Perioperative measures to optimize margin clearance in breast conserving surgery

A Review of Feasible Applications of THz Waves in Medical Diagnostics and Treatments

Introduction: Terahertz (THz) waves with frequencies in the range of 0.1 to 10 THz are electromagnetic radiation with growing applications in various fields of science and technology. Attractive features of this radiation have brought out many novel possibilities for medical diagnostics and treatments with considerable advantages compared to other conventional methods. Methods: In this paper, we present a review of more recent reports on practical applications of THz radiation for diagnostic, biosensing and clinical treatments. The review includes the diagnosis of breast, skin, mouth, cervical, lungs, small intestine, prostate, colon, and stomach cancers, the evaluation of biomolecules, the detection of genetic mutations, the determination of burn depth, the diagnosis of tooth decay, diabetes, and emotional-psychological states, the evaluation of corneal water to diagnose visual diseases, and wound healing monitoring. Further, it embraces the use of THz therapy in reducing the size of the tumor, treating skin cancer, and healing burn wounds, cardiovascular disease, corneal epithelium, angina, and THz heating. Results: This review has emphasized the capabilities of THz waves as a novel tool for future clinical diagnostics and treatments. Conclusion: The paper provides a comprehensive understanding of the feasible potential application of THz waves for clinical purposes and its advantages in comparison with other conventional tools.

Radiological Underestimation of Tumor Size Influences the Success Rate of Re-Excision after Breast-conserving Surgery

Objective

Failure to achieve adequate margins after breast-conserving surgery often leads to re-excision, either by repeat breast-conserving surgery (BCS) or by mastectomy. Despite the high frequency of this problem, the success rate of achieving adequate margins by repeat BCS is not well documented. The objective of this study was to determine the success rate of repeat BCS and identify the factors influencing that rate.

Materials and Methods

A retrospective review was performed of all women undergoing repeat BCS for inadequate margins after initial BCS in our breast unit between 2013 and 2019. Univariate and multivariate analyses were carried out to identify the factors influencing how often adequate margins were achieved after repeat BCS.

Results

One hundred fifty-four patients underwent repeat BCS after initially inadequate margins, of which adequate margins were achieved in 82%. Patients with successful repeat BCS had smaller tumors, had less underestimation of tumor size on imaging, and were less likely to have had cavity shaves taken at their initial BCS. A tumor size more than 50% larger than predicted by imaging was independently associated with failure of repeat BCS in multivariate analysis (odds ratio: 3.6, 95% CI: 1.41-9.20, p = 0.007). Underestimation of tumor size by imaging was commoner and more extensive in patients with larger tumors and those with ductal carcinoma in situ.

Conclusion

Re-excision by cavity shaves has a high success rate and should be offered to all patients who are deemed suitable for the procedure. Patients whose tumors are more than 50% larger than predicted by imaging should be counseled about the higher risk of failure.

Human Serum Albumin Decorated Indocyanine Green Improves Fluorescence-Guided Resection of Residual Lesions of Breast Cancer in Mice

Objective

Achieving negative resection margin is critical but challenging in breast-conserving surgery. Fluorescence-guided surgery allows the surgeon to visualize the tumor bed in real-time and to facilitate complete resection. We envisioned that intraoperative real-time fluorescence imaging with a human serum albumin decorated indocyanine green probe could enable complete surgical removal of breast cancer in a mouse model.

Methods

We prepared the probe by conjugating indocyanine green (ICG) with human serum albumin (HSA). In vitro uptake of the HSA-ICG probe was compared between human breast cancer cell line MDA-MB-231 and normal breast epithelial cell line MCF 10A. In vivo probe selectivity for tumors was examined in nude mice bearing MDA-MB-231-luc xenografts and the FVB/N-Tg (MMTV-PyMT) 634Mul/J mice model with spontaneous breast cancer. A positive-margin resection mice model bearing MDA-MB-231-luc xenograft was established and the performance of the probe in assisting surgical resection of residual lesions was examined.

Results

A significantly stronger fluorescence intensity was detected in MDA-MB-231 cells than MCF 10A cells incubated with HSA-ICG. In vivo fluorescence imaging showed that HSA-ICG had an obvious accumulation at tumor site at 24 h with tumor-to-normal tissue ratio of 8.19 ± 1.30. The same was true in the transgenic mice model. The fluorescence intensity of cancer tissues was higher than that of non-cancer tissues (58.53 ± 18.15 vs 32.88 ± 11.34). During the surgical scenarios, the residual tumors on the surgical bed were invisible with the naked eye, but were detected and resected with negative margin under HSA-ICG guidance in all the mice (8/8). Recurrence rate among mice that underwent resection with HSA-ICG (0/8) was significantly lower than the rates among mice with ICG (4/8), as well as the control group under white light (7/7).

Conclusions

This study suggests that real-time in vivo visualization of breast cancer with an HSA-ICG fluorescent probe facilitates complete surgical resection of breast cancer in a mouse xenograft model.

Differences in Re-excision Rates for Breast-Conserving Surgery Using Intraoperative 2D Versus 3D Tomosynthesis Specimen Radiograph

BACKGROUND

Intraoperative specimen radiographs performed during breast conservation surgery for cancer reduces the need for re-excision for positive margins. We studied 2D versus 3D image-guided cavity margin excision and compared it to final pathology and need for additional surgery.

METHODS

We conducted a retrospective review of 657 breast-conserving operations performed for cancer from 2013 to 2018. Procedures were performed by four surgeons at a single tertiary institution with access intraoperatively to 2D and 3D radiographs. Data collected included demographics, intraoperative margin assessment, final pathology, and re-excision rates.

RESULTS

A total of 466 patients had 2D and 191 had 3D specimen imaging. The 2D group had a lower mean age and a higher body mass index and proportion of minority patients than the 3D group (P < 0.01). In the 3D group, there was a higher percentage of patients with mammographically denser breasts (P < 0.06); 58% of patients in the 3D group had additional imaging-directed cavity margins excised versus 32% of patients in the 2D group (P < 0.01). In the 2D group, 44 patients (9%) had positive final margins versus 8 patients (4%) in the 3D group (P = 0.02). No difference was found on total volume of excision (P = 0.56). The re-excision rate for the 2D group was 11% versus 5% for the 3D group (P = 0.02; adjusted odds ratio = 0.41, 95% confidence interval 0.19-0.86).

CONCLUSIONS

Re-excision rates using both modalities are low. A lower re-excision rate is independently associated with 3D tomosynthesis. This allows surgeons to excise additional margins at the index operation, decreasing reoperations and anxiety/costs for patients.

A comparative study of perioperative techniques to attain negative margins and spare healthy breast tissue in breast conserving surgery

BACKGROUND AND AIM

Traditionally lumpectomy as a part of breast-conserving surgery (BCS) is performed by palpation-guided method leading to positive margins and large excision volumes. There is no evidence suggesting that wide margin excisions decrease intra-breast tumour recurrence. Various perioperative techniques are used for margin assessment. We aimed to compare three commonly used techniques, i.e., ultrasound-guided surgery, palpation-guided surgery and cavity shaving for attaining negative margins and estimating the extent of healthy breast tissue resection.

METHOD

A prospective comparative study was performed on 90 patients who underwent breast conservation surgery for early breast cancer between August 2018 and June 2019. Tumour excision with a minimum of 1 cm margin was done either using ultrasound, palpation or cavity shaving. Histopathological evaluation was done to assess the margin status and excess amount of resected normal breast tissue. Calculated resection ratio (CRR) defining the excess amount of the resected breast tissue was achieved by dividing the total resection volume (TRV) by optimal resection volume (ORV). The time taken for excision was also recorded.

RESULTS

Histopathology of all 90 patients (30 in each group) revealed a negative resection margin in 93.3% of 30 patients in palpation-guided surgery group and 100% in both ultrasound-guided surgery and cavity shaving groups. Two patients (6.7%) from the cavity shaving group had positive margins on initial lumpectomy but shave margins were negative. TRV was significantly less in the ultrasound-guided surgery group compared to the palpation-guided surgery group and cavity shaving group (76.9 cm3, 94.7 cm3 and 126.3 cm3 respectively; p < 0.0051). CRR was 1.2 in ultrasound group compared to 1.9 in palpation group and 2.1 in cavity shave group which was also statistically significant (p < 0.0001).Excision time was significantly less (p < 0.001) in palpation-guided surgery group (13.8 min) compared to cavity shaving group (15.1 min) and ultrasound-guided group (19.4 min).

CONCLUSION

Ultrasound-guided surgery is more accurate in attaining negative margins with the removal of least amount of healthy breast tissue compared to palpation-guided surgery and cavity shaving.

Breast lesion size assessment in mastectomy specimens: Correlation of cone-beam breast-CT, digital breast tomosynthesis and full-field digital mammography with histopathology

To compare the accuracy of breast lesion size measurement of cone-beam breast-CT (CBBCT), digital breast tomosynthesis (DBT) and full-field digital mammography (FFDM).Patients scheduled for mastectomy due to at least 1 malignant breast lesion were included. Mastectomy specimens were examined by CBBCT, DBT, FFDM, and histopathology.A total of 94 lesions (40 patients) were included. Histopathological analyses revealed 47 malignant, 6 high-risk, and 41 benign lesions. Mean histopathological lesion size was 20.8 mm (range 2-100). Mean absolute size deviation from histopathology was largest for FFDM (5.3 ± 6.7 mm) and smallest for CBBCT 50 mA, high-resolution mode (4.3 ± 6.7 mm). Differences between imaging modalities did not reach statistical significance (P = .85).All imaging methods tend to overestimate breast lesion size compared to histopathological gold standard. No significant differences were found regarding size measurements, although in tendency CBBCT showed better lesion detection and cT classification over FFDM.

Comparison of Radioactive Seed Localized Excision and Wire Localized Excision of Breast Lesions: A Community Hospital's Experience

BACKGROUND

Most data comparing wire localized excision (WLE) and radioactive seed localized excision (RSLE) derive from academic institutions with limited data from community hospitals. This study aimed to compare positive margin rates between WLE and RSLE and to determine if there were any differences in specimen volume and operation time.

PATIENTS AND METHODS

A retrospective cohort study was conducted on patients who underwent WLE or RSLE at a Canadian community hospital. Group characteristics were compared as appropriate. Multivariable logistic regression was used determine if the localization techniques were independently associated with having a positive margin. Statistical significance was set as P < .05.

RESULTS

The cohort consisted of 747 (WLE) and 577 (RSLE) patients. Both groups had similar mean age, mean tumor (invasive and ductal carcinoma-in-situ) size, histologic grade distribution, presence of lymphovascular invasion, and extensive intraductal component, nodal status, and hormone receptor and HER2 status. Compared to WLE, patients who underwent RSLE had significantly lower invasive positive margin rates (8.1% vs. 12.3%, P = .03), shorter operation time (39.5 minutes vs. 68.7 minutes, P = .0001), and smaller surgical specimens (21.4 cm³ vs. 30.2 cm³, P = .008). Ductal carcinoma-in-situ positive margin rates were not different between the groups. However, the localization technique was not independently associated with having a positive margin (odds ratio = 1.55; 95% confidence interval, 0.99-2.44).

CONCLUSION

RSLE led to a shorter operation time and smaller surgical specimens compared to WLE, but there was no difference in positive margin rates. RSLE is an effective technique to excise nonpalpable breast lesions in the community setting.

Towards the use of diffuse reflectance spectroscopy for real-time in vivo detection of breast cancer during surgery

Background

Breast cancer surgeons struggle with differentiating healthy tissue from cancer at the resection margin during surgery. We report on the feasibility of using diffuse reflectance spectroscopy (DRS) for real-time in vivo tissue characterization.

Methods

Evaluating feasibility of the technology requires a setting in which measurements, imaging and pathology have the best possible correlation. For this purpose an optical biopsy needle was used that had integrated optical fibers at the tip of the needle. This approach enabled the best possible correlation between optical measurement volume and tissue histology. With this optical biopsy needle we acquired real-time DRS data of normal tissue and tumor tissue in 27 patients that underwent an ultrasound guided breast biopsy procedure. Five additional patients were measured in continuous mode in which we obtained DRS measurements along the entire biopsy needle trajectory. We developed and compared three different support vector machine based classification models to classify the DRS measurements.

Results

With DRS malignant tissue could be discriminated from healthy tissue. The classification model that was based on eight selected wavelengths had the highest accuracy and Matthews Correlation Coefficient (MCC) of 0.93 and 0.87, respectively. In three patients that were measured in continuous mode and had malignant tissue in their biopsy specimen, a clear transition was seen in the classified DRS measurements going from healthy tissue to tumor tissue. This transition was not seen in the other two continuously measured patients that had benign tissue in their biopsy specimen.

Conclusions

It was concluded that DRS is feasible for integration in a surgical tool that could assist the breast surgeon in detecting positive resection margins during breast surgery.

Trail registration NIH US National Library of Medicine–clinicaltrails.gov, NCT01730365. Registered: 10/04/2012 https://clinicaltrials.gov/ct2/show/study/NCT01730365

Digital breast tomosynthesis versus full-field digital mammography-Which modality provides more accurate prediction of margin status in specimen radiography?

OBJECTIVES

To evaluate the reliability of tumor margin assessment in specimen radiography (SR) using digital breast tomosynthesis (DBT) and full-field digital mammography (FFDM) in comparison to postoperative histopathology margin status as the gold standard.

METHODS

After ethics committee approval, 102 consecutive patients who underwent breast conservative surgery for nonpalpable proven breast cancer were prospectively included. All patients underwent ultrasound/mammography-guided wire localization of their lesions. After excision, each specimen was marked for orientation and imaged using FFDM and DBT. Two blinded radiologists (R1, R2) independently analyzed images acquired with both modalities. Readers identified in which direction the lesion was closest to the specimen margin and to measure the margin width. Their findings were compared with the final histopathological analysis. True positive margin status was defined as a margin measuring <1mm for invasive cancer and 5mm for ductal carcinoma in situ (DCIS) at imaging and pathology.

RESULTS

For FFDM, correct margin direction was identified in 45 cases (44%) by R1 and in 37 cases (36%) by R2. For DBT, 69 cases (68%) were correctly identified by R1 and 70 cases (69%) by R2. Overall accuracy was 40% for FFDM and 69% for DBT; the difference was statistically significant (p<0.0001). Sensitivity in terms of correct assessment of margin status was significantly better for DBT than FFDM (77% versus 62%).

CONCLUSION

SR using DBT is significantly superior to FFDM regarding identification of the closest margin and sensitivity in assessment of margin status.

The Value of Preoperative Lesion Dedicated Ultrasound of Breast Cancer before Conserving Surgery for Optimizing Margins

To investigate the effect of US performed immediately before breast conserving surgery (BCS) by radiologist accompanied by the surgeon. All patients scheduled for BCS in the last year (group 1, n = 46) were evaluated with US immediately before surgery. About 108 patients (group 2) who were treated with BCS before the study were included as the control group. Tumor size and localization, the distances between tumor-skin and tumor-pectoralis muscle fascia were noted. Re-excision rate due to positive margins was significantly lower in group 1. Statistically significant difference was detected in re-excision rates for nonpalpable tumors. Preoperative US is an effective and practical method.

Intraoperative Ultrasound Guidance in Breast-Conserving Surgery Improves Cosmetic Outcomes and Patient Satisfaction: Results of a Multicenter Randomized Controlled Trial (COBALT)

Background

Ultrasound-guided breast-conserving surgery (USS) results in a significant reduction in both margin involvement and excision volumes (COBALT trial).

Objective

The aim of the present study was to determine whether USS also leads to improvements in cosmetic outcome and patient satisfaction when compared with standard palpation-guided surgery (PGS).

Methods

A total of 134 patients with T1–T2 invasive breast cancer were included in the COBALT trial (NTR2579) and randomized to either USS (65 patients) or PGS (69 patients). Cosmetic outcomes were assessed by a three-member panel using computerized software Breast Cancer Conservative Treatment cosmetic results (BCCT.core) and by patient self-evaluation, including patient satisfaction. Time points for follow-up were 3, 6, and 12 months after surgery. Overall cosmetic outcome and patient satisfaction were scored on a 4-point Likert scale (excellent, good, fair, or poor), and outcomes were analyzed using a multilevel, mixed effect, proportional odds model for ordinal responses.

Results

Ultrasound-guided breast-conserving surgery achieved better cosmetic outcomes, with 20 % excellence overall and only 6 % rated as poor, whereas 14 % of PGS outcomes were rated excellent and 13 % as poor. USS also had consistently lower odds for worse cosmetic outcomes (odds ratio 0.55, p = 0.067) than PGS. The chance of having a worse outcome was significantly increased by a larger lumpectomy volume (p_trend = 0.002); a volume >40 cc showed odds 2.78-fold higher for a worse outcome than a volume ≤40 cc. USS resulted in higher patient satisfaction compared with PGS.

Conclusion

Ultrasound-guided breast-conserving surgery achieved better overall cosmetic outcomes and patient satisfaction than PGS. Lumpectomy volumes >40 cc resulted in significantly worse cosmetic outcomes.

Reoperations after primary breast conserving surgery in women with invasive breast cancer in Catalonia, Spain: a retrospective study

BACKGROUND

Although complete tumor resection is accepted as the best means to reduce recurrence, reoperations after lumpectomy are a common problem in breast cancer. The aim of this study was to assess the reoperation rates after primary breast conserving surgery in invasive breast cancer cases diagnosed in Catalonia, Spain, between 2005 and 2011 and to identify variations based on patient and tumour characteristics.

METHODS

Women with invasive incident breast cancer identified from the Patient's Hospital Discharge Database [174.0-174.9 codes of the International Classification of Diseases, Ninth Revision, Clinical Modification (ICD-9-CM) as the primary diagnosis] and receiving primary breast conserving surgery were included in the study and were followed up to 3 and 12 months by collecting information about repeat breast cancer surgery.

RESULTS

Reoperation rates after primary breast conserving surgery decreased from 13.0 % in 2005 to 11.7 % in 2011 at 3 months and from 14.2 % in 2005 to 12.9 % in 2011 at 12 months' follow-up. While breast conservation reoperations saw a slight, non-significant increase in the same period (from 5.7 to 7.3 % at 3 months, and from 6.0 to 7.5 % at 12 months), there was a significant decrease in radical reoperation (from 7.3 to 4.4 % at 3 months and from 8.2 to 5.4 % at 12 months). Overall, additional breast surgeries decreased among younger women.

CONCLUSIONS

Despite the rise of breast conserving surgery, reoperation rates following initial lumpectomy in Catalonia decreased by 10 % at 3 and 12 months' follow-up, remaining low and almost unchanged. Ultimately, there was also a significant decrease in mastectomies.

Does Breast Magnetic Resonance Imaging Combined With Conventional Imaging Modalities Decrease the Rates of Surgical Margin Involvement and Reoperation?: A Case-Control Comparative Analysis

The objective of this study was to assess whether preoperative breast magnetic resonance imaging (MRI) combined with conventional breast imaging techniques decreases the rates of margin involvement and reexcision.Data on patients who underwent surgery for primary operable breast cancer were obtained from the Changhua Christian Hospital (CCH) breast cancer database. The rate of surgical margin involvement and the rate of reoperation were compared between patients who underwent conventional breast imaging modalities (Group A: mammography and sonography) and those who received breast MRI in addition to conventional imaging (Group B: mammography, sonography, and MRI).A total of 1468 patients were enrolled in this study. Among the 733 patients in Group A, 377 (51.4%) received breast-conserving surgery (BCS) and 356 (48.6%) received mastectomy. Among the 735 patients in Group B, 348 (47.3%) received BCS and 387 (52.7%) received mastectomy. There were no significant differences in operative method between patients who received conventional imaging alone and those that received MRI and conventional imaging (P = 0.13). The rate of detection of pathological multifocal/multicentric breast cancer was markedly higher in patients who received preoperative MRI than in those who underwent conventional imaging alone (14.3% vs 8.6%, P < 0.01). The overall rate of surgical margin involvement was significantly lower in patients who received MRI (5.0%) than in those who received conventional imaging alone (9.0%) (P < 0.01). However, a significant reduction in rate of surgical margin positivity was only observed in patients who received BCS (Group A, 14.6%; Group B, 6.6%, P < 0.01). The overall BCS reoperation rates were 11.7% in the conventional imaging group and 3.2% in the combined MRI group (P < 0.01). There were no significant differences in rate of residual cancer in specimens obtained during reoperation between the 2 preoperative imaging groups (Group A, 50%; Group B, 81.8%, P = 0.09). In multivariate analysis, multifocal/multicentric breast cancer (odds ratio = 2.38, P = 0.02) and without MRI use (odds ratio = 2.35, P < 0.01) were the major predisposing factors to margin involvement in patients received BCS.Preoperative breast MRI combined with conventional breast imaging results in a lower rate of surgical margin involvement and reoperations in patients who receive BCS.

A prospective pilot study of analysis of surgical margins of breast cancers using high-resolution sonography

To investigate the role of high-resolution specimen sonography (SS) to determine the precise location of the targeted lesion in relation to the six surgical margins; the specimen digital radiography isocenter and the correlation with the rate of re-excision and residual tumour. Freshly excised surgical specimens were scanned by a breast radiologist using a high-frequency linear transducer in a cohort of 25 consecutive women undergoing breast conservation. Sonographic measurements of radial distances from all six margins (superior, inferior, lateral, medial, anterior and posterior) were obtained. Sonographic positive margin status was defined as targeted mass identified <5 mm from the tissue edge. The paired t test was used for statistical comparisons between sonographic and pathological measurements. The median cancer size was 15 mm (range 3.80-42 mm; 95 % CI 9.8-18) on sonography and 16 mm (range 2-60 mm; 95 % CI 15-20) on surgical pathology. SS showed 100 % sensitivity and 59 % specificity in the evaluation of surgical pathology margins. 20 % (5 of 25) patients had positive margins where 60 % were in situ carcinoma. The likelihood of carcinoma at the initial surgical margins was significantly higher in dense breasts (3/6 = 50 % vs 1/17 = 5.8 %; p = 0.04). The deviation of the isocenter of the specimens was found not significant. SS is a valuable tool for identify the cancer within the specimen, and better asses the margins. It is of significant importance in patients with dense breasts where specimen radiography is of limited value.

A nationwide pathology study on surgical margins and excision volumes after breast-conserving surgery: There is still much to be gained

AIM OF THE STUDY

The current study aims to assess margin status in relation to amount of healthy breast tissue resected in breast-conserving surgery (BCS) on a nationwide scale.

METHODS

Using PALGA (a nationwide network and registry of histology and cytopathology in the Netherlands), all patients who underwent BCS for primary invasive carcinoma in 2012-13 were selected (10,058 excerpts). 9276 pathology excerpts were analyzed for a range of criteria including oncological margin status and distance to closest margin, specimen weight/volume, greatest tumor diameter, and with or without localization method. Calculated resection ratios (CRR) were assessed to determine excess healthy breast tissue resection.

RESULTS

Margins for invasive carcinoma and in situ carcinoma combined were tumor-involved in 498 (5.4%) and focally involved in 1021 cases (11.0%) of cases. Unsatisfactory resections including (focally) involved margins and margins ≤ 1 mm were reported in 33.8% of patients. The median lumpectomy volume was 46 cc (range 1-807 cc; SD 49.18) and median CRR 2.32 (range 0.10-104.17; SD 3.23), indicating the excision of 2.3 the optimal resection volume.

CONCLUSION

The unacceptable rate of tumor-involved margins as well as margins ≤ 1 mm in one third of all patients is also achieved at the expense of healthy breast tissue resection, which may carry the drawback of high rates of cosmetic failure. These data clearly suggest the need for improvement in current breast conserving surgical procedures to decrease tumor-involved margin rates while reducing the amount of healthy breast tissue resected.

Symmetric Biomechanically Guided Prone-to-Supine Breast Image Registration

Prone-to-supine breast image registration has potential application in the fields of surgical and radiotherapy planning, image guided interventions, and multi-modal cancer diagnosis, staging, and therapy response prediction. However, breast image registration of three dimensional images acquired in different patient positions is a challenging problem, due to large deformations induced to the soft breast tissue caused by the change in gravity loading. We present a symmetric, biomechanical simulation based registration framework which aligns the images in a central, virtually unloaded configuration. The breast tissue is modelled as a neo-Hookean material and gravity is considered as the main source of deformation in the original images. In addition to gravity, our framework successively applies image derived forces directly into the unloading simulation in place of a subsequent image registration step. This results in a biomechanically constrained deformation. Using a finite difference scheme avoids an explicit meshing step and enables simulations to be performed directly in the image space. The explicit time integration scheme allows the motion at the interface between chest and breast to be constrained along the chest wall. The feasibility and accuracy of the approach presented here was assessed by measuring the target registration error (TRE) using a numerical phantom with known ground truth deformations, nine clinical prone MRI and supine CT image pairs, one clinical prone-supine CT image pair and four prone-supine MRI image pairs. The registration reduced the mean TRE for the numerical phantom experiment from initially 19.3 to 0.9 mm and the combined mean TRE for all fourteen clinical data sets from 69.7 to 5.6 mm.