Synergy加速器治疗床自动摆位准确性的验证

目的：验证图像引导放射治疗中Synergy加速器治疗床位置自动校正（RATM）的准确性。方法 ：Quasar Penta-Guide模体在Brilliance下进行定位扫描,CT图像传送到PrecisePlan治疗计划系统进行计划设计,计划分别传至MOSAIQ和XVI系统。模体在加速器治疗床上摆位后进行CBCT扫描,图像配准后用RATM进行治疗床自动位置校正,用直尺测量激光灯十字线和模体中心十字线的距离作为摆位偏差。选取头部肿瘤患者,CBCT扫描后用骨性标记自动配准,移床后再做一次CBCT扫描,配准后分析残存摆位误差。结果：治疗床的自动最大校正范围为20 mm。模体验证结果显示,在左右、头脚、垂直3个方向自动校正误差均小于2 mm。头部肿瘤患者的残存误差小于2 mm。结论：治疗床远程控制自动摆位的准确性满足临床要求,治疗床自动移动的准确性直接影响治疗效果,需要对治疗床移动的准确性进行验证和采取严格的质量保证措施。     

利用EPID图像金球位置自动跟踪算法研究

摘要：目的：建立一种全新的算法,并利用EPID（Electronic Portal Imaging Device）图像实时读取预埋于体内金球的投影位置,自动重建金球在体内的投影位置坐标。方法：利用所编算法和Matlab软件进行EPID图像读取和处理金球投影位置并自动重建金球在体内的位置坐标。即取通过图像处理和圆曲率识别各自获得的金球投影位置坐标集合的交集为真实的2D坐标,并依此反推到病人体内获得金球位于靶区当中真实的3D重建坐标。结果：本研究共进行了三组实验,每组为两个交角拍摄的EPID片。每组所有EPID片上的金球投影位置探测成功率分别为94．44％,93．75％,94．44％。算法重建的和利用CT扫描在TPS中重建的金球位置的三维坐标最大偏差为2．2mm,最小偏差为0．1mm。该算法于所使用的PC上完成一组（两张交角EPID图像）图像处理和重建的运行时间〈ls。结论：对于多组相交角度拍摄的含金球投影位置的EPID图像,所编算法金球探测成功率比较高,平均为94％,算法重建出的靶区周围金球三维坐标同CT扫描重建出的坐标相比较,偏差在可以接受的范围内。但是该程序参数调节较复杂,而且EPID板接缝处剂量会影响探测成功率．还需要进一步开发自动参数计算程序和消除EPID板接缝处剂量影响。     

C形臂X线机的原位投影增强系统

目的移动C形臂X线机是微创骨科手术中必不可少的成像设备。针对当前微创骨科手术需要反复透视和操作直观性差的问题,本文提出一个针对移动C形臂X线机的原位投影增强系统。方法首先设计了一种双重反射的投影增强模块;然后基于上述模块,提出一种基于动态追踪的系统标定方法,以实现投影光路与X射线光路重合;接下来利用图像的单应性变换关系,分别对投影模块与X射线成像模型间的几何模型偏差和系统残留偏差进行校正,进而优化系统投影精度;最后构建原型系统,测试了系统性能并设计腰椎体膜和猪腿胫骨实验进行验证。结果在精度验证模体距影像探测器不同高度下,系统投影误差为1. 17 mm±0. 19 mm;固定验证模体,在移动C形臂X线机不同摆放角度下,系统投影误差为1. 06 mm±0. 22 mm。腰椎体膜和猪腿胫骨模体实验表明,可直接在患者体表观察到患者骨骼等结构的投影信息。结论本文提出的移动C形臂X线机投影增强系统,能够原位投射患者透视影像,直观地辅助医生术中操作,减少了术中反复透视获取手术工具和患者内部结构位置关系的次数,显示出系统未来临床应用的可行性。     

基于旋转准直器的锥形束CT散射矫正方法

针对锥形束CT（CBCT）图像质量受散射影响比较严重的情况,提出一种基于旋转准直器的CBCT散射矫正方法。该方法在射线源和模体之间放置一个圆形的旋转准直器,并通过准直器的旋转使透过准直器的射线不断沿轴向来回扫描,以获取整个容积图像的投影图像信息,然后利用投影图像的遮挡区域估计整幅图像的散射信息并将其从投影图像中去除,最后利用改进FDK算法重建图像。结果表明,与CBCT图像相比,散射矫正后的重建图像CBCT值的均方根误差从16.00%下降为1.18%,杯状伪影从14.005%下降为0.660%,峰值信噪比从16.959 4提高到31.450 0。CBCT图像质量得到明显提高。     

模体大小对CBCT图像剂量计算的影响

目的：锥形束CT（CBCT）使用宽束X-射线,探测板获取的信号受散射线的影响很大。该文对扫描模体大小及散射体积对CBCT重建图像HU值及剂量计算的影响进行研究。方法：在Elekta Synergy-XVICBCT系统中对不同深度及散射体积的均匀水模和非均匀密度参考模体扫描,并测量感兴趣区域的HU值;建立考虑和不考虑散射的两组HU-物理密度曲线应用于水模及头颈部仿真模体CBCT图像进行剂量计算,与常规CT图像（FBCT）计算结果比较。结果：均匀水模CBCT图像的HU值随水模深度增加先增大后略有减少,随纵轴散射长度增加而减少,变化幅度最大均接近10%。随散射长度增加,非均匀密度参考模体CBCT图像的高密度组织的HU值减少而低密度组织HU值增加,对1.609 g/cm3致密度骨最大减少约1422 HU。均匀水模和头颈部仿真模体CBCT图像使用考虑散射的HU-物理密度修正曲线计算与FBCT图像比较结果为：点绝对剂量（cGy/MU）最大偏差小于1.5%,等剂量线偏差小于2 mm~3 mm,2%/2 mm DTA指数的通过率平均大于97%,明显优于不做散射修正的结果。结论：Elekta Synergy-XVI系统获取CBCT图像的HU值受扫描模体的几何大小及散射体积影响很大,应选择与扫描患者近似几何大小及人体组织等效的HU-密度校准模体。考虑模体大小及散射修正的头颈部模体CBCT图像用于剂量计算能满足临床要求。     

基于一种插值算法的金球位置追踪方法

目的:建立一种算法,从低空间分辨力二维电离室矩阵测得的预埋有金球的穿过模体的剂量分布中读取金球投影位置坐标。方法:(1)利用Octavius 729二维电离室矩阵测得穿过埋有金球的模体的剂量分布;(2)采用一种插值算法将得到的低空间分辨力的剂量分布转换成高空间分辨力的剂量分布;(3)在得到的高空间分辨力的剂量分布上自编算法读取模体内金球投影位置坐标;(4)将得到的金球投影位置坐标与用高空间分辨力EPID图像得到的金球投影位置坐标进行比较。结果:在模体中共有3个金球,在机架角为0°条件下进行测量,计算得到3个金球的投影位置坐标,与金球实际投影位置坐标的最大偏差为2.5 mm,最小偏差为0.1 mm。结论:该插值算法及所编软件可以用于低空间分辨力二维电离室矩阵读取预埋于体内金球的投影位置识别,且软件操作方便快捷,结果可靠。     

C形臂X线投影图像3D建模及其应用

C形臂X线投影图像3D建模是指以C形臂获取的X线2D投影图像为基础,实现骨骼3D模型的术中重建。与单纯的2D切片图像或投影图像相比,3D重建模型不仅含有更为丰富的骨骼外部形状等解剖结构信息,而且还可包含骨密度及强度等骨骼内部多元有用信息。该技术在骨组织活检、椎弓根螺钉植入、髓内钉固定、及手足骨折修复等手术方面具有广阔的应用前景。对C形臂X线投影图像3D建模技术的研究意义、现状及现存问题进行介绍。在此基础上,分析了该技术所涉及的主要研究内容,提出了可分别沿两条主线研究基于普通C形臂2D投影图像的人体骨骼3D解剖模型构建:一、以C形臂按指定角度间隔获取的密集2D投影图像为基础,采用有限角锥束X射线投影合成方法进行3D重建;二、以C形臂在正位、侧位等姿态下获取的少量2D投影图像为基础,采用基于统计可变模型的非刚性配准方法进行3D重建。对每条主线都提出了对应的解决方案。     

运动模体中靶区长度与锥形束CT扫描速度的相关性

目的:研究锥形束CT扫描速度与动态模体中靶区长度的相关性。方法 :选用QUASAR(Modus,Germany)呼吸运动模体,模体内含运动插件,插件中心内嵌入一边长3 cm的立方体,用其来模拟运动靶区。设置模体振幅为0.5、1、2 cm,每一振幅分别设20、15、10次/min三种频率,在每振幅下分别行300°、180°、90°/min运动速度的CBCT扫描。计算CBCT图像靶区长度及靶区长度覆盖率与理论结果比较。结果:振幅为5 mm时,300、180、90°/min扫描时所得不同频率下靶区长度分别为(30.17,30.33,30.5)mm;(31.17,31.83,32)mm;(32.5,33.67,33.67)mm;振幅为10 mm时,300°、180°、90°/min扫描时所得靶区长度分别为(32.67,33.67,35.67)mm;(36,37.5,37.65)mm;(40.17,40.5,41.17)mm;振幅为15 mm时,300°、180°、90°/min扫描时所得靶区长度分别为(39.33,41,41.83)mm;(43,46,46.5)mm;(47.83,48.83,49.17)mm。结论 :CBCT扫描速度、模体振幅以及模体运动频率对靶区长度均有影响。扫描速度越慢,图像所得靶区长度越接近靶区长度真实值,但是各种速度下均小于理论靶区长度。振幅越小时所得靶区长度越接近于靶区理论值,靶区覆盖率越高。临床实践中使用CBCT对动态肿瘤监控时应使用患者平静呼吸的慢速扫描。     

双能锥形束CT线性混合技术提高相对电子密度的准确性

目的:利用高、低能锥形束CT(CBCT)的线性混合图像校正射线硬化,以提高相对电子密度值(RED)的准确性。方法:使用Elekta公司Synergy加速器的CBCT系统成像,高、低能X线峰值管电压分别为120和70 kV,对比单能CBCT图像采用100 kV。使用铝梯测量高、低能X线穿过不同厚度铝材料的衰减,利用迭代扰动法得到能谱分布,进而确定高、低能图像的最优线性混合系数,得到混合图像HU_(mix),用此图像作为新的CBCT图像,建立HU_(mix)-RED校准曲线,计算物质的RED。使用Catphan 500模体、一个头部仿真模体和一个骨盆部仿真模体进行实验,验证本方法的准确性。结果:头部和骨盆部Catphan 500模体实验得到的RED与理论值的相关系数分别为0.995和0.975,优于单能CBCT(0.975和0.953)。头、骨盆部仿真模体实验也显示,较单能CBCT成像方法,本研究提出的方法能有效减少射线硬化伪影,更准确地测量物质的RED。结论:建立了一种CBCT双能线性混合成像方法,可以较准确地测量物质的RED,为提高自适应放射治疗的精度提供了技术支持。     

放疗靶区呼吸运动对CT模拟定位图像重建的几何体积精度的体模实验研究

目的:研究放射治疗病人的不同呼吸运动状态对CT模拟定位扫描的图像重建精度的影响以及对放射治疗计划设计和评估的影响。方法:使用动态体模模拟放疗患者肺部靶区的呼吸运动,测试和计算不同运动周期和幅度下用于治疗计划设计的CT扫描的图像重建几何体积的变化。体模运动单元包含1cm和2cm的两个统一密度的球体和边长3cm的正方体,分别设定在沿CT定位床轴向以±1cm和±2cm的幅度作运动周期为3s,4s,5s,6s和10s的匀速振动。CT扫描条件为螺距1.5,层厚5mm,扫描速度1Slice/s。在CT模拟定位工作站上对扫描的原始数据进行三维图像重建,以自动阈值勾画方式计算模拟靶区体积大小,并与体模的实际几何体积比较确定误差。结果:(1)在体模运动方向有明显的几何体积误差,且可能形成明显的成像间隙。(2)重建的模拟运动靶区体积变化与其物理体积大小和运动状态相关。在选定的CT扫描参数和靶区体积的运动状态下,CT扫描图像重建的体积误差最大达66.7%,在振幅为2cm时相隔2cm的模体图像甚至可能发生部分重迭。(3)靶区图像的几何中心可能发生偏差,从而造成治疗计划设计的射野中心偏差。结论:在呼吸运动幅度和周期分别大于2cm和4s时有必要对定位患者采取呼吸限制方式进行CT模拟定位扫描或根据实际测量结果评估靶区体积误差可能带来的计划误差。     

Linac mechanic QA using a cylindrical phantom

Precise mechanical operation of a linear accelerator (linac) is critical for accurate radiation therapy dose delivery. Quantitative procedures for linac mechanical quality assurance (QA) used in the standard of care are time consuming and therefore conducted on a relatively infrequent basis. We present a method for evaluating the mechanical performance of a linac based on a series of projection portal images of a prototype cylindrical phantom with embedded radiopaque fiducial markers. The marker autodetection process included modeling imager response to the radiation beam where the projected cylinder attenuation yielded a non-uniform image background. The linac mechanical characteristics were estimated based on nonlinear multi-objective optimization of the projected marker locations. The estimated geometry parameters for the tested commercial model were gantry angle deviation 0.075 +/- 0.076 degrees (1 SD), gantry sag 0.026 +/- 0.02 degrees , source-to-axis distance SAD 998.3 +/- 1.7 mm, source-to-detector distance SDD 1493 +/- 5.0 mm, couch vertical motion 0.6 +/- 0.45 mm, couch rotation 0.154 +/- 0.1 degrees and average linac rotation center (1.02, -0.27, -0.37) +/- (0.36,0.333,1.20) mm relative to the laser intersection. The imager shift was [-0.44, 2.6] +/- [0.20, 1.1] mm and the imager orientation was in-plane rotation 0.05 +/- 0.03 degrees , roll -0.14 +/- 0.09 degrees and pitch -0.9 +/- 0.604 degrees . The performance of this procedure concerning marker detection and optimization was examined by comparing the detected set of marker coordinates to its back-calculated counterpart for three subgroups of markers: central, wall and intermediate relative to the center of the phantom. The maximum difference was less than 0.25 mm with a mean of 0.146 mm and a standard deviation of 0.07 mm. The clinical use of this automated procedure will allow more efficient, more thorough, and more frequent mechanical linac QA.     

Using cone-beam CT projection images to estimate the average and complete trajectory of a fiducial marker moving with respiration

Stereotactic body radiotherapy of lung cancer often makes use of a static cone-beam CT (CBCT) image to localize a tumor that moves during the respiratory cycle. In this work, we developed an algorithm to estimate the average and complete trajectory of an implanted fiducial marker from the raw CBCT projection data. After labeling the CBCT projection images based on the breathing phase of the fiducial marker, the average trajectory was determined by backprojecting the fiducial position from images of similar phase. To approximate the complete trajectory, a 3D fiducial position is estimated from its position in each CBCT project image as the point on the source-image ray closest to the average position at the same phase. The algorithm was tested with computer simulations as well as phantom experiments using a gold seed implanted in a programmable phantom capable of variable motion. Simulation testing was done on 120 realistic breathing patterns, half of which contained hysteresis. The average trajectory was reconstructed with an average root mean square (rms) error of less than 0.1 mm in all three directions, and a maximum error of 0.5 mm. The complete trajectory reconstruction had a mean rms error of less than 0.2 mm, with a maximum error of 4.07 mm. The phantom study was conducted using five different respiratory patterns with the amplitudes of 1.3 and 2.6 cm programmed into the motion phantom. These complete trajectories were reconstructed with an average rms error of 0.4 mm. There is motion information present in the raw CBCT dataset that can be exploited with the use of an implanted fiducial marker to sub-millimeter accuracy. This algorithm could ultimately supply the internal motion of a lung tumor at the treatment unit from the same dataset currently used for patient setup.     

Respiratory correlated cone beam CT

A cone beam computed tomography (CBCT) scanner integrated with a linear accelerator is a powerful tool for image guided radiotherapy. Respiratory motion, however, induces artifacts in CBCT, while the respiratory correlated procedures, developed to reduce motion artifacts in axial and helical CT are not suitable for such CBCT scanners. We have developed an alternative respiratory correlated procedure for CBCT and evaluated its performance. This respiratory correlated CBCT procedure consists of retrospective sorting in projection space, yielding subsets of projections that each corresponds to a certain breathing phase. Subsequently, these subsets are reconstructed into a four-dimensional (4D) CBCT dataset. The breathing signal, required for respiratory correlation, was directly extracted from the 2D projection data, removing the need for an additional respiratory monitor system. Due to the reduced number of projections per phase, the contrast-to-noise ratio in a 4D scan reduced by a factor 2.6-3.7 compared to a 3D scan based on all projections. Projection data of a spherical phantom moving with a 3 and 5 s period with and without simulated breathing irregularities were acquired and reconstructed into 3D and 4D CBCT datasets. The positional deviations of the phantoms center of gravity between 4D CBCT and fluoroscopy were small: 0.13 +/- 0.09 mm for the regular motion and 0.39 +/- 0.24 mm for the irregular motion. Motion artifacts, clearly present in the 3D CBCT datasets, were substantially reduced in the 4D datasets, even in the presence of breathing irregularities, such that the shape of the moving structures could be identified more accurately. Moreover, the 4D CBCT dataset provided information on the 3D trajectory of the moving structures, absent in the 3D data. Considerable breathing irregularities, however, substantially reduces the image quality. Data presented for three different lung cancer patients were in line with the results obtained from the phantom study. In conclusion, we have successfully implemented a respiratory correlated CBCT procedure yielding a 4D dataset. With respiratory correlated CBCT on a linear accelerator, the mean position, trajectory, and shape of a moving tumor can be verified just prior to treatment. Such verification reduces respiration induced geometrical uncertainties, enabling safe delivery of 4D radiotherapy such as gated radiotherapy with small margins.     

Evaluation of mechanical precision and alignment uncertainties for an integrated CT/LINAC system

A new integrated CT/LINAC combination, in which the CT scanner is inside the radiation therapy treatment room and the same patient couch is used for CT scanning and treatment (after a 180-degree couch rotation), should allow for accurate correction of interfractional setup errors. The purpose of this study was to evaluate the sources of uncertainties, and to measure the overall precision of this system. The following sources of uncertainty were identified: (1) the patient couch position on the LINAC side after a rotation, (2) the patient couch position on the CT side after a rotation, (3) the patient couch position as indicated by its digital readout, (4) the difference in couch sag between the CT and LINAC positions, (5) the precision of the CT coordinates, (6) the identification of fiducial markers from CT images, (7) the alignment of contours with structures in the CT images, and (8) the alignment with setup lasers. The largest single uncertainties (one standard deviation or 1 SD) were found in couch position on the CT side after a rotation (0.5 mm in the RL direction) and the alignment of contours with the CT images (0.4 mm in the SI direction). All other sources of uncertainty are less than 0.3 mm (1 SD). The overall precision of two setup protocols was investigated in a controlled phantom study. A protocol that relies heavily on the mechanical integrity of the system, and assumes a fixed relationship between the LINAC isocenter and the CT images, gave a predicted precision (1 SD) of 0.6, 0.7, and 0.6 mm in the SI, RL and AP directions, respectively. The second protocol reduces reliance on the mechanical precision of the total system, particularly the patient couch, by using radio-opaque fiducial markers to transfer the isocenter information from the LINAC side to the CT images. This protocol gave a slightly improved predicted precision of 0.5, 0.4, and 0.4 mm in the SI, RL and AP directions, respectively. The distribution of phantom position after CT-based correction confirmed these results. Knowledge of the individual sources of uncertainty will allow alternative setup protocols to be evaluated in the future without the need for significant additional measurements.     

Measurement of inter and intra fraction organ motion in radiotherapy using cone beam CT projection images

A method is presented for extraction of intra and inter fraction motion of seeds/markers within the patient from cone beam CT (CBCT) projection images. The position of the marker is determined on each projection image and fitted to a function describing the projection of a fixed point onto the imaging panel at different gantry angles. The fitted parameters provide the mean marker position with respect to the isocentre. Differences between the theoretical function and the actual projected marker positions are used to estimate the range of intra fraction motion and the principal motion axis in the transverse plane. The method was validated using CBCT projection images of a static marker at known locations and of a marker moving with known amplitude. The mean difference between actual and measured motion range was less than 1 mm in all directions, although errors of up to 5 mm were observed when large amplitude motion was present in an orthogonal direction. In these cases it was possible to calculate the range of motion magnitudes consistent with the observed marker trajectory. The method was shown to be feasible using clinical CBCT projections of a pancreas cancer patient.     

Cone beam CT with zonal filters for simultaneous dose reduction, improved target contrast and automated set-up in radiotherapy

Cone beam CT (CBCT) using a zonal filter is introduced. The aims are reduced concomitant imaging dose to the patient, simultaneous control of body scatter for improved image quality in the tumour target zone and preserved set-up detail for radiotherapy. Aluminium transmission diaphragms added to the CBCT x-ray tube of the Elekta Synergytrade mark linear accelerator produced an unattenuated beam for a central "target zone" and a partially attenuated beam for an outer "set-up zone". Imaging doses and contrast noise ratios (CNR) were measured in a test phantom for transmission diaphragms 12 and 24 mm thick, for 5 and 10 cm long target zones. The effect on automatic registration of zonal CBCT to conventional CT was assessed relative to full-field and lead-collimated images of an anthropomorphic phantom. Doses along the axis of rotation were reduced by up to 50% in both target and set-up zones, and weighted dose (two thirds surface dose plus one third central dose) was reduced by 10-20% for a 10 cm long target zone. CNR increased by up to 15% in zonally filtered CBCT images compared to full-field images. Automatic image registration remained as robust as that with full-field images and was superior to CBCT coned down using lead-collimation. Zonal CBCT significantly reduces imaging dose and is expected to benefit radiotherapy through improved target contrast, required to assess target coverage, and wide-field edge detail, needed for robust automatic measurement of patient set-up error.     

Automatic 3D-to-2D registration for CT and dual-energy digital radiography for calcification detection

We are investigating three-dimensional (3D) to two-dimensional (2D) registration methods for computed tomography (CT) and dual-energy digital radiography (DEDR). CT is an established tool for the detection of cardiac calcification. DEDR could be a cost-effective alternative screening tool. In order to utilize CT as the "gold standard" to evaluate the capability of DEDR images for the detection and localization of calcium, we developed an automatic, intensity-based 3D-to-2D registration method for 3D CT volumes and 2D DEDR images. To generate digitally reconstructed radiography (DRR) from the CT volumes, we developed several projection algorithms using the fast shear-warp method. In particular, we created a Gaussian-weighted projection for this application. We used normalized mutual information (NMI) as the similarity measurement. Simulated projection images from CT values were fused with the corresponding DEDR images to evaluate the localization of cardiac calcification. The registration method was evaluated by digital phantoms, physical phantoms, and clinical data sets. The results from the digital phantoms show that the success rate is 100% with a translation difference of less than 0.8 mm and a rotation difference of less than 0.2 degrees. For physical phantom images, the registration accuracy is 0.43 +/- 0.24 mm. Color overlay and 3D visualization of clinical images show that the two images registered well. The NMI values between the DRR and DEDR images improved from 0.21 +/- 0.03 before registration to 0.25 +/- 0.03 after registration. Registration errors measured from anatomic markers decreased from 27.6 +/- 13.6 mm before registration to 2.5 +/- 0.5 mm after registration. Our results show that the automatic 3D-to-2D registration is accurate and robust. This technique can provide a useful tool for correlating DEDR with CT images for screening coronary artery calcification.     

Variability and accuracy of measurements of prostate brachytherapy seed position in vitro using three-dimensional ultrasound: an intra- and inter-observer study

This paper is a step in investigating whether three-dimensional (3D) ultrasound can be used intraoperatively to replace Computed Tomography (CT) for localization of brachytherapy seeds. In order to quantify the accuracy and variability of seed localization without introducing effects due to tissues, we first report our results with test phantoms. An inter- and intra-observer study was performed to assess the variability of 2 3D ultrasound scan acquisition methods: Tilt 3D scanning and pull-back 3D scanning. Seven observers measured the positions of gold seed markers in an agar phantom twice in each of the three orthogonal image planes. An analysis of variance (ANOVA) was performed to determine the intra- and inter-observer standard errors of measurement (SEM) and the minimum detectable changes in marker position (deltap). Average intra- and inter-observer SEMs for the tilt scan 3D image were 0.36 and 0.40 mm, respectively. Measurements of the pull-back scan 3D image yielded average intra- and inter-observer SEM of 0.46 and 0.49 mm, respectively. A paired difference analysis showed that the lower SEM for the tilt 3D scan image were statistically significant at a significance level of alpha= 0.05. The accuracy of the US measurements was tested by determining marker coordinates from CT images of the phantom in a stereotactic head frame. CT coordinates were matched to the ultrasound (US) coordinates by means of an affine transform. Average matching errors in x, y, and z were 0.02, 0.10, and -0.02 mm, respectively.