With the model of equivalent charge distribution, we calculated the exact electrostatic force acting on the real ͑conical͒ tip of an atomic force microscope. This model applies to a conductive tip in front of a conductive plane. We compared the equivalent charge model with several analytic models used to date to approximate the electrostatic forces and discussed their degree of validity. We estimated the contribution of the cantilever to the total force and showed, on the basis of theoretical calculations and experimental results, that the contribution of cantilever may constitute the essential part of the electrostatic force in the range of distances used in electrostatic force microscopy in the air.

The field of spinal cord MRI is lacking a common template, as existing for the brain, which would allow extraction of multi-parametric data (diffusion-weighted, magnetization transfer, etc.) without user bias, thereby facilitating group analysis and multi-center studies. This paper describes a framework to produce an unbiased average anatomical template of the human spinal cord. The template was created by co-registering T2-weighted images (N = 16 healthy volunteers) using a series of pre-processing steps followed by non-linear registration. A white and gray matter probabilistic template was then merged to the average anatomical template, yielding the MNI-Poly-AMU template, which currently covers vertebral levels C1 to T6. New subjects can be registered to the template using a dedicated image processing pipeline. Validation was conducted on 16 additional subjects by comparing an automatic template-based segmentation and manual segmentation, yielding a median Dice coefficient of 0.89. The registration pipeline is rapid (~15 min), automatic after one C2/C3 landmark manual identification, and robust, thereby reducing subjective variability and bias associated with manual segmentation. The template can notably be used for measurements of spinal cord cross-sectional area, voxel-based morphometry, identification of anatomical features (e.g., vertebral levels, white and gray matter location) and unbiased extraction of multi-parametric data.

We present a method to determine the local dielectric permittivity of thin insulating layers. The measurement is based on the detection of force gradients in electric force microscopy by means of a double pass method. The proposed experimental protocol is simple to implement and does not need any modification of standard commercial devices. Numerical simulations based on the equivalent charge method make it possible to carry out quantification whatever the thickness of film, the radius of the tip, and the tip-sample distance. This method has been validated on a thin SiO 2 sample for which the dielectric permittivity at the nanoscale has been characterized in the literature. We also show how we can quantitatively measure the local dielectric permittivity for ultrathin polymer film of poly͑vinyl acetate͒ and polystyrene.