DCE-MR imaging of orbital lesions: diagnostic performance of the tumor flow residence time τ calculated by a multi-compartmental pharmacokinetic tumor model based on individual factors

Abstract

Background

Differentiating benign from malignant orbital lesions by imaging and clinical presentation can be challenging.

Purpose

To differentiate benign from malignant orbital masses using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) based on tumor flow residence time τ calculated with the aid of a pharmacokinetic tumor model.

Material and Methods

Sixty patients with orbital masses were investigated by 3-T MRI including dynamic sequences. The signal intensity-time curve after i.v. contrast medium administration within lesions was approximated by Gd-concentration profiles on the basis of model calculations where the tumor is embedded in a whole-body kinetic model. One output of the model was tumor flow residence time τ, defined as the ratio of the tumor volume and the tumor blood flow rate. Receiver operating characteristic (ROC) curves were used to analyze the diagnostic performance of τ. The results were compared with those of K^trans, k_ep, v_e, iAUC, and ADC.

Results

Thirty-one benign and 29 malignant orbital masses were identified (reference standard: histopathology, clinical characteristics). Mean τ was significantly longer for benign masses (94 ± 48 s) than for malignant masses (21 ± 19 s, P < 0.001). ROC analysis revealed the highest area under the curve (AUC = 0.94) for τ in orbital masses compared to standard methods.

Conclusion

Tumor flow residence times τ of benign and malignant orbital masses are valuable in the diagnostic work-up of orbital tumors. Measures of diagnostic accuracy were superior for τ compared to ADC, K^trans, v_e, and iAUC.

Keywords

Head/neck magnetic resonance diffusion/perfusion orbit contrast agents – intravenous tissue characterization

Introduction

Patients with orbital mass lesions commonly present with protrusion of the eyeball to their physician. The orbit comprises a wide variety of tissues, giving rise to a number of different orbital lesions (1). Magnetic resonance imaging (MRI) studies help in identifying such lesions; however, many lesions cannot be classified by their clinical presentation and imaging appearance only (2). In these cases, biopsy may be necessary.

Diffused-weighted imaging (DWI) can be useful in differentiating benign from malignant masses by calculating the apparent diffusion coefficient (ADC) (3,4). Dynamic contrast-enhanced (DCE)-MRI allows generation of time-intensity curves of gadolinium (Gd)-based contrast medium (CM) and provides information on tissue vascularization (5). It is well-known that the growth of malignant tumors depends on angiogenesis (6). The course of signal intensities over time has been shown to contribute to the differential diagnosis of lesions in different body regions, in particular in the breast, and to the prediction of outcome (7 –9).

Pharmacokinetic models have been developed to extract quantitative information from signal intensity curves. The so-called Extended Tofts Model considers exchange rates of fluids between interstitium (= extravascular extracellular space [EES]) and plasma (10). The parameters generated by this model are K^trans (= volume transfer constant between blood plasma and EES in abnormal tissue), k_ep (= efflux rate constant from EES to blood plasma), v_e (= EES volume per unit volume of tissue), and iAUC (= initial area under the Gd-based time-intensity curve [t < 60 s]). Brix et al. developed a two-compartment exchange model where tissue contains EES and plasma. They also considered blood flow (11). In 2011, a physiologically based multi-compartmental pharmacokinetic model for CM distribution in normal human tissue was developed (12) and later extended to tumors (13). It was shown that a single kinetic parameter, tumor flow residence time τ, allows to classify the time-intensity curves into benign (>200 s) and malignant (<200 s) curve shapes (the actual numbers are model-specific). The model includes personalized parameters (weight of the patient and tumor volume) and the parameters of Gd CM administration (concentration, dose, and injection rate).

The purpose of the present study was to investigate the diagnostic accuracy of tumor flow residence time τ in differentiating benign from malignant orbital masses by comparison with quantitative parameters previously studied.

Material and Methods

Patients

This prospective study was approved by the institutional review board and registered under ClinicalTrails.gov (ID NCT01884207). A total of 89 patients with orbital masses were recruited consecutively by the outpatient ophthalmology clinic between May 2013 and June 2014. Twenty-nine patients did not fulfill the study requirements (no reference standard or incomplete index test) and were excluded. A total of 60 patients were included in the final analysis. The final diagnosis (reference standard) was based on either histopathology (n = 34; 20 benign, 14 malignant), ophthalmoscopy (n = 14; 0 benign, 14 malignant), pathognomonic imaging findings (n = 6; 6 benign, 0 malignant), clinical follow-up over at least six months (n = 4; 4 benign, 0 malignant), or unequivocal clinical diagnosis (n = 2; 1 benign, 1 malignant). Results of the index test (pharmacokinetic model) were not available to physicians involved in the final diagnosis. Vice versa, information on the reference standard was not available to scientists involved in the pharmacokinetic studies.

Imaging techniques

MRI was performed on a 3-T system with a maximum gradient amplitude of 45 mT/m and a maximum slew rate of 200 mT/m/ms (MAGNETOM Skyra, Siemens Healthcare, Erlangen, Germany). A 20-channel headcoil was used for the DWI (SE-EPI) and DCE (TWIST) sequences. The CM was administered at a dose of 0.1 mmol Gd/kg and a rate of 2 mL/s followed by a 20-mL saline flush administered at the same rate. In 53 cases, gadoterate (Dotarem® [500 mmol/L]) and in seven patients gadobutrol (Gadovist® [1000 mmol/L]) were administered. The technical parameters of the imaging protocol are summarized in Table 1.

Table 1.

Technical parameters of the imaging protocol.

Sequence	TR (ms)	TE (ms)	Resolution (mm)	FOV (mm)	ST (mm)	Acquisition time (min:s)
T1-TSE	650	9.1	0.39 × 0.39	100 × 81	2	3:04
T2-TSE	3500	69	0.42 × 0.42	100 × 81	1	3:53
DWI (SE-EPI)*	5000	100	1.13 × 1.13	144 × 144	3	5:12
DCE (TWIST)	5.1	2	1.21 × 0.83	160 × 160	2.5	5:49^†
3D-T1-GRE	15	4.2	0.42 × 0.42	80 × 65	1	3:37

*b-values: 0 and 1000 s/mm² (three directions).

^†75 measurements with 4.65 s temporal resolution.

TR, repetition time; TE, echo time; FOV, field of view; ST, slice thickness; TSE, turbo spin-echo; 3D, three-dimensional; GRE, gradient echo; DWI, diffusion-weighted imaging; SE, spin-echo; EPI, echo planar imaging; DCE, dynamic contrast-enhanced; TWIST, time-resolved angiography with stochastic trajectories.

Image analysis

The diameter of the orbital mass was determined on T1-weighted (T1W) or T2-weighted (T2W) images in three planes (transverse, coronal, and sagittal). Total tumor volume V_t was calculated as an ellipsoid. DCE images were analyzed using the scanner’s integrated post-processing software Tissue 4D (Siemens Healthcare). A freehand region of interest (ROI) was placed in the mass by an MR-fellowship-trained reader (with two years of MR reading experience) on the conventional image and mapped onto the perfusion image by the software. In addition, a freehand ROI was placed in the mass on DWI at b = 0 s/mm² and b = 1000 s/mm², and ADC values were calculated using the following formula: ADC = ln (I b = 0/I b = 1000)/(b = 1000 s/mm² – b = 0 s/mm²).

In a second step, a senior MR-fellowship-trained reader (with eight years of MR reading experience) checked ROI placement of the ROI and a consensus was reached. Fig. 1 shows examples of how ROIs are placed in the lesions on the perfusion maps. K^tran^s, k_ep, v_e, and iAUC were calculated using the “Extended Tofts Model.” The arterial input function (AIF) needed for calculating the Tofts parameter was determined from the intermediate sampling rate.

Fig. 1.

How ROIs were placed in the lesion by two MR-fellowship-trained radiologists in consensus. The top row depicts the T2W images, the bottom row depicts the DCE (TWIST) sequences with perfusion maps and the ROIs placed in the lesions. Final diagnosis from left to right: hemangioma, conjunctival carcinoma, lymphoma, and uveal melanoma.

The time-dependent contrast-enhanced signal intensities were taken from the ROI as a basic set for the model calculations. Tumor blood flow residence time τ is the ratio of the tumor blood volume and tumor blood flow k_f. This parameter was determined by fitting the calculated local Gd-concentrations to the signal intensity-time curves with tumor blood flow k_f as principal unknown variable. Finally, sensitivity and specificity of ADC and the parameters calculated using the Extended Tofts Model were determined and compared with those of the flow residence time τ.

The kinetic model

The pharmacokinetic tumor model evolved from a physiologically based whole-body model (12). The CM is administered into a peripheral vein, reaches the vena cava with the blood stream, is taken up by the right heart, pumped into the pulmonary circulation, and leaves the left heart into the aorta, which supplies the organs with arterial blood. Passing from arteries to veins, the blood is collected in the vena cava and the circuit starts again. During their passage through the circulation, the CM molecules are in exchange with the interstitial volume and low-molecular-weight and hydrophilic CMs are continuously renally excreted. Essential parameters are blood flow, exchange rates between plasma and interstitium, the renal excretion rate, and the various organ volumes. These parameters are taken over from the initial model (12) and determine the bolus shape and CM concentration as a function of time. A tumor located anywhere along the circulation path can be regarded as a small extra organ and the tumor volume, V_t, can be determined from morphological MR images.

In the current model, a tumor-supplying vessel with blood flow k_f (mL/s) sprouts from an artery supplied by the ascending aorta. As before, two viable parts, center and rim of the tumor, are considered (13). Plasma in viable tumor tissue is in exchange with the tumor interstitium with rates k_pi and k_ip (s). The tumor vessels drain into a vein of the cerebral circulation with the same flow, k_f.

Three parts of the tumor are considered, i.e. blood/plasma, EES, and intracellular extravascular space (IES; not available for the administered Gd-CM) plus necrotic tissue with volume ratios of blood:EES:IES = 1:1.7:4.3 with tumor volume V_t = V_blood + V_EES + V_IES. For homogeneous CM distribution, these ratios determine the Gd-concentration in the tumor voxels.

Tumor exchange rates between plasma and interstitium are related to the plasma and interstitial volumes of the tumor. Following the distributional phase, the concentrations in these two parts should approach a common value and should furthermore decline due to excretion. Unspecific, hydrophilic and low-molecular-weight CM are renally excreted, and their kinetic behavior was modeled by linear rate equations. Concentration-time profiles were calculated along the blood circuit by digitally solving the rate equations using Mathematica 8.0 (2010) (Wolfram Research, Inc., Champaign, IL, USA). The finite length of the administration time of some seconds prohibits a closed analytical solution. The bolus shape and the CM concentration at any time and location along the blood circulation path (including tumor) are calculated. An AIF is not necessary.

The calculated Gd-concentrations were fitted to the signal intensities measured at 26 equally distributed time points by minimizing the standard deviation as a function of tumor-supplying blood flow k_f (mL/s). This is the sole variable parameter; all other rates and volumes including individual tumor volume V_t are fixed. Tumor flow residence time τ is calculated according to τ = V_blood/k_f (s).

Before fitting the Gd-concentrations to the signal intensities, these were converted to Gd-concentrations. A series of aqueous Gd-solutions were imaged with the same TWIST sequence as used in patients. From the resulting SI-versus-Gd-concentration curve, the SI (measured) was converted into the Gd-concentrations fed into the fitting procedure. Both the calculated and the measured data were normalized to 1 for the maximal value in the time window.

Statistical analysis

Statistical analysis was performed using the “R” software (R version 3.1.2. Copyright © 2014, The R Foundation for Statistical Computing, Vienna, Austria). The Shapiro–Wilk normality test served to test for normal distribution. Student’s t-test, the Mann–Whitney U-test, or χ² test (for gender) were used to analyze the data for differences between the benign and malignant mass groups. Descriptive statistics as well as measures of diagnostic accuracy such as sensitivity, specificity, positive predictive value, negative predictive value, likelihood ratios, and diagnostic odds ratios were calculated. Receiver operating characteristic (ROC) analysis was performed using logistic regression. The optimal threshold for the residence time was based on the Youden Index, i.e. the threshold at which the sum of sensitivity and specificity reaches its maximum. Finally, ROC curves were generated and the common parameters and τ were compared by the bootstrap test or De Long’s test for two correlated ROC curves. The ROC analysis was also extended to the combinations of τ with other parameters to assess the combined diagnostic performance using multiple logistic regression to estimate the diagnostic parameters. P ≤ 0.05 was set to indicate statistical significance.

Results

Patient characteristics

Thirty-one patients had benign orbital masses and 29 patients had malignant masses. A subset of ocular melanoma (n = 14) contributed to the group with malignant masses. The final diagnosis of all masses is given in Table 2. Age was normally distributed and there was no significant difference between the benign and malignant mass group (P = 0.707). There was also no significant difference between the benign and malignant group in terms of sex (P = 0.827) or body weight and tumor volume (P = 0.264 and 0.518; respectively).

Table 2.

Final diagnoses of orbital masses and number of cases included.

Diagnosis	n	Outcome
Aesthesioneuroblastoma	1	Malignant
Amyloidosis	1	Benign
Angioma	1	Benign
Carcinoma	3	Malignant
Cyst	1	Benign
Dacryocystitis	2	Benign
Grave's	1	Benign
Hemangioma	5	Benign
Hematoma	1	Benign
Lipoma	2	Benign
Lymphoma	8	Malignant
Lymphangioma	1	Benign
Melanoma	1	Malignant
Meningioma	3	Benign
Metastasis	2	Malignant
Myxoma	1	Benign
Neurofibroma	1	Benign
Ocular (uveal) melanoma	14	Malignant
Pseudotumor/lymphatic/granulation tissue	5	Benign
Pyocele/mucocele	2	Benign
Sarcoid	1	Benign
Schwannoma	1	Benign
Thrombosis	1	Benign
Unspecified benign	1	Benign

Demographic data and parameter results are given in Table 3. All parameters (τ, ADC, K^trans, k_ep, and iAUC) were statistically significantly different between benign and malignant masses (P < 0.001) except for v_e (P = 0.198) (Table 4). When the large subset of ocular melanomas was excluded, the significant difference between the two groups (benign and malignant) persisted for τ (P < 0.001), ADC (P = 0.008), K^trans (P = 0.007), k_ep (P < 0.001), and iAUC (P = 0.008) but not for v_e (P = 0.879).

Table 3.

Demographic data and parameter results (mean ± standard deviation).

	Benign (n = 31)	Malignant (n = 29)	P	All (n = 60)
Age (years)	55.26 ± 17.87	56.78 ± 12.46	0.707	56.0 ± 15.64
Sex (n)			0.827
Men	19	16		35
Women	12	13		25
Body weight (kg)	83.87 ±19.29	77.76 ±14.6	0.264	80.92 ± 17.45
Tumor volume (cm³)	3.22 ± 5.32	4.52 ± 9.35	0.518	3.85 ± 7.57
ADC (* 10⁻³ mm²/s)	1.27 ± 0.57	0.81 ± 0.44	0.008	1.04 ± 0.56
K^trans (mL/min)	0.1 ± 0.08	0.23 ± 0.14	0.007	0.16 ± 0.13
k_ep (mL/min)	0.68 ± 0.84	1.37 ± 0.80	<0.001	1.02 ± 0.89
v_e (mL)	0.25 ± 0.14	0.19 ± 0.08	0.198	0.22 ± 0.11
iAUC	6.43 ± 4.7	11.2 ± 5.39	<0.001	8.73 ± 5.58
τ (s)	94.07 ± 48.21	21.09 ± 19.10	<0.001	58.8 ± 52.03

P gives the statistical test results for the comparison of the two groups (benign and malignant). For P < 0.05 the two distributions are significantly different.

Table 4.

Measures of diagnostic accuracy of τ, ADC, K^trans, k_ep, v_e, and iAUC.

	τ	ADC	K^trans	k_ep	v_e	iAUC
Threshold	39.05	814.09	0.11	0.62	0.29	7.96
Specificity	0.87	0.87	0.68	0.74	0.32	0.74
Sensitivity	0.93	0.72	0.83	0.93	0.90	0.72
Accuracy	0.90	0.80	0.75	0.83	0.60	0.73
True negative	27	27	21	23	10	23
True positive	27	21	24	27	26	21
False negative	2	8	5	2	3	8
False positive	4	4	10	8	21	8
Negative predictive value	0.93	0.77	0.81	0.92	0.77	0.74
Positive predictive value	0.87	0.84	0.71	0.77	0.55	0.72
LR+*	7.15	5.61	2.57	3.61	1.32	2.81
LR–^†	0.08	0.32	0.25	0.09	0.32	0.37
Pre-test probability	0.48	0.48	0.48	0.48	0.48	0.48
Pre-test odds	0.94	0.94	0.94	0.94	0.94	0.94
Post-test odds	6.69	5.30	2.43	3.38	1.23	2.63
Post-test probability	0.87	0.84	0.71	0.77	0.45	0.72
AUC (ROC analysis)	0.94	0.78	0.80	0.85	0.60	0.76

*Positive likelihood ratio.

^†Negative likelihood ratio.

Residence time τ

The hydrophilic low-molecular-weight Gd-chelates are distributed rapidly over plasma and interstitium and excreted renally. Fig. 2 shows that flow k_f and thus residence time τ largely determine the shape of the Gd-concentration profile over the period of about 350 s considered for SI measurement. The figure shows curves of calculated Gd-concentrations in the tumor as the sum of the blood/plasma and interstitial space concentrations after CM administration (at t = 0) with residence time τ as variable parameter. The model included personalized parameters such as body weight, tumor volume as measured in the standard T1W or T2W images, and parameters of Gd-administration (dosage, volume, and administration rate). In Fig. 3 the administration and initial bolus shapes are indicated: (i) for the administration of Gadovist at a Gd-concentration of 1000 mmol/L; and (ii) for the administration of Dotarem with a concentration of 500 mmol/L. Both CM were administered at the same dose of 0.1 mmol/kg body weight and at the same speed of 2 mL/s but the first for 3.75 s (patient ID3) and the second for 7.5 s. The bolus shapes are very similar with a shift in the maxima by about 3 s. At 30 s, the bolus profiles convene. For this patient (ID3) with a benign tumor, τ = 102.1 s was calculated for Gadovist. Performing the calculation for the lower concentrated Dotarem led to a slightly lower value of τ = 100.6 s. Fig. 4a shows an example for a benign tumor with a long blood flow residence time of 107.3 s and Fig. 4b shows an example for a malignant tumor with a short flow residence time of 25.3 s.

Fig. 2.

Calculated Gd-concentrations (mmol/L) in tumor as a function of time after CM administration with flow residence time τ (s) as parameter. At later times after CM administration, tumor concentrations decrease, as in normal tissue, because of renal elimination of the CM.

Fig. 3.

CM administration pulse and bolus (output left heart) profiles and calculated Gd-concentrations (mmol/L) vs. time (s). The CM was administered at a concentration of 500 mmol/L (Dotarem) or 1000 mol/L (Gadovist), both at 2 mL/s, for 7.5 s and 3.75 s, respectively, followed by a saline flush of 20 mL at 2 mL/s. The duration of administration (here 7.5 s and 3.75 s) was adapted to the patient’s weight and CM concentration.

Fig. 4.

(a) Example of a benign tumor (hemangioma) with long plasma flow residence time (τ = 107.3 s), top row: T1-TSE, T2-TSE, Gd-enhanced 3D-T1-GRE; and (b) example of a malignant tumor (lymphoma) with short flow residence time (τ = 25.3 s), bottom row: T1-TSE, T2-TSE, Gd-enhanced 3D-T1-GRE. The last column of images plotted direct outputs from the Mathematica fitting calculations for the signal intensities (dots) measured at 26 points (about every 13 s), the curves for the calculated Gd-amount in blood, EES, and the total tumor normalized to one (from bottom to top).

Diagnostic accuracy of τ

Benign orbital masses showed a monotonous signal increase with a long residence time (τ) whereas malignant lesions were characterized by a rapid signal increase and subsequent wash-out with a short residence time (τ).

A threshold τ = 39 s separated benign from malignant orbital masses with a sensitivity of 0.93 and a specificity of 0.87 (Fig.5). Table 4 summarizes measures of the diagnostic accuracy of τ, ADC, K^trans, k_ep, v_e, and iAUC. ROC analysis revealed the highest area under the curve for τ (AUC = 0.937) compared to ADC, K^trans, k_ep, v_e, and iAUC. Comparison of the ROC curves of τ with the ROC curves of ADC, K^trans, k_ep, v_e, and iAUC revealed a significant difference between τ and ADC (P = 0.03), between τ and K^trans (P = 0.04), between τ and iAUC (P = 0.009), and between τ and v_e (P < 0.001) (Fig.6). For the τ-values, it was observed that the standard deviations between measured and calculated data were significantly lower for benign than for malignant masses.

Fig. 5.

Boxplots demonstrating a significant difference in τ between benign and malignant tumors (P < 0.001). A τ of 39 s best separates benign from malignant orbital masses with 0.93 sensitivity and 0.87 specificity.

Fig. 6.

ROC curves of τ, K^trans, k_ep, ADC, iAUC, and v_e to differentiate benign and malignant orbital masses (n = 60 patients).

The ROC analysis was also extended to the combinations of τ with k_ep and iAUC in a multiple logistic regression model (lowest P values in Table 3). Concerning the area under the curve of the ROC curves, the inclusion of τ led to 0.942 for τ with k_ep and for τ with k_ep and iAUC. The other combinations stayed below 0.942. Combing these parameters with τ did not seem to be advantageous compared with τ alone.

Discussion

Our results show that the use of a tumor model embedded in a multi-compartmental pharmacokinetic whole-body model of humans allows very precise differentiation of benign and malignant orbital masses. The residence times (τ) of benign lesions are significantly longer than those of malignant lesions (P < 0.001). A residence time of 39 s is the best cut-off, separating benign from malignant orbital masses with 0.93 sensitivity and 0.87 specificity. The sensitivity and specificity of residence time τ are higher than those of k_ep and significantly higher than those of ADC, K^trans, v_e, and iAUC. The model we introduced here incorporates personalized values, such as body weight, tumor volume, and parameters of Gd-CM administration.

Tumor flow residence time τ = V_blood/k_f [s] is determined from the time-concentration profile of the Gd-CM. The CM molecules flowing into the tumor with the blood stream are also in exchange with the tumor interstitium. Depending on the exchange rates, the Gd-molecules swing back and forth between plasma and interstitial space before they leave the tumor with the blood stream. In the model presented here, tumor blood flow k_f was the sole variable parameter for fitting the local tumor Gd-CM concentration to the radiologically determined signal intensity-time curves and served to calculate tumor flow residence time τ = V_blood/k_f. τ corresponds to the mean residence time of earlier models (14), Here τ is the residence time under fast blood flow conditions compared to the (slower) exchange time between plasma and interstitial space or non-permeable (non-exchangeable) CM molecules such as macromolecules or Gd-chelates attached to corpuscular blood components. Concerning this matter, so far only animal studies are available (15,16). For very fast plasma-interstitium exchange, the plasma and interstitium can be regarded as one unit with a tumor residence time (V_blood + V_EES)/k_f equivalent to the system’s mean residence time. The inclusion of cases with flow and exchange times on the same order of magnitude would mathematically leave the framework of clarity.

Our model differs from those of Brix and Tofts in the variables and fitting procedures. In our model, the plasma/interstitium exchange rates (k_pi/k_ip) are determined by the distribution volume of the tumor V_d (tumor) (= V_blood + V_EES). This means that we assume equilibrium concentrations in plasma and interstitium past the distribution phase, so that only blood flow k_f of the tumor is varied. In contrast, three parameters are independently fitted to the clinical data in the Brix model (14) and the Tofts models (19,20).

The changes in MRI signal intensity induced by CMs are of an indirect nature. One does not directly determine the concentration of the Gd-chelates as calculated in the kinetic models, but one measures the effect of Gd-chelates on water-proton relaxation. Aside from the Gd-chelate and field-specific relaxation rates, three time windows and their overlapping periods contribute to the signal intensity of water protons: the refocusing of the TWIST pulse sequence; capillary flow (leading to τ) in the voxels; and extra-/intracellular water exchange, which for erythrocytes is on the order of 0.03 s (17). When volume flow is fast, a steady state might not be reached and only the extracellular water protons are relaxed.

An AIF was not needed. The pulse shape was automatically obtained and could be followed to any point in the circulation. The onset of the pulse shape is delayed according to the length of the passage between left heart output and target input. While Violon (18) introduced a delay time, we could address this issue by increasing or decreasing the length of the artery feeding the tumor vessel.

DCE-MRI studies performed by other groups demonstrated differences in curve patterns between benign and malignant orbital lesions (21,22). However, most studies investigated DWI, showing its value in the diagnostic evaluation of orbital masses (3,4,23 –28). In an earlier study, we investigated the diagnostic performance of multi-parametric MRI (DWI and DCE imaging) compared to standard anatomical imaging (T1W and T2W sequences) was evaluated (29). In this study, τ performed significantly (P = 0.03) better than ADC in terms of both sensitivity and specificity.

The difference in CM administration times, e.g. 7 s (Dotarem) or 3.5 s (Gadovist) for a 70-kg person, has an effect on short (s) but not on long observation times (min). The influence on tumor τ-values is negligible.

Our model, where the tumor vasculature is a small detail of a multi-compartmental physiologically based whole-body kinetics, can be refined especially for malignant tumors with sharp increases in SI. Here, the flow in the artery, from which the tumor vessel sprouts, could become rate limiting.

Our study has some limitations. The study population also included cases (n = 3) where no vascularity was evident on the conventional sequences (e.g. pyocele, cyst). We left these cases in the study population to reflect the referral pattern and because the diagnosis of these entities is not always easy based on conventional (non-enhanced T1W and T2W) sequences only. The malignant masses included ocular melanomas, which can be diagnosed ophthalmoscopically with 99.7% accuracy (30), and MRI is usually performed to rule out extraocular spread. Excluding these melanomas did not affect the results and differences in τ between benign and malignant orbital masses were still significant (P < 0.001). Another limitation is that not all patients had biopsies and satisfy reference gold standard with histology. Also, image analysis and ROI placement were performed by two experienced readers in consensus in one reading session. ROI placement was not evaluated for inter- or intra-observer variability, which may be a methodological limitation. However, the lesions were easily identified on conventional images and relatively large (mean tumor volume of 3.85 ± 7.57 cm³). Another limitation is that the kinetic model assumes the tumor volume ratio of plasma:EES:IES to be 1:3:7.6 (ratio of blood:EES:IES = 1:1.7:4.3). There is evidence that this ratio is much different in solid tumors compared to normal tissue, and similar residence times were observed in malignant tumors by Vaupel at al. (31). v_e is not significantly different for benign and malignant tumors, which might support the assumption of one common volume ratio V_plasma:V_EES =1:3 for benign and malignant tumors. A final limitation is that we did not compare the diagnostic performance of τ with the visual analysis of standard morphological (non-enhanced or enhanced T1W and T2W images) or functional (DCE or DWI) sequences to see if τ can improve diagnostic performance in the clinical setting. However, the goal of our study was to test a tumor model embedded in a multi-compartmental pharmacokinetic whole-body model and identify features allowing differentiation of benign and malignant orbital lesions.

In conclusion, we demonstrate that tumor flow residence times (τ) derived from individual parameters are significantly different in benign and malignant orbital masses (P < 0.001). Measures of diagnostic accuracy are superior for τ compared to standard parameters such as ADC, K^trans, v_e, and iAUC.

Footnotes

Author note

To Immo Lawaczeck for his 50th MD anniversary.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Katharina Erb-Eigner is supported by the ‘Rahel Hirsch Program’ funded by the Charité – Universitätsmedizin Berlin.

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