How to Modeling Ultrasound Propagation & Energy Distribution From a Curved Surface Through Three Distinct Homogenous Media?

Question

I am working on a problem involving a cylindrical US transducer designed for radial emission. Positioned vertically (axial length perpendicular to the ground), the transducer emits energy circumferentially in 360 degrees from all points along its curved, axial shell (Surface Area: 37.699 mm^2). Power is supplied continuously for 10 seconds to the transducer and distributed uniformly across this curved emitting surface. ~50% of the electrical input is converted into heat, and the remaining ~50% is converted into mechanical/US energy. The transducer dimensions are: Axial length/height = 6 mm, radial length (non-emitting diameter) = 2 mm, Radius of curvature = 1 mm. The transducer operates within a biological lumen (37C), held coaxial with the lumen by an inflated cooling balloon. The balloon circulates cooled normal (0.9%) saline of known volume and flow rate. Wave propagation from any point on the transducer's emitting surface travels radially through: (Medium 1: 4.2 mm of cooled, circulated saline), (Medium 2: 1.3 mm), and thereafter through (Medium 3). The material properties for all media (e.g., acoustic impedance, density, speed of sound, etc.) are well-defined. I am seeking advice on physics-based approaches, simulation tools, or accessible models capable of accommodating radial US distribution from a curved surface, fluid circulation's impact on wave propagation in Medium 1, and propagation through three homogenous, but distinct, media. Importantly, I aim to avoid reliance on advanced coding or scripting. A practical, cost-effective solution suitable for academic or small business use is especially valuable. Any guidance - whether through simulation platforms, existing models, or expert recommendations - is immensely appreciated. Accurate modeling of wave propagation and energy distribution is vital to me and thank you very much for your time and any assistance!

Answer 1

You are asking the community to design something for you that would require a small team of experts at least one year to do. You will find them on the R&D staff of any company that manufactures medical ultrasound equipment. They will be expensive.