Algorithm for multi-curve-fitting with shared parameters and a possible application in evoked compound action potential measurements

Background: Experimental results are commonly fitted by determining parameter values of suitable mathematical expressions. In case a relation exists between different data sets, the accuracy of the parameters obtained can be increased by incorporating this relationship in the fitting process instead of fitting the recordings separately. Methods: An algorithm to fit multiple measured curves simultaneously was developed. The method accounts for parameters that are shared by some curves. It can be applied to either linear or nonlinear equations. Simulated noisy measurement results were created to compare the introduced method to the straight forward way of fitting the curves separately. Results: The analysis of the simulated measurements confirm, that the introduced method yields more accurate parameters compared to the ones gained by fitting the measurements separately. Therefore it needs more computer time. As an example, the new fitting algorithm is applied to the measurements of the evoked compound action potentials (ECAP) of the auditory nerve: This leads to promising ideas to reduce artefacts generated by the measuring process. Conclusion: The introduced fitting algorithm uses the relationship between multiple measurement results to increase the accuracy of the parameters. Its application in the field of ECAP measurements is promising and should be further investigated.