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Nano and Micro Technologies

Nano and Micro Technologies - Poster Session E

Poster Z1 - Using Sparse Inferred Dynamics to Estimate Acoustic Forces in 12-well plates

Saturday, October 26, 2024
10:00 AM - 11:00 AM EST
Location: Exhibit Hall E, F & G

Introduction:  The effects of non-resonant low intensity ultrasound ( on cellular growth, motility, and cytoskeletal rearrangement of cells is an area of study that has not been given substantial attention. Several attempts have been made to estimate the forces that ultrasound pressure waves create in the dishes of 12, 24, and 36-well plates, although most of these have dealt with standing wave conditions only [4]. Even in the case of standing waves the dynamics and dominant forces can be extremely complicated to model, and making direct force direct measurements remains challenging [3].

This work presents a machine learning-informed method of attempting to infer the dynamics of non-resonant low intensity ultrasound pressure due to an ultrasound transducer placed beneath a dish in a 12-well plate, whose acoustic pressure is transmitted through polystyrene and into the liquid-filled environment of an active cell culture. We use the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm [1,2] to discover the simplest form of the dynamics governing the dominant effects in our experimental model, with training data generated using a python implementation of the k-wave modeling software. Numerical solutions to the discovered partial differential equations allow us to estimate the forces being exerted within the dishes of the array, and make predictions about the expected impact on different cellular systems.

We compare our force estimates with other acousto-fluidic models, such as those from the study of standing and non-resonant waves in microfluidic channels, and find good agreement between the theories.

Materials and

Methods:  All models were carried out using open source Python implementations of k-wave and SINDy (PySINDy). We used the SINDy PDEFind algorithm, which utilizes the weak-form of SINDy as applied to partial differential equations [2] to learn the governing dynamics of the pressure field on both sides of the polystyrene-water boundary. Our plans for the near-future involve designing a micro-controlled, high precision x-y-z stage and data processing routine that will permit direct hydrophone measurements to be taken. This data will be used to check our model against and to obtain experimental training data for refined model discovery

Results, Conclusions, and Discussions: Our approach uses a sparsified machine learning method to infer the governing dynamics of non-resonant, low intensity ultrasound acoustics in a 12-well plate, where the pressure field is generated by a transducer whose wave pulse propagates through the polystyrene and into the liquid-filled environment of a cell culture. Training data obtained from our simulations indicate that the ultrasonic dynamics in the cellular environment is modeled by a modified form of the damped wave equation, where the second derivative with respect to time can be ignored. The learned PDE provides useful insight into which dynamical terms dominate, allowing us to determine which physical parameters to tune to achieve desired pressure profiles.

We obtained pressure estimates in the range of 0.1 to 1 MPa, for various transducer conditions, and along the central axis of the transducer. The pressure estimates we obtained are in close agreement with modeling results for standing wave ultrasonic waves in microfluidic chambers, but have the advantage of offering additional physical insight by studying the inferred terms of the governing PDE. It allows us to make reasonable estimates of the local ultrasonic pressure field, and yields information necessary to understanding the forces experienced by living cells in the presence of the pressure field.

This approach to modeling has significance to the field of mechanobiology, specifically the impact of low intensity ultrasound on cell wall fluctuations, cell motility, cell adhesion, and intracellular cytoskeletal dynamics which can inform future inquiries in the areas of cancer metastasis, tissue engineering, and supporting living systems in low and micro-gravity conditions. Our work in the near-future will involve the development of a high precision, micro-controlled system in which direct hydrophone measurements will be collected, both to use as a check on our current model and to obtain experimental training data to refine the learned dynamics. Models of the specific forces on cells and subcellular structures due to the pressure fields we have described require a more detailed analysis. But several well developed theories exist in which our pressure field can be used, in conjunction with cell motility data, to determine the dominant forces at play.

Acknowledgements (Optional):