formerly Veeco Metrology) operated in ambient air. Wide-area images showing cell groups were acquired using a J scanner with a maximum scan range of 125 × 125 μm 2 x-y range and ±2.774 μm z range with the AFM was operated in contact mode, using silicon nitride tips with a nominal tip radius of 20 nm and a cantilever spring constant k = 0.58 N/m. Close-up images of cell-scaffold interactions were acquired using an E scanner with a maximum scan range of 13.5 × 13.5 μm 2 x-y range and ±1.54 μm z range with the AFM was operated in tapping mode, using etched silicon tips with a nominal tip radius of 10 nm and a drive frequency of ∼320 kHz.
Image Processing Methods
Digital image processing techniques were implemented with MATLAB version 7.6.0 (R2008a) (The MathWorks, Natic, MA). Digital images were exported as ASCII files from the Nanoscope Software version 5.30r3.sr3 by converting the units to nanometer. Four different types of two-dimensional finite impulse response digital filters were evaluated in this work: frequency domain Gaussian and Butterworth high-pass filters, spatial domain high-pass filters, and high-boost filters. The Gaussian and Butterworth high-pass filters were implemented over frequency domain with normalized cutoff frequencies (ω/π) from 0 to 1 and with integer degrees from 1 to 5. As a final step, histogram equalization was applied for contrast enhancement (MATLAB R ).
Gaussian High-Pass Filter (Ghpf) Implementation
Image enhancement in the frequency domain is based on the computation of the two-dimensional discrete Fourier transform (DFT) of the input image, followed by multiplication of the result by a filter transfer function. The final output is obtained by taking the inverse two-dimensional DFT of the product. The fast Fourier transform, the computationally efficient algorithm (Frigo and Johnson, ’98) for computing DFT, was performed for all of the DFT computations throughout this work.
The two-dimensional DFT of an M × N pixel image was calculated as
EQUATION (1): Not extracted; please refer to original document.
where x and y are the spatial variables, f(x,y) is the raw image, u and v are the frequency domain variables, and F is the two-dimensional DFT of the M × N pixel image. The GHPF transfer function was implemented as
EQUATION (2): Not extracted; please refer to original document.
where D 0 is the cutoff frequency and D (u,v) is the distance from (u,v) to the origin. To apply the GHPF to the image, F (u,v) and H (u,v) were multiplied by array multiplication. u,v) and the inverse two-dimensional DFT defined as
G(u,v) = F(u,v)H(
EQUATION (3): Not extracted; please refer to original document.
was applied, and the final GHPF result was obtained.
High-Boost Filtering Implementation
High-boost, or high-frequency emphasis, filtering is based on adding a specified percent of the original image to the high-pass filtered image (Gonzalez and Woods, 2008) . This addition restores the low-frequency components that were lost in the highpass filtering operation, so the resulting image may look more like the original image. This was attractive for reinclusion of cell surface features. A high-boost filter was implemented as
EQUATION (4): Not extracted; please refer to original document.
where Y is the filter output, A is the amplification factor, O is the original image, and H is the high-pass filtered image.
Histogram Equalization For Contrast Enhancement
A histogram equalization was performed in order to enhance the contrast of the filtered images. The image contrasts were enhanced by transforming the values in the filtered image, so that the histogram of the output image had a roughly equal number of pixels mapped to each of its 256 levels. The histogram equalization operation converted the low-contrast and dark images to relatively higher contrast and brighter images.
In this section, we first identify the feature definition problem found in distinguishing thin neural cell processes and edges from the tissue-culture surfaces that have nanoscale features. Our quantitative problem diagnosis procedure is presented next. The optimal filter design based on the problem diagnosis is then given, and finally, the biomedical interpretations drawn from analyzing images with missing versus complete information are discussed.
Feature Definition Problem
A composite AFM height image of a threeastrocyte group on a nanofibrillar surface is shown in Figure 1(a) . The feature definition is poor for both the cell edges and the cellular processes (extensions with which a cell explores its environment). The structures marked by arrows in the AFM height image of Figure 1 (a) could be either nanofibers or cellular processes. Close-ups of potentially important cellscaffold interactions (dashed box in Fig. 1(a) ) were investigated by AFM tapping mode phase images. As shown in Figure 1(b) , this did not improve the feature definition. The problem is that the cellular edges and processes are approximately the same order in height as the background nanofibers, ∼100 to 200 nm.
Systematic Approach To Problem Diagnosis
A diagnostic approach based on standard AFM section measurements was developed. Individual section measurements of the nanofibrillar surface and an astrocyte cell body are shown in Figure 2 (a)/(b) and (d)/(e). A one-dimensional DFT was then applied to the section measurement data of Figure 2(b) and (e). This converted the section measurements into the frequency domain where the harmonic components could be studied and analyzed. The magnitudes of the DFT spectra were then calculated, and the logarithmic DFT spectra were plotted. The logarithmic DFT spectra shown in Figure 2 (c) and (f) can be used to identify the key differences between the cell and nanofibrillar surfaces, which can then be used to create an optimal filter design. In the present case, the differences were 1. The one-dimensional DFT spectra in Figure 2(c) and (f) demonstrated that the amplitude of the zero-frequency sample of the cell profile was approximately fivefold higher than the amplitude of the zero frequency of the nanofibrillar profile. This suggested that attenuation of the zero-frequency sample and the other low-frequency components with a high-pass filter would result in deemphasizing the astrocyte surface relative to the nanofibers so that the astrocyte surface could be distinguished from the nanofibrillar background. This is known as dynamic range enhancement. 2. The nanofibrillar surface had sharper features, meaning more power in the higher frequency harmonics than the astrocyte surface. The highfrequency harmonic region above cutoff frequency 0.5 (red dotted lines) had 52% more power than the same frequency region for the astrocyte DFT spectrum. 3. The low-frequency harmonics of astrocytes and nanofibers were overlapping in the DFT spectra ( Fig. 2(c) and (f)). Therefore, total elimination of cell surface information while retaining the nanofibrillar surface information is not possible by filtering techniques. However, because the high-frequency components of nanofibrillar surface had more power than the high-frequency components of astrocyte surfaces, as shown in Figure 2 (c) and (f), amplification of the high-frequency components would exaggerate the difference between nanofibers and astrocytes. This is achieved by using a high-pass, not a low-pass, filter. The results of a preliminary test using a GHPF, shown in space and k-space domains in Figure 3 , confirmed this approach. When the GHPF surface profiles shown in Figure 3(a) and (c) are compared, we see that the nanofibrillar surface has higher edge features than the astrocytes. Figure 3(b) and (d) show that the high-frequency harmonics of nanofibrillar substrate has more power than the high-frequency harmonics of astrocyte surface. These quantitative differences are the basis for the subsequent successful filter design.
Optimal Filter Design Based On Problem Diagnosis
The Gaussian and Butterworth frequency domain high-pass filters were implemented by changing the order and the cutoff frequency of the filter. Optimum results were obtained with a GHPF transfer function of order 1 and normalized cutoff frequency 0.5. The perspective plot of the GHPF transfer function of order 1 and normalized cutoff frequency 0.5 is shown in Figure 4 (a) and the radial cross section of the transfer function is shown in Figure 4(b) . Figure 4(a) shows that the Gaussian frequency domain high-pass filter is positional invariant or isotropic. Application of the Butterworth filter yielded noisier results, therefore identifying the optimized GHPF as preferable.
Spatial domain filters were also investigated, both as an alternative to frequency domain filter and because of our interest in high-boost filtering, a variant of spatial filtering, for return of cell features to filtered images. Spatial domain filters require the specification of a mask. In the present work, 3 × 3, 5 × 5, and 7 × 7 spatial high-pass masks were investigated, and 3 × 3 mask size was identified as optimal. High-boost filtering was therefore performed using a 3 × 3 spatial high-pass mask. Amplification factors of 1.05, 1.10, 1.15, and 1.20 were implemented, and 1.15 was optimum. However, the high-boost filtering technique was not successful in our case because return of the 15% of the original image also compressed the dynamic range to the point where cellular edge and process feature definitions were unacceptably reduced. Furthermore, analysis of spatial domain transfer functions (not shown) revealed positional anisotropy that would introduce distortions into filtered images of randomly oriented nanofibers. These investigations enabled the systematic selection of the GHPF as best for our investigations.