Repair of Failed Cells

Markov chains theory provides a powerful tool for modeling several important processes in electrochemistry and electrochemical engineering, including electrode kinetics, anodic deposit formation and deposit dissolution processes, electrolyzer and electrochemical reactors performance and even reliability of warning devices and repair of failed cells. The way this can be done using the elegant Markov chains theory is described in lucid manner by Professor Thomas Fahidy in a concise chapter which gives to the reader only the absolutely necessary mathematics and is rich in practical examples. 

Modeling Electrochemical Phenomena via Markov Chains and Processes gives an introduction to Markov Theory, then discusses applications to electrochemistry, including modeling electrode surface processes, electrolyzers, the repair of failed cells, analysis of switching-circuit operations, and other electrochemical systems... 

Here, i corresponds to the number of failed cells. The time required to reach k failed cells is now given by the time to reach state k when starting in state 0. This is known as a phase-type distribution (Neuts, 1981), but the inter-repair time distribution in this particular case is also known as a hypoexponential distribution ... 

Other defense mechanisms are also available. Cells have effective transport systems which pump out foreign chemicals. Our cells are very good at repairing chemically damaged DNA (deoxyribonucleic acid see Chapter 9 for a more detailed discussion of DNA) and even this event is not fatal. Only when the capacity for the cell to repair itself is overwhelmed does disease result. Again, dose is the determining factor. Finally, if all else fails, cells that become carcinogenic often induce an immune response to themselves and are eliminated by this route. When these mechanisms have been exhausted, or, in the case of extreme age, when they have become worn out, disease occurs. 

The poly-adenosine diphosphate-ribose polymerase (PARP) (Table II) was essential for DNA repair in ancient fungi and remains in use in Aspergillus and Neurospora species. The PARP protein interacts with the entire protein metabolism (catalytic activities) of the cell in a stimulatory fashion. Haploid fungal cells with defective PARP die diploid cells survive, but undergo increased mutational events. In one case, loss-of-function phosphatases fail to deactivate MAPK, resulting in hyphal hyperprolifreation (Figure 63). Human cancer cells use PARP to initiates... 

In this paper we proposed a model for partial repair (or imperfect maintenance) based on the superposition of renewal processes. We showed how this model may he used to determine an approximate (asymptotic) proh-ahihty distribution of the time between repairs. Failed cells or components are not repaired until a predefined fraction of the total number has failed. 

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