Statistics of approximately self-affine fractals: Random corrugated surface and time series

In Situ Electrochemical Impedance Spectroscopic Method for Determination of Surface Roughness and Morphological Convexity

A novel in situ electrochemical impedance spectroscopy (EIS) method is developed for the determination of RMS roughness (h), electroactive roughness factor (R_c^*), and morphological convexity (H̅*) of the electrode surface. Our method uses the angular frequency of maximum phase (ω_M) in anomalous Warburg impedance to extract in situ RMS roughness (h). The compact electric double layer (C-EDL) formation frequency (ω_H) is used to extract the electroactive roughness factor and morphological convexity. The theory unravels the inverse square root dependence of h on ω_M through an elegant equation, h=D/ωM, where D is the diffusion coefficient of electroactive species. Similarly, the equation for the electroactive roughness factor is R_c^* = ω_H⁰/ω_H and ω_H⁰ is the smooth electrode C-EDL formation frequency. These equations are validated for the nanoparticles deposited and mechanically roughened Pt electrodes. Finally, this in situ method is applicable for both low and high roughness electrodes which transcend the limitations of contemporary methods.

Fractal Analysis of Cancer Cell Surface

Fractal analysis of the cell surface is a rather sensitive method which has been recently introduced to characterize cell progression toward cancer. The surface of fixed and freeze-dried cells is imaged with atomic force microscopy (AFM) modality in ambient conditions. Here we describe the method to perform the fractal analysis specifically developed for the AFM images. Technical details, potential difficulties, points of special attention are described.

Towards early detection of cervical cancer: Fractal dimension of AFM images of human cervical epithelial cells at different stages of progression to cancer

We used AFM HarmoniX modality to analyse the surface of individual human cervical epithelial cells at three stages of progression to cancer, normal, immortal (pre-malignant) and carcinoma cells. Primary cells from 6 normal strains, 6 cancer, and 6 immortalized lines (derived by plasmid DNA-HPV-16 transfection of cells from 6 healthy individuals) were tested. This cell model allowed for good control of the cell phenotype down to the single cell level, which is impractical to attain in clinical screening tests (ex-vivo). AFM maps of physical (nonspecific) adhesion are collected on fixed dried cells. We show that a surface parameter called fractal dimension can be used to segregate normal from both immortal pre-malignant and malignant cells with sensitivity and specificity of more than 99%. The reported method of analysis can be directly applied to cells collected in liquid cytology screening tests and identified as abnormal with regular optical methods to increase sensitivity.

FROM THE CLINICAL EDITOR

Despite cervical smear screening, sometimes it is very difficult to differentiate cancers cells from pre-malignant cells. By using AFM to analyze the surface properties of human cervical epithelial cells, the authors were able to accurately identify normal from abnormal cells. This method could augment existing protocols to increase diagnostic accuracy.

Emerging of fractal geometry on surface of human cervical epithelial cells during progression towards cancer

Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation.

Cell surface as a fractal: normal and cancerous cervical cells demonstrate different fractal behavior of surface adhesion maps at the nanoscale

Here we show that the surface of human cervical epithelial cells demonstrates substantially different fractal behavior when the cell becomes cancerous. Analyzing the adhesion maps of individual cervical cells, which were obtained using the atomic force microscopy operating in the HarmoniX mode, we found that cancerous cells demonstrate simple fractal behavior, whereas normal cells can only be approximated at best as multifractal. Tested on ~300 cells collected from 12 humans, the fractal dimensionality of cancerous cells is found to be unambiguously higher than that for normal cells.

Dependence of friction on roughness, velocity, and temperature

We study the dependence of friction on surface roughness, sliding velocity, and temperature. Expanding on the classic treatment of Greenwood and Williamson, we show that the fractal nature of a surface has little influence on the real area of contact and the static friction coefficient. A simple scaling argument shows that the static friction exhibits a weak anomaly mu ~ A(0)(-chi/4), where A0 is the apparent area and chi is the roughness exponent of the surface. We then develop a method to calculate atomic-scale friction between a microscopic asperity, such as the tip of a friction force microscope (FFM) and a solid substrate. This method, based on the thermal activation of the FFM tip, allows a quantitative extraction of all the relevant microscopic parameters and reveals a universal scaling behavior of atomic friction on velocity and temperature. This method is extended to include a soft atomic substrate in order to simulate FFM scans more realistically. The tip is connected with the support of the cantilever by an ideal spring and the substrate is simulated with a ball-spring model. The tip and substrate are coupled with repulsive potentials. Simulations are done at different temperatures and scanning velocities on substrates with different elastic moduli. Stick-slip motion of the tip is observed, and the numerical results of the friction force and distribution of force maxima match the theoretical framework.