Ktrans Calculation Using Reference Method Corrected Native T10 for Breast Cancer Diagnosis : Journal of Medical Physics

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Original Article

Ktrans Calculation Using Reference Method Corrected Native T10 for Breast Cancer Diagnosis

Negi, Pradeep Singh1,2,; Mehta, Shashi Bhushan1,2; Jena, Amarnath1,2; Rana, Prerana1

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Journal of Medical Physics 48(1):p 19-25, Jan–Mar 2023. | DOI: 10.4103/jmp.jmp_90_22
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The objective of the study is to use multiple tube phantoms to generate correction factor at different spatial locations for each breast coil cuff to correct the native T10 value in the corresponding spatial location of the breast lesion. The corrected T10 value was used to compute Ktrans and analyze its diagnostic accuracy in the classification of target condition, i.e., breast tumors into malignant and benign.

Materials and Methods: 

Both in vitro phantom study (external reference) and patient’s studies were acquired on simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) Biograph molecular magnetic resonance (mMR) system using 4 channel mMR breast coil. The spatial correction factors derived using multiple tube phantom were used for a retrospective analysis of dynamic contrast-enhanced (DCE) MRI data of 39 patients with a mean age of 50 years (31–77 years) having 51 enhancing breast lesions.


Corrected and non-corrected receiver operating characteristic (ROC) curve analysis revealed a mean Ktrans value of 0.64 min−1 and 0.60 min−1, respectively. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and overall accuracy for non-corrected data were 86.21%, 81.82%, 86.20%, 81.81%, and 84.31%, respectively, and for corrected data were 93.10%, 86.36%, 90%, 90.47%, and 90.20% respectively. The area under curve (AUC) of corrected data was improved to 0.959 (95% confidence interval [CI] 0.862–0.994) from 0.824 (95% CI 0.694–0.918) of non-corrected data, and for NPV, it was improved to 90.47% from 81.81%, respectively.


T10 values were normalized using multiple tube phantom which was used for computation of Ktrans. We found significant improvement in the diagnostic accuracy of corrected Ktrans values that results in better characterization of breast lesions.


Cancer is a leading cause of death in women before the age of 70 years and breast cancer is the most commonly diagnosed cancer in women among all other cancers.[1] Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast is the modality of choice to characterize tumor into malignant and benign. The pattern of the contrast enhancement in the tumor tissue over a period of time, i.e., time activity curve of tumor in routinely done high spatial resolution DEC-MRI, can characterize the tumor tissue based on three types of curves, i.e., (1) wash in and wash out (curve Type 3) denoting malignant characteristic, (2) initial rise and plateau (curve Type 2) denoting indeterminate: either benign or malignant characteristic, and (3) persistent rise (curve Type 1) denoting benign characteristic. However, the classification of a lesion on DCE-MRI as benign or malignant still remains a challenge.[2–8]

Pharmacokinetic (PK) parameters, i.e., transfer constant (Ktrans), extracellular volume (ve), and flux rate constant (kep) rely on the quantification of vascular events through compartmental modeling. It is a highly potential method to classify the tumor into benign or malignant groups. A sharp rise in the enhancement curve is reported in the malignant tissue as compared to benign and normal tissues of the breast because of the neoangiogenesis in the malignant tissues.[8–11] High and low Ktrans values of the tumor denote the malignant and benign tissue, respectively. Ktrans, which is a quantitative parameter, is known to be influenced by a host of interlinked factors. These factors mostly include a large field of view (FOV) required for bilateral breast imaging, off-center positioning of the patient’s torso inside the transmitting whole-body radiofrequency (RF) birdcage coil thus resulting in unequal loading effects and RF nonlinearity in the transmitter/receiver system or coils are factors that influence B1 homogeneity causing flip angle error in the magnetic resonance (MR) pulse sequence.[12] These factors can propagate error in the computation of native T1, which is a key factor in the computation of Ktrans. Many researchers had focused to correct the flip angle by improving B1 homogeneity across the breast coil cuffs and that in turn corrected the T10 at each spatial location to improve Ktrans computation.[13–19] Other factors affecting Ktrans computation are arterial input function (AIF) and time-intensity curve of the lesion. AIF which is influenced by high temporal resolution data sampling is mostly addressed through fast MRI sequences and high-field magnet system. Suitable mathematical modeling has been used to achieve accurate curve fit of the time-intensity curve. To reduce the acquisition time (TA) in the calculation of Ktransvalue while still maintaining the adequate diagnostic accuracy has been a matter of research.[20–22] These observations underscored the fact that factors influencing the estimation of Ktrans needs to be adequately addressed so that it can be used as a reliable parameter in the clinical setting. Many approaches such as variable flip angle (VFA): multiple flip angles (MFA), dual flip angle (DFA), and driven equilibrium single pulse observation of T1 with high-speed incorporation of RF field in homogeneities (DESPOT1-HIFI) etc have been used to improve T10 by correcting the B1 inhomogeneity.[20–24] The most common method used to derive T10 is using VFA; in this method, multiple data points were sampled to correct the flip angle errors which improves the computational accuracy of T10.[16–19,22–27] It has also been reported that DFA with 2° and 15° flip angles; takes lesser TA than MFA, gives results nearest to the MFA technique for the assessment of PK parameters in the head-and-neck malignancies.[22] In the last few years, Jena et al. tried to directly normalize T10 values in bilateral breast tissue instead of B1 correction of breast coil cuffs.[20,21] In that method, a single tube phantom prefilled with a material of known T1 value was used as an external standard for native T1 correction and the corrected T10 was used for the computation of Ktrans values. That method was found useful in improving the diagnostic accuracy of Ktrans in clinical cases. Later on, Negi et al.[28] adopted an in vitro reference method to normalize T1 distribution using an in-house designed multiple tube phantom placed within the breast coil cuffs and T1 was calculated using DFA protocol. The T1 values were normalized in the molecular magnetic resonance (mMR) breast coil-cuff by applying correction factors derived for each spatial location and observed that before the application of correction factors, T1 distribution was inhomogeneous in different parts of each breast coil cuff as well as between the left and right coil cuff. The homogeneity improved in mMR breast coil after correction.[28]

In contrast to earlier literatures, where researchers attempted to homogenize the B10 distribution[16–19] that was ultimately used to correct the T10 value, our current study aimed to use the index test, i.e., multiple tube phantom to generate correction factor at different spatial locations for each breast coil cuff to correct the native T1 value in the corresponding spatial location of the breast lesion. The corrected T10 value was then used to compute the Ktrans and analyze its diagnostic accuracy in the classification of target condition, i.e., breast tumors into malignant and benign.


Both in vitro phantom study and retrospective patient’s studies were acquired on simultaneous positron emission tomography (PET/MRI) Biograph mMR system 3.0 T (Siemens, Erlangen, Germany) using 4 channel mMR breast coil. The acquisition of phantom image was done using DFA method to derive correction factor for T1 value at each spatial location.[28] The correction factor so obtained was then applied to Native T10 values of breast lesions of 39 patients that was spatially synchronized with the lesion. The patients were selected consecutively from the database between 2018 and 2021 with a mean age of 50 years (31–77 years) having a total 51 lesions who had undergone breast PET/MRI study as part of their diagnostic/staging workup with proven cancer on histopathology before or done subsequently after their PET/MRI scan. The demography of the study cohort is given in Table 1. The study protocol was approved by the ethics committee of the institute and waiver of consent was allowed owing to the retrospective nature of study related to patients.

Table 1:
Demography of study cohort

Phantom creation and study

In Multiple tube phantoms, each phantom contains 19 tube that were filled with the contrast solution i.e., water and Gd-DTPA ([diethylenetriamine pentaacetic acid gadodiamide (Omniscan)]; 0.1 mMol) which was mixed in the ratio of 10:1. The phantom was designed in such a way that it would fully occupy the cuff space when placed inside the breast coil [Figure 1].

Figure 1:
(a) Showing multiple tube phantom (19 tubes) filling the space of both cuffs of breast coil. (b) Both patient and phantom study spatially synchronized using Syngovia software: The correction factor of the nearest tube to the tumor highlighted by arrow, was applied to correct the T10 of tumor

Phantoms were positioned one in each cuff, corresponding to the isocenter of the magnet using light localizer. After localizer images obtained, 2° flip angle proton density and 15° flip angle non-fat suppressed T1-weighted images volumetric interpolated body examination (VIBE) with time to echo (TE) 1.8 ms, repetition time (TR) 5.2 ms, FOV 360 mm, slices 24, TA 12.3 s, resolution 256 × 256 and voxel size 3.9 mm × 1.4 mm × 4.0 mm[21,24] were acquired for computation of T1 value at each spatial location (total of 684 data locations for each coil cuff: 19 tubes × 36 slices) [T1 values were calculated using Equation 1 of Supplementary Materials].


Patient studies and synchronization with phantom study

All patients were imaged in the prone position with each breast placed in the breast coil cuff at the isocenter of the magnet. Patients had undergone high temporal resolution, i.e., 4.1 s postcontrast 15° VIBE (TE 1.8 ms, TR 5.2 ms, FOV 360 mm, slices 24, TA 4.1s, resolution 256 × 256, and voxel size 3.9 mm × 1.4 mm × 4.0 mm) with a total TA of ~60 s; this imaging protocol was sandwiched in a routine high spatial resolution DCE MRI.[20]

Precontrast 15° images subtracted from the last postcontrast series of dynamic data was used for localizing enhancing lesion in the breast parenchyma. MRI protocols were performed in a fix table position with the same matrix size (256 × 256) for both phantom study and patient’s study for inter-study (phantom study and patient study) spatial correlation. Since both patient and phantom study were done using the same breast coil, the correction factor achieved from the phantom for each x, y coordinate of the breast coil space remain same for the corresponding (x, y coordinate) of the breast image done using the same breast coil. When the lesion is located between multiple tubes, then we had taken averaged correction factor value of all surrounding tubes for that spatial location. The same method was applied for large-size lesion covering more than one tube; in this scenario, the average correction value of all involved tubes was taken. The correction factors derived by the phantom study, nearest or overlapped to the breast lesion were applied to the lesions in all 39 patients to correct the T10 values and used for computing Ktrans values. The Ktrans values in breast lesions before and after applying the correction factor were compared to verify the diagnostic accuracy of this method [Details of T10 correction and Ktrans computation are described in the Supplementary Materials and Supplementary Figures 1-4]. Region of interest (ROI) drawn on visible breast lesion on the 15° flip angle subtracted image, was copied and pasted on the corresponding 2° flip angle image and all postcontrast 15° dynamic series for native T1 and Ktrans calculation. Both patient and phantom study were spatially synchronized using Syngovia software (version VB 10B, M/s, Siemens Healthineers, Germany), [Figure 2].

Figure 2:
The schematic diagram of sandwiched protocol showing time intensity graph and Cgdtissue curve (for Ktrans calculation) of malignant and benign breast lesion

Statistical analysis

The two-tailed paired t-test was performed between corrected and non-corrected Ktrans, and corrected and non-corrected T10 value which was divided into malignant and benign groups. The corrected and non-corrected Ktrans values were correlated with the clinical reference standard, i.e., histopathological findings. Using logistic regression analysis for both corrected and non-corrected Ktrans data, the true positive, true negative, false positive, false negative, and accuracy were calculated. Receiver operating characteristic (ROC) curve analysis on this data was done to calculate area under curve (AUC), sensitivity, and specificity. The power of the study was calculated to be 82%. The statistical analysis was performed using MedCalc statistical software package (version 19.8-64 bit (MedCalc Software Ltd, Ostend, Belgium); Windows Vista/7/8/10). A P value < 0.05 was considered to be statistically significant. The tumor T10 difference between the left and right breast was calculated by subtracting the T10 values of the right and left breast divided by greater value of T10 between the two, in the end, the result was multiplied by 100.


Phantom study

The difference in T1 values observed across ROIs between right and left side of breast coil was significant (P < 0.001). After correction, no significant difference was noted suggesting convergence of mean T1 value and regression of standard deviation (P = 0.091) across spatial locations in the coils. The mean T1 value before the correction was 6.08 ± 1.02 ms and 5.38 ± 1.06 ms in right and left breast coil, respectively, which after correction was changed to 6.12 ± 0.26 ms and 6.03 ± 0.28 ms.

Patient study

The estimated T10 values of 51 (22 benign and 29 malignant) enhancing breast lesions without phantom correction were 1469 ± 310 ms in the left breast and 1832 ± 527 ms in the right breast which was found to be statistically significant at a P = 0.004. However, while the estimated T10 values of tumor with phantom correction were 1590 ± 476 ms in the left breast and 1737 ± 611 ms in the right breast which was found to be statistically insignificant, i.e., P = 0.34. The difference between T10 value of the right and left breast was statistically insignificant after correction [a detailed distribution of T10 values in breast coil is given in Supplementary Table 1]. The tumor T10 difference between the left and right breasts was 19.8%, which was reduced to 8.4% after correction. The average size of the malignant lesions was 3.37 cm (range: 0.8–8.4 cm) and of benign lesions was 2.41 cm (range: 0.7–11.7 cm). The results for the mean of corrected and non-corrected Ktrans for benign and malignant lesions are summarized in Table 2. The mean of non-corrected Ktrans value for malignant lesions was 0.81 ± 0.83 min−1 and corrected Ktrans value was 0.92 ± 0.75 min−1 (P = 0.01). The mean of non-corrected Ktrans value for benign lesions was 0.30 ± 0.24 min−1 and for corrected Ktrans value was 0.27 ± 0.18 min−1 [P = 0.008, Figure 3].

Table 2:
Effect of multiple tube phantom on T10 and Ktrans in breast lesions
Figure 3:
The effect of T10 correction on characterization of lesion based on its Ktrans value. Non-corrected image of lesion. (a) showing benign nature i.e., yellow and green color and after correction the image. (b) of the same lesion shows malignant nature i.e., red in color. (As pointed out by arrow)

The mean Ktrans of total lesions (benign + malignant) before correction was 0.60 min−1 and after correction was 0.64 min−1. Before correction 4 patients were false positive and 4 patients were false-negative with a 0.38 min−1 cut-off value for Ktrans and after correction, it was 3 false positive and 2 false negative with 0.50 min−1 cutoff.

Corrected and non-corrected ROC curve analysis revealed a mean Ktrans value of 0.64 min−1 and 0.60 min−1, respectively. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and overall accuracy for non-corrected data were 86.2%, 81.8%, 86.2%, 81.8%, and 84.3%, respectively, and for corrected data, the values were 93.1%, 86.3%, 90%, 90.4%, and 90.2%, respectively. The AUC for non-corrected data was 0.82 (95% confidence interval [CI] 0.69–0.91) and for corrected data were 0.95 (95% CI 0.86–0.99) [Figure 4]. The AUC was improved from 0.82 to 0.95 and also NPV was improved from 81.8%–90.4%.

Figure 4:
ROC curve and results of statistical analysis of non-corrected. (a) and corrected (b) Ktrans. ROC: Receiver operating characteristic


Reliable estimation of T10 of tissue under investigation is a prerequisite for accurate measurement of PK parameters. This assumes importance because of increasing application of PK parameters to assess the neoangiogenesis property of cancer, in particular breast cancer diagnosis, to use it as a response evaluation tool in future and to assess the efficacy of newer coming drugs.[13,14,16–18]

In this study, we tried to improve the accuracy of PK parameters by directly normalizing T10 at each spatial location of breast coil cuffs by applying correction factor derived from the phantom study. Our approach was different from other workers who had worked on homogenizing the B10 distribution[16–19] that ultimately helped to achieve more accurate T10 value.

This technique was using multiple correction factors at different spatial locations for each breast coil cuff to correct the native T1 value in the corresponding spatial location of the breast lesion compared to the study of Jena et al. which was using a single correction factor for both coil cuffs that were not spatially synchronized with the breast lesion thus making our method technically different than single tube phantom technique.[20–21] The current method of multiple tubes had the advantage of having correction factors at multiple spatial locations in the cuff space that can be applied directly to the nearby or overlapping tumor which makes the technique more robust.

Unlike other workers who had used MFA,[16–19,23,24,26,27,29,30] we were using DFA (2° and 15°) to calculate T10, that has been reported to give results nearest to MFA for PK parameters estimation[22] with lesser scan time. This lesser scan time helped in the formulation of sandwiched imaging protocol in this study to adopt ~1.0 min TA slot for high temporal resolution sequences (at 4.1 s with 14 data points) in a routine DCE MRI study. The temporal resolution and TA are important parameters in the computation of Ktrans. Each is associated with its own limitations and there is a trade-off between imaging volume with temporal resolution that ultimately effects the signal-to-noise ratio of the image; and also, between clinically acceptable time-conserving imaging protocol with diagnostic accuracy. Attempts had been made by Veltman et al. in 2008 to design time efficient imaging protocol by including a high temporal resolution protocol within a routine high spatial resolution DCE-MRI of the breast for patient comfort.[25] Jena et al. had computed Ktransat various time of acquisition, i.e., between 30 s and 90 s and demonstrated comparable diagnostic accuracy at 60 s to 90 s data with AUC of 0.98 for Ktrans in differentiating benign from malignant breast lesions.[20] In the current study with temporal resolution and TA of 4.1 s and ~60 s respectively, we found AUC for Ktrans to be 0.95 which was an improvement over the study by Veltman et al. who had AUC of 0.82[25] using 4.1 s temporal resolution and 90 s TA. Tsai et al.[16] also used shorter temporal resolution and TA of 4.49 s and 90 s, respectively, in their study though they have only studied malignant lesions.

In our study, we found that mean T10 value of malignant lesions was overestimated by 1.60% in the left breast and overestimated by 12.9% in the right breast. The mean T10 value of benign lesions was underestimated by 17% in the left breast and underestimated by 8.59% in the right breast. This was in line with the study of Tsai et al.[16] in which before B1 correction T10 values were overestimated by 50% in the left breast and had 7% underestimation in the right breast This further substantiates our findings of the presence of T10 inhomogeneity across breast coils.

The primary objective of our study was to estimate Ktrans value which was derived by directly correcting the T10 value and to check the diagnostic accuracy of corrected Ktrans. There was a significant change in the mean Ktrans value of both benign and malignant lesions after correction, i.e., P = 0.008 and 0.01. The mean Ktrans value was underestimated by 16.6% in the left breast and by 12.2% in the right breast in malignant lesions. In case of benign lesions, mean Ktrans value was overestimated by 18.2% in the left breast and overestimated by 10% in the right breast. Whereas in a study by Bedair et al.[17] mean Ktrans of lesions in the right breast was decreased by 41%, and increased by 46% in the left breast after correction. Tsai et al.[16] used B1 corrected and non-corrected T10 for the computation of PK parameters in 1.5T MRI system and found that because of T10 variation, i.e., in the non-B1 corrected data, the Ktrans value was getting 41% underestimated in left breast and 10% overestimated in the right breast.

In the studies of Bedair et al.[17] and Tsai et al.,[16] only malignant cases were enrolled and unlike them, we had enrolled patients with enhancing breast lesion and classified them into malignant and benign types on the basis of Ktrans values. These findings were later correlated with clinical reference standard to assess the diagnostic accuracy of Ktrans. In fact, this is the first research article in which attempt has been made to find out the diagnostic accuracy of Ktrans in classifying breast tumors by using multiple tube phantom for spatially correcting breast coil for native T1.

Our overall accuracy, sensitivity, NPV, PPV, AUC, and 95% CI values were improved after correction, i.e., from 84.3%, 86.2%, 81.8%, 86.2%, 0.82%, and 0.69%–0.91%, respectively, to 90.2%, 93.1%, 90.4%, 90%, 0.95%, and 0.86%–0.99%, respectively, which was in line with our assumption. Thus, it proved that phantom-generated correction factors can be synchronized with in vivo spatially located breast lesions.

However, we had some limitations in our study. First, the work has been done manually, and software computation will help to improve the speed and will reduce the manual errors. Second, the study had a small cohort and needs to be verified with a large sample size. Third, tissue equivalent material having T1 value matching with the glandular tissue could be used to improve the results in a future study. Fourth, this technique is still in its infancy phase and therefore lacks in some aspects one of which is the patient effect on the homogeneity of B1 field which thus ultimately effect Native T1 distribution. We have planned to include this aspect in the next phase of this study. Finally, a comparative evaluation of B1 corrected T1 and directly corrected T1 would have given us an insight into the relative diagnostic accuracy of computed Ktrans between these two techniques. In conclusion, we had normalized T10 values using the multiple tube phantom technique, which was used for the computation of Ktrans. We had found improvement in the diagnostic accuracy by using corrected Ktrans values that results in a better characterization of breast lesions.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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                Dynamic contrast-enhanced magnetic resonance imaging; Ktrans; molecular magnetic resonance breast coil; T10

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