Imaging protocol
All MRI exams were performed on a 1.5-T scanner (Vision/Sonata hybrid System, Siemens, Erlangen, Germany). Conventional T1-weighted as well as dual-echo proton density- and T2-weighted turbo spin-echo sequences offered complete coverage of the body region in question and were used for localising the quantitative study. The field of view and the choice of the coil depended on the site of the tumour and were determined on the basis of the potential highest signal-to-noise ratio and adequate spatial coverage. Two possible schemes were used for the field of view (FOV), either 200 × 200 mm or 400 × 400 mm as masses differed substantially in their size and location. The T2 quantitative MRI protocol consisted of two-dimensional (2D) single-slice multi-echo spin-echo based on a 2D multi-echo spin-echo Carr-Purcell-Meiboom-Gill sequence with alternating 180° radiofrequency pulses under the phase-alternating-phase-shift scheme [17]. The final result was a single-slice, proton density-to-T2-weighted sequence with repetition time equal to 2,500 ms, 25 equidistant spin echoes, with the first echo time (TE) at 13.4 ms, echo spacing 13.4 ms, and last TE at 335 ms. Slice thickness was 5 mm and a rectangular reconstruction matrix (384 × 320 pixels) was chosen. A selective refocusing radiofrequency pulse scheme was utilised for elimination of stimulated echoes [18].
Patient population and histopathology
The imaging protocol was submitted and approved by the local ethics committee. All patients signed an informed consent for the use of clinical and imaging data for research purposes. Patients with primary lipomatous tumours who underwent MRI examination under a prospectively set protocol from July 2017 to February 2019 prior to the planned surgical excision were included in the study. Patients with recurrent or residual tumours and those submitted to preoperative treatment were excluded. Subsequently, we excluded from analysis one patient due to severe motion artifacts and two patients that refused to perform the examination because of claustrophobia. A total of 24 patients with primary lipomatous tumours of the lower limb (n = 11), the upper limb (n = 7), and the retroperitoneal area (n = 6) were included.
The surgeon marked the specimen with sutures or surgical staples at predefined points in order to enable the actual three-dimensional orientation of the specimen in relation with the patient’s body and to warrant the implementation of sections of the tumour along a true axial plane. For each patient, at least three slices (at the top and bottom end and a slice in the middle of the tumour) were analysed for differentiation, cell type, cellular atypia, cellularity, mitotic activity, vascularity, and presence of necrosis. Histopathologic analysis revealed six lipomas, four well-differentiated liposarcomas, three myxoid liposarcomas, four pleomorphic liposarcomas, and seven dedifferentiated liposarcomas. Within tumours of increased heterogeneity, the pathologist guided the radiologist to identify regions indicative of myxoid or fibrous composition as well as areas of well differentiated or poorly differentiated tissue on the MRI slices.
Data preprocessing
In the multi-echo spin-echo phase-alternating-phase-shift sequence, the first echo signal is not accurate because of B1 field inhomogeneity [18, 19] and is usually either extrapolated or ignored. In this study, we did not correct for the first echo as extrapolation process requires the choice of a proper model and this would in turn introduce bias to the next step of monoexponential or biexponential fitting model selection. The first TE was therefore the second acquired at 26.8 ms from the original sequence.
T2 relaxometry (Mexp method)
All numerical calculations concerning Mexp T2 relaxometry were implemented in Python 3.5 (www.python.org) apart from the inverse Laplace transform method which was implemented in Matlab 2015a (Mathworks, Natick, MA, USA). The graphical user interface and result visualisation were accomplished by the use of PyQt4 and PyQtGraph (www.pyqtgraph.org) libraries respectively. The mathematical framework and technical details for the T2 relaxometry are presented below.
Supposing a signal S(TEk), measured at echo times TEk (k = 1, 2 ,…, K), the decay of the transverse magnetisation can be represented as the sum of up to N exponential decays as shown in (1).
$$ S\left({\mathrm{T}\mathrm{E}}_{\mathrm{k}}\right)-e\left({\mathrm{T}\mathrm{E}}_{\mathrm{k}}\right)=\sum \limits_{i=i}^N{A}_{\mathrm{i}}\exp \left(-\frac{{\mathrm{T}\mathrm{E}}_{\mathrm{k}}}{\mathrm{T}{2}_{\mathrm{i}}}\right),\kern1em N=1,2 $$
(1)
e(TEk) was considered to be the vector containing the mean background noise for every TE which was subtracted from the signal. Our analysis was based on searching a maximum of two components since the protocol did not permit to search for very short T2 values since the first TE was at 26.8 ms. Every voxel curve was fitted twice in Eq. (1) for all N (N = 1,2) meaning both monoexponential and biexponential fit as a preparatory step by using non-linear least squares. The number of exponentials per voxel fit was determined by the highest \( {\overline{R}}^2 \) described in the “Goodness of fit” section and will be referred to as R2 criterion hereinafter. The search space for each unknown variable was set as Ai, (i = 1, 2) in [0, 2,000], T21 ∈ [27, 120] ms and T22 ∈ [120.1, 2,500] ms. For the case of N = 1 the T21 was set to [27, 2,500] ms. The intervals for T2i were determined firstly by sequence limitations to detect very short T2 solid or tightly bound components and secondly by reported T2 values in bibliography [20,21,22,23] for weakly bound and free water components. More extensive information on the Mexp method is presented in [16].
Goodness of fit
Having an analytical form of the model fitted to the data, the adjusted R squared \( \left({\overline{R}}^2\right) \) can be computed in order to acquire information about the goodness of fit. \( {\overline{R}}^2 \) was considered more suitable for this study than R2 since it takes into account the number of data points (K), the number of the explanatory variables (m) of the model function and the residuals between the model function (Gi) and the data (yi) as can be seen in Eqs. (2) and (3). Index i stands for the number of the measured data points.
$$ {\overline{R}}^2=1-\left(1-{R}^2\right)\frac{K-1}{K-m-1} $$
(2)
$$ {R}^2=1-\frac{\sum_{i=1}^k{\left({G}_i-\overline{y}\right)}^2}{\sum_{i=1}^k{\left({y}_i-\overline{y}\ \right)}^2} $$
(3)
A graphical representation of the workflow used in this study is shown in Fig. 1.
Voxelwise analysis
For each patient, an expert radiologist with more than 12 years of experience in body MRI annotated the tumour region for the patient cohort. Voxelwise parametric maps were produced by the Mexp method for all patients. All voxels assigned as tumour from all patients were used to constitute five tissue categories (benign lipoma, well-differentiated liposarcoma, myxoid liposarcoma, poorly differentiated liposarcoma, pleomorphic liposarcoma) according to the histopathologic diagnosis. The radiologist also annotated healthy subcutaneous fat ROIs for each patient to be used for reference purposes.
Classification analysis
Initially, a stratified 5-fold cross validation technique was applied to the dataset in order to prevent sample selection bias. From the Scikit-learn python library [24], logistic regression was used for the discrimination between the two classes, i.e., malignant and benign tissue types, and for the calculation of sensitivity and specificity metrics. More specifically, benign tissue category contained the lipoma and health subcutaneous fat, while malignant category included ROIs from well-differentiated liposarcomas, myxoid liposarcomas, pleomorphic liposarcomas, and dedifferentiated liposarcomas. The statistical metrics used for the analysis were as follows: mean value, standard deviation (SD), and the 90th percentile for each one of % model prevalence, T21 and T22 values.