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Original papers

Factors that influence ultrasound evaluation of breast tumor size

Jin Xu

1*

, Ge Ma

2,3*

, Mengdi Liang

2

, Yue Wang

2

, Hong Pan

2

, Li Li

4

, Cuiying Li

5

, Wenbin Zhou

2

, Shui Wang

2,3

*The authors share the first authorship

1Department of Breast and Thyroid Surgery, Nanjing First Hospital, Nanjing Medical University, Nanjing, 2Department of Breast Surgery, The First Affiliated Hospital with Nanjing Medical University, Nanjing, 3Jiangsu Key Lab of Cancer Biomarkers, Prevention and Treatment, Jiangsu Collaborative Innovation Center For Cancer Personalized Medicine, School of Public Health, Nanjing Medical University, Nanjing, 4Department of General Surgery, Huashan Hospital, Fudan University, Shanghai, 5Department of Ultrasound in Medicine, the First Affiliated Hospital with Nanjing Medical University, Nanjing, China

Received 08.11.2018 Accepted 31.01.2019 Med Ultrason

2019, Vol. 21, No 2, 144-151

Corresponding author: Shui Wang, MD

Department of Breast Surgery, The First Affili ated Hospital with Nanjing Medical University, 300 Guangzhou Road, 210029 Nanjing, China Phone: 0086-25-83718836 ext. 6456 Fax: 0086-25-83718836

E-mail: [email protected]

Introduction

Breast cancer is the most commonly diagnosed can- cer in women. In recent years, breast-conserving surgery and minimally invasive treatment are becoming more ap- pealing to women with early stage breast cancer [1]. Ul-

trasonography (US) is a traditional technique for imaging breast masses that is advantageous in terms of its safety and usability. US measurement of breast cancer tumor size is a routine pre-surgery examination. The accurate measure of breast cancer tumor size is a precondition for individualized treatment. Previous studies have reported that tumor type and histological size are the key compo- nents associated with underestimation of tumor size [2-6]

and the gland density does not affect the US evaluation of tumor size [7]. It has reported that the maximal tumor di- ameter assessed by US is within 5 mm of the pathologic tumor size in 79.8% of cases [4].

The molecular subtypes of breast cancer and core biopsy are widely used in individualized therapy [8].

However, to our knowledge, the relationship between US measurement of tumor size and molecular subtyping or Abstract

Aims: To determine the factors influencing ultrasound breast tumor size assessment accuracy. Material and methods:

Five factors (tumor type, molecular subtype, histological size, histological grade, and breast density) were used to assess the measurement accuracy of breast ultrasound in tumor size. Size underestimation was defined as ultrasound index lesion di- ameter < histological size by at least 5 mm. Results: Breast ultrasound underestimated tumor size significantly, especially in cases with intraductal components (p=0.002). There was a tendency for higher size underestimation in breast cancer tumors with high–histological grade (p=0.03), human epidermal growth factor receptor type 2 (HER2)-overexpressing breast cancer tumors (p=0.02) and hormone receptor (HR)−/HER2+ breast cancer tumors (p=0.008). Furthermore, core biopsy revealed higher probability of size underestimation with intraductal components (p=0.002). Size underestimation was more frequent with larger histological size (p<0.001). Masses in non-dense breasts were significantly underestimated (p=0.036) compared to dense breasts. Conclusions: The size underestimation was influenced by pathological type, molecular subtype, and histologi- cal size. The pathological results of core biopsy were conducive for predicting tumor size pre-surgery in precise breast cancer diagnosis.

Keywords: breast cancer; ultrasound; tumor size; molecular subtype; core biopsy

DOI: 10.11152/mu-1747

Xu, Ma

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the pathological results of core biopsy has not been re- ported.

In the present study, we enrolled a large population of patients with breast cancer to determine the factors that influence the accuracy of US breast tumor size assess- ment, especially the molecular subtyping.

Material and methods

Inclusion and exclusion criteria

We enrolled in this retrospective analysis 1028 pa- tients with primary breast cancer who had underwent sur- gery in Jiangsu Breast Disease Center, the First Affiliated Hospital with Nanjing Medical University between Janu- ary 2011 to June 2015. The study was approved by local Ethics Committee. The inclusion criteria were: 1) US and pathological information could be obtained and reviewed in the medical inquiry system; 2) no local treatment before surgery. The exclusion criteria were as follows:

1) neoadjuvant chemotherapy prior surgery; 2) multiple lesions that could not be distinguished in the US or path- ological reports; 3) mass with inhomogeneous echo or microcalcification spots without low echo area. In figure 1 the flow diagram of analysis process is detailed.

Tumor size measurement in US

US was performed using a 3–14 MHz linear transduc- er (iU22; Philips Medical Systems, Bothell, WA, USA and MyLab Twice (Esaote S.p.A., Genova, Italy). Pa- tients were required to lie in a supine position with their breasts exposed when the ultrasound was performed. All examinations and evaluations were made by a radiolo- gist with more than 10 years of experience. A single low echo area was identified as the index lesion. Every con- troversial focus was diagnosed by two radiologists. The index lesion was sorted using the Breast Imaging Report- ing and Data System (BI-RADS) and measured in three dimensions with US (fig 2). With the patient in the proper position, the radiologist scanned the breast in general to determine the location of the mass and the largest diam- eter of the tumor was measured, which was considered as the longest axis. The methods of the tumor size measure- ments are referred to in the previous study of our research group [1,9]. The halo or the edges of the speckles were included in the measurements of ultrasound [10,11]. If the observation error of three measurements was larger than 5 mm, the measurement was conducted and deter- mined by another senior radiologist until the error was less than 5 mm. Then the three measures were averaged and a note as to the sonographic limits per lesion.

Classification of breast density

Mammography was performed using two digital full- field instruments (Senographe 2000D, GE, Fairfield,

USA). The breast density was categorized according to the 4th edition of the BI-RADS proposed by the Ameri- can College of Radiology (ACR). We divided patients into two groups according to different breast density, to evaluate if breast density was an influencing factor of US evaluation of breast tumor size.

Core biopsy

Core biopsy was performed with an automated Bard Magnum gun and a 14-gauge needle under ultrasound guidance. Based on the core biopsy pathological reports, the cases were divided into four groups: atypical ductal hyperplasia, pure ductal carcinoma in situ (DCIS), inva- sive carcinoma (IC, including pure IC [pIC] and a mix- ture of IC and DCIS) and other types.

Fig 1. Flow diagram of screened and excluded patients

Fig 2. Ultrasonography (linear transducer with a frequency of 3–14 MHz) of a mass in 10 o’clock position in the right breast shows a hypoechoic irregular mass. The breast tumor size was measured in three dimensions: a) two major axes perpendicular to each other: b) the third major axis perpendicular to the previ- ous two.

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Tumor size measurement in pathology

After surgery, the breast specimen was sliced sequen- tially into 5 mm sections perpendicular to the long axis of the tumor involving the treated tumor and adjacent tis- sue. The pathological measurements were in terms of the microscopic borders of the tumors. The histological size was 5 mm × number of slices containing tumor cells. The maximum dimension of the mass in US was compared with the largest diameter in histology.

Classification of postoperative pathological types Based on the postoperative pathological reports, the tumor types were divided into four groups: ductal carci- noma in situ (DCIS), invasive ductal carcinoma (IDC), invasive lobular carcinoma (ILC) and other tumors (in- cluding mucinous carcinoma and papillary carcinoma).

The IDC cases were divided into two groups: IDC with intraductal components (IDC+DCIS) and pure IDC. Hor- mone receptor (estrogen receptor [ER] and progesterone receptor [PR]) status, as well as human epidermal growth factor receptor type 2 (HER2) status, has guided breast

cancer subtype grouping. In this study, 638 cases with complete ER and PR status and HER2 expression level were divided into three classic groups: HR+HER2−/+

(ER+, PR-/+, HER2−/+), HR−HER2− (ER−, PR−, HER2−), and HR−HER2+ (ER−, PR−, HER2+). The Scarff-Bloom-Richardson system was applied to classify the histological grade [12,13].

Definition of overestimation and underestimation Size underestimation was defined as image index le- sion diameter < histological size by at least 5 mm. Over- estimation was defined as image index lesion diameter >

histological size by at least 5 mm. The measurement was defined as precise when the deviation between image and histology was <5 mm.

Statistical analysis

Results were expressed as mean ± standard deviation (SD). For all cases, the largest diameter of a tumor was used as the size reference in both the imaging and patho- logical reports. The mean difference between ultrasound and histology of the various groups was calculated, and Table I. Correlation between the accuracy of ultrasound evaluation and pathological size. A difference between ultrasound and pathological size <5 mm was defined as accurate. A difference >+5 mm was considered overestimation and <-5 mm was considered underestimated.

Factor Total UnderestimatedAccuracy of ultrasound measurementAccurate Overestimated p-value

Total 720 191 (27%) 406 (56%) 123 (17%)

Tumor type 720 0.002

DCIS 70 26 30 14

Pure IDC 421 103 253 65

IDC+DCIS 156 47 82 27

ILC 14 10 4 0

Other 59 31 10 18

Histological grade 564 0.013

I and II 304 64 193 47

III 260 83 140 38

ER status 712 0.325

Positive 553 139 320 94

Negative 152 47 79 26

PR status 704 0.454

Positive 469 117 270 82

Negative 235 69 128 38

HER2 status 638 0.02

Positive 160 58 74 28

Negative 478 111 291 76

Ki-67 692 0.67630

Low 189 52 101 36

High 503 133 286 84

Molecular subtype 638 0.008

HR+HER2−/+ 492 125 288 79

HR−HER2− 89 20 57 12

HR−HER2+ 57 24 20 13

HER2 – human epidermal growth factor receptor type 2; HR – hormone receptor; IC – invasive carcinoma; DCIS – ductal carcinoma in situ;

IDC – invasive ductal carcinoma; ILC – invasive lobular carcinoma; ER – estrogen receptor; PR – progesterone receptor

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the t-test was performed. Univariate analysis was carried out using the chi-square test or Fisher’s exact test. In all cases, p-values were two-tailed, and p-values <0.05 were considered statistically significant. All statistical analy- ses were performed using SPSS version 21.0 (SPSS, IBM; Chicago, IL, USA).

Results

Overall performance

The 708 patients screened out from 1028 patients with 720 lesions were included to evaluate the accuracy of ultrasound in preoperative tumor size assessment of breast cancer.

The mean age of the included 708 patients was 51.80 years (median 50 years, range 25-93 years). The mean pathological tumor size was 23.4±13.2 mm. The mean difference between the US and histological size was −2 mm (p=0.002). In Table I the number of different tumor type and accuracy of ultrasound measurement is detailed.

The mean breast cancer tumor size discrepancy of the pure IDC cases between US and histology was −1.6 mm (22.8 mm vs. 21.2 mm, p<0.01). The mean tumor

size discrepancy was −4.6 mm (25.5 mm vs. 20.9 mm, p<0.01) and −2.4 mm (25.5 mm vs. 23.1 mm, p<0.01) for the DCIS and IDC+DCIS cases, respectively. At -5 mm level, DCIS cases showed the highest ultrasound un- derestimation.

A total 564 IDC tumors (including pure IDC and IDC+DCIS) were divided into two groups according to histological grade. The mean size discrepancies in low and high histological grade compared with US were

−0.99 mm and −3.02 mm, respectively (p=0.003). At -5 mm level, there were more underestimated cases in the high histological grade group than in the low histological grade group (p=0.010).

Table I lists the factors influencing misestimation. At

±5 mm level, tumor type (p=0.002), histological grade (p=0.010), HER2 status (p=0.02) and molecular subtype (p=0.008) significantly influenced US measurement.

There was no evidence that ER status (p=0.325), PR sta- tus (p=0.454), or Ki-67 value (p=0.676) could be used to predict US measurement alone.

As the largest group of breast cancer, the group of pure IDC was analyzed separately and this subgroup analysis suggested the same result. At ±5 mm level, his- Table II. Correlation between the accuracy of ultrasound evaluation and pathological size in the group of pure IDC. A difference between ultrasound and pathological size < 5 mm was defined as accurate. A difference > +5 mm was considered overestimation and

< -5 mm was considered underestimated.

Factor Total UnderestimatedAccuracy of ultrasound measurementAccurate Overestimated p-value

Total 421 103(24.5%) 253(60.1%) 65(15.4%)

Histological grade 394 101 238 55 0.048

I and II 208 43 136 29

III 186 58 102 26

ER status 415 100 252 63 0.871

Positive 314 74 193 47

Negative 101 26 59 16

PR status 415 100 252 63 0.915

Positive 265 62 162 41

Negative 150 38 90 22

HER2 status 392 94 243 55 0.025

Positive 79 27 39 13

Negative 313 67 204 42

Ki-67 412 101 246 65 0.712

Low 96 25 54 17

High 316 76 192 48

Molecular subtype 392 94 243 55 0.021

HR+HER2−/+ 293 69 184 40

HR−HER2− 70 13 49 8

HR−HER2+ 29 12 10 7

Histological tumor size (mm) 421 103 253 65

< 20 229 18 172 39

20–50 181 74 81 26

> 50 11 11 0 0

HER2 – human epidermal growth factor receptor type 2; HR – hormone receptor; ER – estrogen receptor; PR – progesterone receptor

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tological grade (p=0.048), HER2 status (p=0.025), and molecular subtype (p=0.021) significantly influenced ul- trasound measurement (Table II).

US-guided core biopsy was performed in 489 of 720 lesions. Of the 489 lesions, 55 were atypical ductal hy- perplasia. The remaining 434 lesions were divided into three groups: DCIS, IC, and other types. Of these, 52 lesions (11.98%) were DCIS; 376 cases (86.64%) were IC, of which 315 cases (72.58%) were pIC and 61 cases (14.06%) were IC with intraductal components (IC+D- CIS). Six cases (1.38%) were other type (such as muci- nous carcinoma). According to the ±5 mm level, biop- sy pathology reports indicated that breast cancer with a higher DCIS component was more likely to be under- estimated,which was consistent with the results of the follow-up surgical pathological reports (fig 3). Given the limitation of tissue sampling in core biopsy, nearly half (25/52, 48.1%) of the DCIS cases were upgraded to inva- sive cancer after surgery. According to ±5 mm level, the underestimated cases were 11/27 in DICS, 14/25 in DCIS upgrade. The results show no difference in the accuracy of US between the DCIS group and the DCIS-upgrade group (p=0.628).

Impact of histological tumor size

The results comparing image size to pathological size of the different tumor staging are presented in fig 4. A total of 387 cases had tumor size <20 mm on US. The mean tumor size derived from ultrasound was 16.60 mm, while the mean histological size was 14.61 mm (p<0.01).

In comparison to the overestimation of small tumors, US obviously underestimated tumor size in the patient group with higher stage tumors. The mean difference be- tween US measured tumor size and pathological meas- ured tumor size was −4.55 mm (p<0.01) and −33.61 mm (p<0.01) in group II (histological size between 20–50 mm) and group III (histological size >50 mm) tumors, respectively. Table III shows the consistency of US es- timation when tumor pathological stage increased. US measurement tended to overestimate the size of small tumors while tending to underestimate the size of large tumors. According to the ±5 mm level, ultrasound under- estimated 33/387 cases (8.53%) in group I (histological size <20 mm), 135/309 cases (43.69%) in group II, and 23/24 cases (95.83%) in group III (p<0.001). In the sub- group analysis of pure IDC, ultrasound underestimated 18/229 cases (7.86%) in group I (histological size <20 mm), 74/181 cases (40.88%) in group II, and 11/11 cases (100.00%) in group III (p<0.001).

BI-RADS classification of breast tumors

Based on the BI-RADS classification, 518 tumors were divided into five groups. According to the ±5 mm level, 3/8 (37.5%) BI-RADS 3, 19/48 (39.58%) BI-RADS

4A, 18/61 (29.51%) BI-RADS 4B, 38/193 (19.69%) BI- RADS 4C, and 50/208 (24.04%) BI-RADS 5 were un- derestimated. According to the ±5 mm level, there was no significant difference between the BI-RADS 4B, 4C, and 5 groups (p=0.387). (Table IV).

Breast density

In this study, mammography was performed on 373 patients in our hospital. Masses in non–dense type (ACR Fig 4. Scatter plot of the relationship between pathological size and difference between ultrasound and histology sizes for all tumors.

Fig 3. Percentage of underestimation in tumor types according to core biopsy results. According to the ±5 mm level, the higher the DCIS component, the more likely it is to be underestimated (p = 0.002).

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1-3) breasts were significantly underestimated (p=0.036) compared to dense type (ACR 4) breasts (fig 5). Age and menopausal status, which are the factors that may affect female breast density, had no effect on the evaluation of ultrasonography accuracy.

Discussions

Methodologically, US is subjective to some extent. In addition, it is difficult to ensure that the measurement of pathological specimens is determined based on three-di- mensional US measurements. To address these issues, in this study, every dimension of the exponential lesion was measured three times by the same radiologist to minimize the error. In the comparison of pathology and US results, the two largest diameters were chosen to partially reduce the non-correspondence of pathology and US results.

Regarding non-mass lesions, Yang et al [14] report- ed that US did not help to characterize the morphology or extent of calcification in symptomatic DCIS. In our study, non-tumor lesions showed microcalcifications and more frequently destroyed echoes of the gland under US imaging, which was related to the pathological type of DCIS.

In this study, the difference between US imaging and histology reports was −2 mm. The corresponding data in other studies were −8 mm and −4.2 mm, respectively [2,15]. A reduction in the underestimation of tumor size may be related to equipment upgrades. Another possible explanation is that, as a strong subjective test, US has been popularized in developing countries such as China in the past decades, enriching the experience of ultra- sound doctors.

Regarding various tumor types, other studies have calculated linear regression between ultrasound measure- ments and pathological size of different tumor types, and Table III. The accuracy of ultrasound evaluation in different groups of the histological size

Ultrasound size (mm) Histologic size (mm)

≤20 20-50 ≥50

≤20 301 101 6

20-50 84 198 14

≥50 2 10 4

Table IV. Correlation between the accuracy of ultrasound evaluation and BI-RADS category. A difference between ultrasound and pathological size < 5 mm was defined as accurate. A difference > +5 mm was considered overestimation and < -5mm was considered underestimated.

Ultrasound classification (n=518) UnderestimatedAccuracy of ultrasound measurementIdentical Overestimated p-value

BI-RADS 3/4A (n=56) 22 29 5 0.011

BI-RADS 4B/4C/5 (n=462) 106 263 93

ranked the degree of underestimation as IDC < IDC+ILC

< ILC [15]. We found that underestimation of size was common for DCIS components cases. Satake et al [16]

attributed the size underestimation to deformation of the breast tissue larger than the caliber and the fibrosis around the catheter involved may cause structural distor- tion on the ultrasound. However, there was no significant difference in pathology and imaging for the ILC group.

The likely cause may be that the sample size of this type of tumor in our study is small.

The assertion that histological grade is an independ- ent prognostic factor dates back to 1991 [13]. However, few researchers have determined the relationship be- tween histological grade and US imaging. In this study, high-grade malignancies were associated with underesti- mation of the severity of low-grade malignancies. Highly malignant tumors can cause irregular shapes and fuzzy echoes, which can adversely affect the measurement of tumor size.

Perou et al [17] referred to the concept of molecu- lar subtype of breast cancer in 2000, which proved to be a milestone in the progress of breast cancer treatment.

Studies have increasingly shown that molecular biologi- cal markers such as ER, PR, and HER2 are closely re- lated to the biological characteristics of cancer. The main Fig 5. Masses in non–dense type (ACR 1-3) breasts were sig- nificantly underestimated compared to dense type (ACR 4) breasts.

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goal of this study was to explore the accuracy of tumor size measurements in different molecular biology states.

The results showed that the size of HER2+ cases was underestimated, but no similar phenomenon was found in ER+ or PR+ cases. Wojcinski et al [18] reported that HER2+ showed a high rate of structural deformation in surrounding tissues; this interpretation is consistent with our results. In clinical experience, breast cancer cases usually include three subtypes: cavity, HER2 overexpres- sion and triple negative, although more detailed classifi- cation methods are gradually accepted. Our data indicate that the HER2 overexpression subtype clearly exhibits US underestimation compared to the other two subtypes.

The underestimation of size can be attributed to the fuzzy boundary caused by the greater degree of HER2 overex- pressing tumor infiltration. It was noted that HER2 posi- tive was statistically significantly associated with tumor vasculature [19]. However, in some indicators related to prognosis or tumor cell biological behavior, the HER2 overexpression subtype is expected to fall between the other two subtypes, while the triple negative subtype is associated with a poor prognosis [20,21]. In addition, triple-negative breast cancer is not a single entity but a series of different diseases [22]. The heterogeneity of tri- ple-negative breast cancer can explain the results to some extent. Due to the complexity of triple-negative breast cancer, a prospective study of the agreement between US features and molecular subtypes is expected.

As a common means of preoperative diagnosis, the 2015 European Society of Cancer Surveillance Breast Cancer Clinical Practice Guide [23] requires a core bi- opsy. There are differences in pathology reports between core biopsy and subsequent surgery. In addition, the pathology report of the core biopsy is important for se- lecting the appropriate surgical procedure. Based on the results of the core biopsy, we divided patients into three groups and obtained similar results. The DCIS compo- nents are also a key factor in underestimating the size.

It is worth mentioning that core biopsy is susceptible to inherent sampling errors, resulting in underestimation [24]. We also studied the factors of pathological escala- tion and did not find evidence that the DCIS histologi- cal escalation of the core biopsy would lead to further underestimation of ultrasound imaging. Taking into ac- count the above two points, we have reason to believe that the use of core biopsy pathology report will facilitate accurate measurement of tumor size before surgery. At the same time, due to the characteristics of DCIS, if the results of the core biopsy include DCIS components, we should use some other image examinations, such as mag- netic resonance imaging (MRI), before breast-conserving surgery.

In addition to the pathological type, histological size is also a key influencing factor. For small lesions (<2 cm), we detected an overestimation of approximately 2 mm (p<0.01). Pathological methods can explain almost indistinguishable deviations. Usually, the difference is small and may not have significant clinical value. How- ever, we can conclude that tumor size is accurate or not underestimated in ultrasound examination. At the same time, as the size of histology increases, more sizes are underestimated. Others authors reported similar results [3,5]. Severe underestimation in large size cases may be associated with limitations of US probes and broader in- filtration of advanced tumors.

BI-RADS classification is a recognized principle in the evaluation of breast lesions. Category 3 and 4A are often benign lesions. Interestingly, low-grade tumors (supposed to be breast cancer) were underestimated. A possible explanation is that some of the malignant fea- tures, including malignant halos, are ignored in these misdiagnosed cases.

Breast density has been reported to be associated with breast mass sensitivity in a mammography but not with US or MRI [7]. According to the fourth edition of BI-RADS proposed by ACR, this study classifies female breasts into four categories. In dense breast tissue (ACR 4), the extent of the disease is slightly too high and the size of the non-compact breast tissue (ACR 1-3) is un- derestimated. The reason for this difference is that vari- ous breast tissue densities exhibit different background imaging and affect the measurement of breast lesions. No significant differences were found when age and meno- pausal status were used as the basis for classification.

Limitations

Although the diameters were measured in three ra- dial directions in both the US and pathological speci- mens, only the largest diameter was compared in this study. Therefore, in a few cases, the diameters of the US and pathological specimens become unequal.

We tried to compare the dimensions by calculating the volume. However, since this is a retrospective study, it is no longer possible to accurately assess the irregular vol- ume of a tumor. In addition, the US and pathology data for this large sample study were obtained by different radiologists and pathologists, although they were all sen- ior doctors. In addition, pathological sampling methods still need to be improved. Finally, other factors may be related to the measurement of tumor size, such as wheth- er a core biopsy was performed prior to surgery, and the stiffness of the tumor. Further prospective studies are necessary.

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Conclusions

The use of US inevitably leads to an underestimation of the extent of the disease. Underestimated size is af- fected by pathological type, molecular subtype and his- tological size. The pathological results of the core biopsy help predict tumor size before accurate breast cancer di- agnosis.

Acknowledgements

This work was supported in part by the National Nat- ural Science Foundation of China (81572607, 81572595, 81502299, and 81502286); the Natural Science Founda- tion of Jiangsu Province (BK2011853, BK2011855 and BK20141023);the Program for Development of Inno- vative Research Team in the First Affiliated Hospital of NJMU (IRT-008) and a project Funded by the Priority Academic Program Development of Jiangsu higher Edu- cation Institutions (PAPD).

Conflict of interest: none References

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The cyclosporine amorphization was probably a consequence of its interaction with copolymers in SDD-CsA/P-α-CD, P-β-CD and P-γ-CD as was confirmed by 13 C CPMAS NMR

In this paper, more effort has been done to fabricate bulk dense BST ceramics from submicron down to nanometer size using the two-step sintering method, and the dielectric

In this study, the antimicrobial activity of colloidal silver nanoparticles prepared by the sol-gel method was investigated, and the turbidity, viscosity and pH of the colloidal

Based on the atomic force microscopy analysis, it was found that the grain size, thickness and surface roughness were strongly influenced by deposition time.. (Received October