The problem

The project aims were to (a) undertake a literature review of the mathematical modelling of ultrasound waves in liquids containing scatterers with particular regard to the identification of parameters such as cell elasticity properties in fluidic bioprocess, (b) identify the most suitable model for bioprocess applications and implement the model in a computer program, (c) compare the model output with experimental data and (d) implement the inverse problem that automates the recovery of a subset of the system parameters from experimental data. All of these objectives were met and in some instances surpassed.

The approach

After a lengthy literature survey the most appropriate model for the task was the Epstein, Cahart, Allegra Hawley (ECAH) model. The model provides estimates for the attenuation and phase velocity of ultrasound waves in suspension as a function of the system parameters and frequency. This is precisely the form of the data that is captured by the experimental apparatus and so a direct validation can be performed. The model relies on a number of assumptions such as the particles are spherical and small compared to the wavelength, any changes in temperature or pressure due to the absorption of waves can be neglected, the velocity and pressure of sound waves are small, and the particles are well dispersed so can be considered as isolated scatterers. With these assumptions equations for the propagation of a compression, transverse and thermal wave in particle-laden fluid can be derived by considering conservation laws, a stress-strain relationship and thermodynamic equations of state. Both the full model that requires some time consuming matrix inversions and an approximate model were then implemented in a MATLAB program. The model output was then compared to a range of experimental data such as suspensions of silica particles and titanium dioxide particles in water. In each case the theoretical attenuation and velocity spectra had reasonable agreement with the experimental data. The sensitivity of the model to each of the system parameter was then explored to assess the viability of an inverse problem methodology in recovering each of these parameters. A methodology for the inverse problem was then designed involved the minimisation of the least squares calculation between the theoretical and experimental data. This was subsequently implemented in MATLAB and a range of system parameters recovered. The methodology is fairly robust and the company will be testing and assessing its ability against a range of bioprocess data.

"This internship allowed me to have the experience of working in a commercial environment. In particular, being part of a multidisciplinary team and keeping to tight deadlines. As Bioinnovel is a new venture I was given an insight into how such companies start up and grow, with the associated funding and staffing considerations. I am very happy to be continuing my work with Bioinnovel, after this internship, and look forward to working closely with the experimentalists and tackling the challenging modelling problems planned," said intern Anna Lishman, University of Strathclyde.