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A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques.

ABSTRACT: Viscoelastic characterization of materials at the micro- and the nanoscale is commonly performed with the aid of force-distance relationships acquired using atomic force microscopy (AFM). The general strategy for existing methods is to fit the observed material behavior to specific viscoelastic models, such as generalized viscoelastic models or power-law rheology models, among others. Here we propose a new method to invert and obtain the viscoelastic properties of a material through the use of the Z-transform, without using a model. We present the rheological viscoelastic relations in their classical derivation and their z-domain correspondence. We illustrate the proposed technique on a model experiment involving a traditional ramp-shaped force-distance AFM curve, demonstrating good agreement between the viscoelastic characteristics extracted from the simulated experiment and the theoretical expectations. We also provide a path for calculating standard viscoelastic responses from the extracted material characteristics. The new technique based on the Z-transform is complementary to previous model-based viscoelastic analyses and can be advantageous with respect to Fourier techniques due to its generality. Additionally, it can handle the unbounded inputs traditionally used to acquire force-distance relationships in AFM, such as ramp functions, in which the cantilever position is displaced linearly with time for a finite period of time.

SUBMITTER: Uluutku B

PROVIDER: S-EPMC8474069 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:To optimally assess oscillatory phenomena within physiological variables, spectral domain transforms are used. A discrete Fourier transform (DFT) is one of the most common methods used to attain this spectral change. In traumatic brain injury (TBI), a DFT is used to derive more complicated methods of physiological assessment, particularly that of cerebrovascular reactivity (CVR). However, a practical application of a DFT will introduce various errors that need to be considered. This study will evaluate the pulse amplitude DFT derivation of intracranial pressure (AMP) to highlight how slight differences in DFT methodologies can impact calculations. Utilizing a high-frequency prospectively maintained data set of TBI patients with recorded arterial and intracranial blood pressure, various cerebral physiological aspects of interest were assessed using the DFT windowing methods of rectangular, Hanning, and Chebyshev. These included AMP, CVR indices (including the pressure reactivity and pulse amplitude index), and the optimal cerebral perfusion pressure (with all methods of CVR). The results of the different DFT-derived windowing methods were compared using the Wilcoxon signed-ranked test and histogram plots between individual patients and over the whole 100-patient cohort. The results for this analysis demonstrate that, overall and for grand average values, there were limited differences between the different DFT windowing techniques. However, there were individual patient outliers to whom the different methods resulted in noticeably different overall values. From this information, for derived indices utilizing a DFT in the assessment of AMP, there are limited differences within the resulting calculations for larger aggregates of data. However, when the amplitude of spectrally resolved response is important and needs to be robust in smaller moments in time, it is recommended to use a window that has amplitude accuracy (such as Chebyshev or flat-top).

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A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques.

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