相关论文: Mathematics of nerve signals
The action potential propagating in a nerve fibre generates accompanying mechanical and thermal effects. The whole signal is therefore an ensemble which includes primary and secondary components. The primary components of a signal are the…
The recent theoretical and experimental studies have revealed many details of signal propagation in nervous systems. In this paper an attempt is made to unify various mathematical models which describe the signal propagation in nerve…
This paper attempts to review our studies on the propagation of signals in nerves over the past decade. The need for interdisciplinary studies is stressed that helps to understand the physical mechanisms of coupling the electrical,…
Recent studies have revealed the complex structure of nerve signals in axons. There is experimental evidence that the propagation of an electrical signal (action potential) is accompanied by mechanical and thermal effects. In this paper,…
The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal…
Recent studies have revealed the complex structure of nerve signals in axons. Besides the electrical signal, mechanical and thermal effects are also detected in many experimental studies. In this paper, the mathematical models of heat…
In this paper mathematical models are formulated in order to simulate heat production and corresponding temperature changes which accompany the propagation of an axon potential. Based on earlier experimental results, several models are…
We investigate different mechanical effects which accompany the nerve pulse propagation by using mathematical modeling. The propagation process is composed by three connected phenomena: (i) the action potential (electrical signal) which is…
The propagation of an action potential (AP) in a nerve fibre is accompanied by mechanical and thermal effects. In this paper an attempt is made to build up a mathematical model which couples the AP with a possible pressure wave (PW) in the…
For the purposes of abstract theory of signal propagation, a signal is a submanifold of a Riemannian manifold. We obtain energy inequalities, or upper bounds, lower bounds on energy in a number of specific cases, including parameter spaces…
Currently, biological signaling is envisaged as a combination of activation and movement, triggered by local molecular interactions and molecular diffusion, respectively. However, we here suggest, that other fundamental physical mechanisms…
Biological membranes mainly consist of lipids and proteins. While the proteins have many functions as single molecules, the membrane as a whole displays physical properties that cannot be explained on the single molecule level. For example,…
Biological signaling is imagined as a combination of activation and transport. The former is triggered by local molecular interactions and the latter is the result of molecular diffusion. However, other fundamental physical principles of…
In signal processing, a signal is a function. Conceptually, replacing a function by its graph, and extending this approach to a more abstract setting, we define a signal as a submanifold M of a Riemannian manifold (with corners) that…
This paper deals with the mathematical modelling of signal propagation in nerve fibres. Due to the complexity of the processes where electrical, mechanical, and thermal effects are coupled, a phenomenological approach helps to build…
Cellular signaling is essential in information processing and decision making. Therefore, a variety of experimental approaches have been developed to study signaling on bulk and single-cell level. Single-cell measurements of signaling…
Membranes are present in all cells and tissues. Mathematical models of cells and tissues need a compact mathematical description of membranes with a resolution of about 1 nm. Membranes isolate cells because ions have difficulty penetrating…
This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models…
The textbook picture of nerve activity is that of a propagating voltage pulse driven by electrical currents through ion channel proteins, which are gated by changes in voltage, temperature, pressure or by drugs. All function is directly…
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…