### Abstract

Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the longstanding issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 X 10(9) field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 256(3) field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 20(2) pistons, respectively, thus facilitating future real-time thermal dose predictions.

Original language | English (US) |
---|---|

Pages (from-to) | 2001-2012 |

Number of pages | 12 |

Journal | IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |

Volume | 58 |

Issue number | 9 |

State | Published - Sep 2011 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Acoustics and Ultrasonics
- Instrumentation

### Cite this

*IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control*,

*58*(9), 2001-2012.

**Fast ultrasound beam prediction for linear and regular two-dimensional arrays.** / Hlawitschka, Mario; McGough, Robert J.; Ferrara, Katherine W.; Kruse, Dustin E.

Research output: Contribution to journal › Article

*IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control*, vol. 58, no. 9, pp. 2001-2012.

}

TY - JOUR

T1 - Fast ultrasound beam prediction for linear and regular two-dimensional arrays.

AU - Hlawitschka, Mario

AU - McGough, Robert J.

AU - Ferrara, Katherine W.

AU - Kruse, Dustin E.

PY - 2011/9

Y1 - 2011/9

N2 - Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the longstanding issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 X 10(9) field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 256(3) field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 20(2) pistons, respectively, thus facilitating future real-time thermal dose predictions.

AB - Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the longstanding issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 X 10(9) field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 256(3) field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 20(2) pistons, respectively, thus facilitating future real-time thermal dose predictions.

UR - http://www.scopus.com/inward/record.url?scp=84856443710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856443710&partnerID=8YFLogxK

M3 - Article

C2 - 21937338

AN - SCOPUS:84856443710

VL - 58

SP - 2001

EP - 2012

JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

SN - 0885-3010

IS - 9

ER -