Closed-Form Solutions of the Diffusion Equation to Model Prospective Nanodevice to Anticipate Diabetes Kidney Disease Through Electric Forces

摘要

We paid attention to the usage of the diffusion equation to model the flux of charged proteins through the human kidney. This is considered as one of the first signals of the renal damage in diabetic patients due that this anomalous flux of albumin goes through the zone of urine formation. This can be sustained under the hypothesis that the glucose's dipole moment would cancel the negative charges located over the inner layers of the renal glomerulus, leaving theses areas unprotected for stopping proteins and other charged compounds. Thus we introduce the concept of electric force that is used as mediator between charged proteins and a nanodevice. These electric forces are expected to provide motion to the nanodevice fact that represents an advantage in the sense that while this prospective nanodevice moves would emit an electromagnetic pulse to an external receiver. Concretely in this paper, we solve the diffusion's equation to calculate the albumin excretion rate (AER). By knowing the possible space-time trajectories of the flux of albumin this would serve for an efficient deployment of nanodevices that would anticipate the very beginning of the disease in a scenario where nano-devices are part of a network of the Internet of Bio-Nano Things.