Ultrasound Beam Focusing Considering the Cutaneous Fat Layer Effects

Transcription

1 Ultrasound Beam Focusing Considering the Cutaneous Fat Layer Effects A. B. M. Aowlad Hossain 1*, Laehoon H. Kang 1 Deartment of Electronics and Communication Engineering Khulna University of Engineering & Technology Khulna-903, Bangladesh aowlad0403@yahoo.com Deartment of Biomedical Engineering Kyung Hee University Youngin-si, Reublic of Korea * Corresonding author Received: Setember 7, 01 Acceted: December 8, 01 Published: January 8, 013 Abstract: Commercial medical ultrasound scanners assume average sound velocity of 1540 m/s while sound seed varies at different tissues. This assumtion limits focusing uality and degrades contrast and resolution, articularly for atients with fatty abdominal wall. This aer resents a simle two layer model to demonstrate the effect of ultrasound beam focusing uality in inhomogeneous medium based on Huygens s rincile. A time delay function for ultrasonic hase array has been derived using in vivo information of fat layer and considering refraction in the interface of two layers. Simulated beam attern and corresonding beam rofiles at the focal deth using conventional delay time and that for roosed two layer model are comared. An exerimental setu was designed to assess the image uality using a commercial ultrasound scanner and a hantom of two layers with different sound velocity. Simulated and exerimental results indicate that obtained images using time delays for two layer model show better contrast resolution. Keywords: Ultrasound beam focusing, Fat layer effects, Sound seeds, Beamforming, Ultrasound imaging. Introduction In ultrasound imaging, hased-array transducers are used for beam focusing and steering. Beam focusing is the major factor that determines the lateral satial resolution in ultrasound imaging. In conventional ultrasound scanner, it is assumed that the ultrasound beam travels in a homogeneous media at a constant seed. However, human body consists of many different organs and tissues in which the sound velocity may change significantly. Non-uniform sound velocity makes aberration in the beam focusing, which may result in degradation of contrast and satial resolution. In abdomen imaging, the fat layer underneath the skin may have significant effects on beam focusing erformance when the fat layer is very thick. Fat tissue has the average sound seed of 1460 m/s which is much slower than the average sound seed in the muscle, 1540 m/s. The difference in sound seed and the refraction on the fat surface introduce error in hase delay calculation for transmit and receive beam formation using hase array and hence make aberration at the focal oint. Aberration leads to degradation of resolution, causes a sreading in the main lobe energy and gives rise to high isolated side lobes in the beam attern and hence off axis resonse become significant [1, ]. 63

2 There are many methods to minimize the effect of aberration roblem [3-13]. Most of the methods analyze the received echo signal in the air of different elements or elements grous to measure the deviation from exected arrival times. These deviations are used to modify time delays for received beamformer. A cross-correlation based method for estimation of arrival time fluctuations was roosed by S. W. Flax and M. O Donnel [3]. M. Fink described a time reversal mirror, which carries information about the ulse including arrival time and amlitude distortions. But this method reuires a oint reflector in the insonified medium [5]. A method based on seckle brightness is roosed by Nock et al. where the time delays are calculated corresonding to brightness maximization over a region of interest [6]. K. W. Rigby et al. resented some estimation and correction of time delays based on cross correlation and summing of echo signals in neighboring elements airs [9-11]. S.-E. Måsøy et al. roosed aberration estimation algorithm to estimate arrival time and amlitude fluctuations with signals from random scatterers in both freuency domain [1] and time domain [13] and analyzed variance of the estimates. Most of the existing methods consider the roagation medium as homogeneous and neglect refraction of acoustics rays in the interface of different tissue layers. Furthermore there are very few research works on aberration correction using in vivo information. In order to consider refraction, information about fat layer thickness and sound velocity are necessary to calculate the time delay. So to calculate more accurate time delay to obtain better focus uality and hence better resolution in ultrasound imaging in inhomogeneous media using hase array, in vivo information about fat layer thickness and sound velocity in the medium should be incororated in time delay calculations. In this work, we evaluate the effect of fat layer on the beam focusing uality using two layer model of sound wave roagation. The time delay function is derived using in vivo information of fat layer thickness and velocity of sound roagation through the inhomogeneous medium. Simulation and exerimental results using time delays based on both conventional and roosed method are resented. Materials and methods Effects of fat layer on beam focusing uality We first investigated the effects of a cutaneous fat layer on the beam focusing uality. With the two layer model shown in Fig. 1, we calculated the beam rofiles at the assumed focal deth. The sound seeds of the layer 1 (fat) and layer (non-fatty tissues) were assumed to be 1460 m/s and 1540 m/s, resectively. On to of the fat layer, (n + 1) oint sources are linearly laced with the interval of. Fig. 1 Two layer model with linear array of oint sources 64

3 A wavefront roagates away from an exciting oint source at the seed of sound in the roagating media and it does so eually in all directions. Therefore after a given time it has formed a sherical wavefront with a radius roortional to the time interval. Considering adiabatic condition the acoustics wave euation in the homogeneous medium with sound velocity c can be written as: 1 = (1) c t The solution of wave euation for a oint source in unbound homogeneous medium can be exressed as: = 0 e i ( ωt kr) r () ω π where ω = πf and k = =. In the above euation, 0 is the constant amlitude for all c λ sources, r is the radial distance, f is the freuency, ω is the angular freuency, λ is the wavelength and k is the wave number. Amlitude decaying factor r 1 is alied in the above euation in order to satisfy the law of conservation of energy. When a number of oint sources excited simultaneously or in different instant of time, the sherical wavefronts generated from the sources may add together or cancelled out each other due to hase differences. Hence constructive or destructive interference occur as a result of suerosition of wavefronts from different oint sources. The resultant wavefront will be the algebraic sum of the individual waves which can be written as: = N j = 1 0 e i( ω( t τ j ) krj ) r j (3) where t is the reference time, τ j is delay time for j-th source, source and N is total number of oint sources. r j is radial distance from j-th If the oint sources are excited with delay τ j starting from t = 0 then, = N j = 1 0 e i( ωτ j krj ) r j (4) Now according to Huygens s Princile, each oint on that wavefront acts as a source of successive wavefronts, which roagate in the same fashion. Therefore in the interface of two layers roagating wavefront gives rise to secondary sources, each of which radiates wavefronts. These sources aear continuously at all ositions in the interface and combined together to roduce new wavefronts in accordance to their individual hase. The wavefronts in the second layer can be calculated as: 65

4 = where M = 1 e i( kr ) r and is the magnitude and angle of -th secondary source ressure, r is radial distance from -th source and M is total number of oint sources and for second layer. k (5) is the wave number The beam attern in the imaging lane can be shown from these ressure distributions. To kee the continuity in ressure distribution throughout two layers a multilication factor ( ) eual to the ratio of energy in interface (secondary sources) to rimary sources is introduced with in the denominator. r m f = M = 1 e i( kr ) m f r (6) where, normalizing factor E E on the interface (secondary source): E = = m f =, energy on the transmitter surface: 1 M 1. 1 N 0 E =, energy Derivation of hase delay function to comensate the fat layer effects Ultrasound beam focusing is alignment of roagating waves from oint sources to a secific oint at the same time. Focusing can be accomlished by delayed excitation of oint sources. The delay time can be calculated from the geometrical relationshi of acoustics ray ath through medium of different velocity. The calculated delay times can be used for both transmit and receive beamforming to investigate the fat layer effects. Fig. shows the geometrical relationshi of acoustics ray ath to a secific focal oint. Fig. Derivations of time delays for two layer model 66

5 The delay time for i-th oint source comared to center oint source is derived. The roagation times are: t d F d CB BA = (7) c AD + and t ABC = + c1 c c1 Therefore roagation delay between i-th oint source and center oint source to reach at focal oint is the difference between above two roagation times. Referring to Fig. 3, ath length CB and BA can be calculated as: d F d CB = and BA = cosθ 1 cosθ (8) So the roblem is reduced to calculation of θ 1 and θ. From the geometry, we can write: d tanθ 1 + ( F d) tanθ = X (9) From Snell s law for refraction of non-erendicular sound waves through medium of different velocity, we have, 1 c1 d tan(sin ( sinθ ) + ( F d) tanθ = X (10) c Numerical methods are alied for solving above euation to obtain the values of θ 1 and θ which are used to calculate the time delay between oint sources. Fig. 3 shows the difference in roagation times as well as difference in excitation times for the oint sources considering different thickness of fat layer in comarison with single layer. Fig. 3 (a) Elements-wise difference in roagation time from that of single layer case for different fat layer thickness, (b) Excitation delay for 64 elements with center to center sacing of 0.3 mm and focal deth of 10 cm along center line for different thickness of fat layer. Excitation starts from most distant element with resect to center element. For steering case, the erendicularly distant oint source on the surface from the focal oint is considered as reference oint for time delay calculation. 67

6 Results and discussion Simulation results To analyze the effect of fat layer on the focus uality we simulated ultrasound beam attern based on oint source model of sound wave roagation. The beam atterns has been obtained by alying the conventional time delay and calculated time delay considering various fat layer thicknesses to excite oint sources. In this simulation we considered an array of 56 oint sources with center to center sacing of 0.3 mm and a focal deth of 10 cm. The beam rofiles in the focal deth obtained using time delays considering single layer for different fat layer thickness are comared. Fig. 4 shows the simulated beam attern in both single layer and double layer and beam rofiles with fat layer thickness of 4 cm at the focal deth of 10 cm. It is observed that the beam rofile obtained from the homogeneous model has a wider and weaker main lobe than that obtained from the two layer model. This is due to the shifting of focal oint from desired location. As the fat thickness increases, the aberration also increases. Fig. 4 (a) Simulated beam attern for homogeneous medium, (b) Simulated beam attern using time delays calculated from two layer model, (c) Simulated beam attern using time delays calculated from single layer model, (d) Comarison of beam rofiles along focal deth for single and two layer, and (e) Comarison of beam rofiles along focal deth using single layer time delay with fat layer thickness of cm, 4 cm, and 6 cm 68

7 Exerimental results We made a hantom using butter fat, agar, gelatin, and water to imlement two layer model of medium with different sound seeds. The 1.7 cm thick uer layer was made of butter fat, agar, gelatin, and water to mimic fat layers and the 8.3 cm thick lower layer was made of agar, gelatin, and water to mimic non-fatty layers. To calculate the hase delays based on the exact sound seed of each layer, we measured the sound seeds of the layers at searate A-mode exeriments. It has been found that the uer and lower layers have the sound seeds of 1645 m/s and 1695 m/s, resectively. To evaluate the lateral resolution, we inserted two nylon monofilaments with the diameter of mm in arallel and mm aart from each other in the lower layer as shown in Fig. 5. We used a commercial ultrasound scanner (GE Healthcare, LOGIQ P5) to take linear scan images. The ultrasound scanner has a 18-element linear hase array robe with the element-to-element interval of 0.3 mm, where 64 elements are active for beamforming. Fig. 5 Phantom of two layer model We have formed three kinds of images from the RF echo data to comare the image uality. Among them, one directly from the ultrasound scanner which makes the image with the assumed sound seed of 1540 m/s, and two from the receive beam formation using the time delays calculated for the single layer with the sound seed of 1695 m/s and two layer models with the sound seed of 1645 m/s and 1695 m/s, are shown in Fig. 6. Fig. 6b shows the ROI images of nylon monofilament inserts for better comarison. In all cases, the scanner average sound seed of 1540 m/s is used for transmit beamforming. The image obtained after received beamforming with the sound seed of 1645 m/s and 1695 m/s in the two layer model, shows a little better contrast as well as lateral resolution. With the two-layer hantom which has small sound seed difference between the layers, the effect of taking account of two layers in calculating hase delays seems to be marginal. However, in human imaging where the sound seed of fatty tissue is much slower than the hantom, the effect is exected to be bigger than in the case of hantom imaging with conventional transmit beamforming using average sound seed. We are now trying to develo new hantoms which better mimics fatty tissues in terms of sound velocity. The roosed model considered refraction of sound waves due to inhomogeneity and corresonding roagation aths for time delay calculation rather than consideration of straight beam ath in most of the existing methods. Focusing has been imroved for more accurate time delays calculated from two layer model but with extra comutational burden. Additional studies are necessary to automatically estimate fat layer thickness and sound seeds from echo signals for clinical alication of the roosed method. 69

8 Fig. 6 (a) Images of the hantom for different models and (b) ROI images of nylon monofilament inserts Conclusion Two different models of sound wave roagation through inhomogeneous media are resented to find the time delay function that can be used for beamforming in ultrasound imaging. Degradation in the beam focusing uality has been observed in the single layer model as the effect of fat layer. The time delay functions have been derived in the double layer model considering the refraction of acoustic waves on the interface of two layers as well as the different roagation seeds through medium. Both simulation and exerimental results show imrovements in image uality with finer beam focusing. Acknowledgements This study was suorted by the grants from the National Research Foundation of Korea ( ) and the grant from the Ministry of Knowledge and Economy of Korea ( ). 70

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10 A. B. M. Aowlad Hossain, Ph.D. Dr. A. B. M. Aowlad Hossain received his B.Sc. in Electrical & Electronic Engineering from Khulna University of Engineering & Technology (KUET) and M.Sc. in Electrical & Electronic Engineering from Bangladesh University of Engineering & Technology (BUET) in 00 and 005 resectively. He joined in KUET as a lecturer in 005. Dr. Hossain comleted his Ph.D. in Biomedical Engineering from Kyung Hee University, Korea in 01. Currently he is an assistant rofessor in the deartment of ECE, KUET. His research interests are ultrasound imaging, ultrasound and x-ray elasogarhy etc. He has ublished about 15 aers. Laehoon Kang, M.Sc. Mr. Laehoon Kang obtained his B.Sc. in Biomedical Engineering and M.Sc. in Biomedical Enginneering from Kyung Hee University, Reublic of Korea in 008 and 010 resectively. Now he is continuing his Ph.D. in medical imaging system lab of the same university. His research areas are ultrasound imaging, MRI etc. 7