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Published on: August 30, 2019
Experimental designs for a benign paroxysmal positional vertigo model
Santiago Campos-Barreiro1, Jesús López-Fidalgo
1Department of Mathematics, Institute of Mathematics applied to Science and Engineering University of Castilla-La Mancha Avda, Camilo José Cela 3, 13071-Ciudad Real, Spain. Jesus.LopezFidalgo@uclm.es
Background:
The pathology of the Benign Paroxysmal Positional Vertigo (BPPV) is detected by a clinician through maneuvers consisting of a series of consecutive head turns that trigger the symptoms of vertigo in patient. A statistical model based on a new maneuver has been developed in order to calculate the volume of endolymph displaced after the maneuver.
Methods:
A simplification of the Navier-Stokes problem from the fluids theory has been used to construct the model. In addition, the same cubic splines that are commonly used in kinematic control of robots were used to obtain an appropriate description of the different maneuvers. Then experimental designs were computed to obtain an optimal estimate of the model.
Results:
D-optimal and c-optimal designs of experiments have been calculated. These experiments consist of a series of specific head turns of duration Δt and angle α that should be performed by the clinician on the patient. The experimental designs obtained indicate the duration and angle of the maneuver to be performed as well as the corresponding proportion of replicates. Thus, in the D-optimal design for 100 experiments, the maneuver consisting of a positive 30° pitch from the upright position, followed by a positive 30° roll, both with a duration of one and a half seconds is repeated 47 times. Then the maneuver with 60° /6° pitch/roll during half a second is repeated 16 times and the maneuver 90° /90° pitch/roll during half a second is repeated 37 times. Other designs with significant differences are computed and compared.
Conclusions:
A biomechanical model was derived to provide a quantitative basis for the detection of BPPV. The robustness study for the D-optimal design, with respect to the choice of the nominal values of the parameters, shows high efficiencies for small variations and provides a guide to the researcher. Furthermore, c-optimal designs give valuable assistance to check how efficient the D-optimal design is for the estimation of each of the parameters. The experimental designs provided in this paper allow the physician to validate the model. The authors of the paper have held consultations with an ENT consultant in order to align the outline more closely to practical scenarios.
