Machine learning models based on FEM simulation of hoop mode vibrations to enable ultrasonic cuffless measurement of blood pressure

Ravinder Kumar; Vishal Kumar; Collin Rich; David Lemmerhirt; Balendra; J Brian Fowlkes; Ashish Kumar Sahani

doi:10.1007/s11517-024-03268-9

Machine learning models based on FEM simulation of hoop mode vibrations to enable ultrasonic cuffless measurement of blood pressure

Med Biol Eng Comput. 2025 Jan 6. doi: 10.1007/s11517-024-03268-9. Online ahead of print.

Authors

Ravinder Kumar¹, Vishal Kumar², Collin Rich³, David Lemmerhirt³, Balendra², J Brian Fowlkes⁴, Ashish Kumar Sahani²

Affiliations

¹ Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA. ravinderkumar702@gmail.com.
² Department of Biomedical Engineering, Indian Institute of Technology, Ropar, Punjab, India.
³ Sonetics Ultrasound Inc, Ann Arbor, MI, USA.
⁴ Basic Radiological Science Division, University of Michigan, Ann Arbor, MI, USA.

PMID: 39760966
DOI: 10.1007/s11517-024-03268-9

Abstract

Blood pressure (BP) is one of the vital physiological parameters, and its measurement is done routinely for almost all patients who visit hospitals. Cuffless BP measurement has been of great research interest over the last few years. In this paper, we aim to establish a method for cuffless measurement of BP using ultrasound. In this method, the arterial wall is pushed with an acoustic radiation force impulse (ARFI). After the completion of the ARFI pulse, the artery undergoes impulsive unloading which stimulates a hoop mode vibration. We designed two machine learning (ML) models which make it possible to estimate the internal pressure of the artery using ultrasonically measurable parameters. To generate the training data for the ML models, we did extensive finite element method (FEM) eigen frequency simulations for different tubes under pressure by sweeping through a range of values for inner lumen diameter (ILD), tube density (TD), elastic modulus, internal pressure (IP), tube length, and Poisson's ratio. Through image processing applied on images of different eigen modes supported for each simulated case, we identified its hoop mode frequency (HMF). Two different ML models were designed based on the simulated data. One is a four-parameter model (FPM) that takes tube thickness (TT), TD, ILD, and HMF as the inputs and gives out IP as output. Second is a three-parameter model (TPM) that takes TT, ILD, and HMF as inputs and IP as output. The accuracy of these models was assessed using simulated data, and their performance was confirmed through experimental verification on two arterial phantoms across a range of pressure values. The first prediction model (FPM) exhibited a mean absolute percentage error (MAPE) of 5.63% for the simulated data and 3.68% for the experimental data. The second prediction model (TPM) demonstrated a MAPE of 6.5% for simulated data and 8.73% for experimental data. We were able to create machine learning models that can measure pressure within an elastic tube through ultrasonically measurable parameters and verified their performance to be adequate for BP measurement applications. This work establishes a pathway for cuffless, continuous, real-time, and non-invasive measurement of BP using ultrasound.

Keywords: ARFI; Blood pressure; FEM; Hoop mode frequency; Machine learning.