Massachusetts General Hospital, 55 Fruit St., Boston, MA, USA

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1 Parameter Comparison Between Fast-Water-Exchange-Limit-Constrained Standard and Water-Exchange-Modified Dual-Input Tracer Kinetic Models for DCE-MRI in Advanced Hepatocellular Carcinoma Sang Ho Lee 1(&), Koichi Hayano 2, Dushyant V. Sahani 2, Andrew X. Zhu 3, and Hiroyuki Yoshida 1 1 3D Imaging Research, Department of Radiology, Massachusetts General Hospital and Harvard Medical School, 25 New Chardon St., Suite 400C, Boston, MA 02114, USA {lee.sangho,yoshida.hiro}@mgh.harvard.edu 2 Division of Abdominal Imaging and Intervention, Department of Radiology, Massachusetts General Hospital, 55 Fruit St., Boston, MA, USA {khayano,dsahani}@partners.org 3 Division of Hematology and Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, and Dana-Farber/Partners Cancer Care, 55 Fruit St., Boston, MA 02114, USA azhu@partners.org Abstract. Dynamic contrast-enhanced MRI (DCE-MRI) data have often been analyzed using classic standard tracer kinetic models that assume a fast-exchange limit (FXL) of water. Recently, it has been demonstrated that deviations from the FXL model occurs when contrast agent arrives at the target tissue. However, no systematic analysis has been reported for the liver tumor with dual blood supply. In this study, we compared kinetic parameter estimates from DCE-MRI in advanced hepatocellular carcinoma that have the same physiological meaning between five different FXL standard dual-input tracer kinetic models and their corresponding water-exchange-modified (WX) versions. Kinetic parameters were estimated by fitting data to analytic solutions of five different FXL models and their WX versions based on a full two-site-exchange model for transcytolemmal water exchange or a full three-site-two-exchange model for transendothelial and transcytolemmal water exchange. Results suggest that parameter values differ substantially between the FXL standard and WX tracer kinetic models, indicating that DCE-MRI data are water-exchange-sensitive. Keywords: Hepatocellular carcinoma Dual-input tracer kinetic analysis Water exchange Dynamic contrast-enhanced MRI Springer International Publishing Switzerland 2014 H. Yoshida et al. (Eds.): ABDI 2014, LNCS 8676, pp , DOI: / _4

2 34 S.H. Lee et al. 1 Introduction Dynamic contrast-enhanced MRI (DCE-MRI) enables quantification of the vascular characteristics of tissue and tumor [1], and has a potential role in monitoring hepatocellular carcinoma (HCC) response to systemic therapy [2]. Assessment of hemodynamic changes in the liver is especially challenging because of the dual blood supply to this organ [3]. The ability to accurately quantify the proportions of blood supply to HCC from the hepatic arterial system and from the portal venous system in vivo, as well as the microvascular density of the tumor tissue, may be of clinical value for diagnosis and treatment. Indeed, dual-input tracer kinetic models of DCE- MRI have become increasingly important for quantitative analysis of hepatic perfusion [4, 5]. Accurate estimation of kinetic parameters from DCE-MRI data still remains a challenging issue, especially when additional model parameters, such as intercompartmental water exchange rates, are included [6]. A tissue voxel typically consists of four water-containing compartments, two cellular compartments (red blood cells (RBC), and parenchyma cells) and two extracellular compartments (plasma space and interstitial space). It is widely accepted that water exchange between RBC and plasma is extremely rapid because of the high water permeability of the RBC membrane [7], and thus plasma and RBC can be considered a single water compartment with a single T1. The most commonly used models of tracer kinetics do not take into account the water exchange, which effectively assume that water exchange is in the fast exchange limit (FXL) [8]. This assumption enables the model to use a simple linear relationship between the relaxation rate of the tissue and the contrast agent (CA) concentration in the tissue. However, using this assumption may lead to underestimates of tissue CA concentration and inaccurate estimates of kinetic parameters [9] because the dependence of the relaxation rate on CA can be changed from the linear relationship to nonlinear dependences in tissue when the compartmental distributions of CA and water molecules are different [10]. Nevertheless, the importance of vascular-interstitial (transendothelial) and cellular-interstitial (transcytolemmal) water exchange in the analysis of DCE-MRI data is still debatable [11]. Water exchange would have a quantifiable effect on clinical T1-weighted DCE- MRI parameter estimates particularly when DCE-MRI data are acquired using a low flip angle [12]. Several variations of the tracer kinetic model have been proposed to evaluate the effect of water exchange on estimates of kinetic parameters including the two-site-exchange (2SX) and three-site-two-exchange (3S2X) models [6]. To date, there is no study that systematically compares DCE-MRI perfusion measurements between FXL standard dual-input tracer kinetic models and their corresponding water exchange-modified (WX) versions with different physiologic scenarios in the capillarytissue system for the liver. The aim of this study was to compare kinetic parameter estimates and address the question of whether they are different or similar between the FXL standard model and its WX version, with use of five different dual-input tracer kinetic models, in the analysis of DCE-MRI data in advanced HCC.

3 Parameter Comparison Between Fast-Water-Exchange-Limit 35 2 Methods 2.1 Dual-Input Function The liver receives blood from the hepatic artery and the portal vein, so the net input function C in ðþ t is modeled as a weighted sum of the two input functions: C in ðþ¼cc t A ðþþ t ð1 cþc PV ðþ, t where c, C A ðþ, t and C PV ðþ t are the arterial flow fraction, arterial blood concentration (in g/ml), and portal blood concentration (in g/ml), respectively. Each of C A ðþand t C PV ðþwas t modeled as the superposition of a bolus shape (first-pass) and its shape after modification by the body transfer function (recirculation), describing a sums-of-exponentials function [13]. By each imposing the time lags of the first-pass bolus arrival to the hepatic artery and the portal vein (t Lag;A1 and t Lag;PV1 ), and those from the first-pass to the recirculation onset (t Lag;A2 and t Lag;PV2 ), C A ðþand t C PV ðþbecome t C A ðþ¼a t B;A t t Lag;A1 e l B;A ðtt Lag;A1 Þ uttlag;a1 ( a B;Aa G;A ðtt Lag;A1 t Lag;A2 Þe l B;Aðtt Lag;A1t Lag;A2 Þ l B;A l G;A 1 e l G;Aðtt Lag;A1t Lag;A2 Þ e l B;A ðtt Lag;A1 t Lag;A2 Þ ) l B;A l G;A utt Lag;A1 t Lag;A2 ; C PV ðþ¼a t B;PV t t Lag;PV1 e l B;PV ðtt Lag;PV1 Þ uttlag;pv1 a n B;PVa G;PV t t Lag;PV1 t Lag;PV2 e l B;PV ðtt Lag;PV1 t Lag;PV2 Þ l B;PV l G;PV 1 e l G;PVðtt Lag;PV1t Lag;PV2 Þ e l B;PVðtt Lag;PV1 t Lag;PV2 Þ ) l B;PV l G;PV ut ð t Lag;PV1 t Lag;PV2 ; where ut ðþis the unit step function. ð1þ ð2þ 2.2 Tracer Kinetic Modeling We consider dual-input sources of the plasma flow F to the liver: arterial plasma flow F A, and portal plasma flow F PV. Assuming that C A ðþand t C PV ðþcan t be sampled from DCE-MR images, the concentration in tissue, C T ðþ, t can be expressed as follows: C T ðþ¼ t C in ðþ t v P Q P t t Lag;T þ vi Q I t t Lag;T ¼ v P C PðÞþvI t C IðÞ; t ð3þ 1 H LV where H LV is the hematocrit of blood in large vessels ( 0.45) [14], v P is the fractional plasma volume, is the fractional interstitial volume, Q P ðþis t the impulse response

4 36 S.H. Lee et al. function of the plasma compartment (in ml/min/ml), Q I ðþ t is the impulse response function of the interstitial compartment (in ml/min/ml), t Lag;T is the time lag (delay) (in min) to account for the difference in bolus arrival time between C in ðþand t C T ðþ, t C P ðþis t the spatially averaged CA concentration of the plasma compartment, C 1 ðþis t the spatially averaged CA concentration of the interstitial compartment, and is the convolution operator, respectively. We analyzed the DCE-MRI data with use of five different kinetic models: the Tofts-Kety (TK) model [15], extended TK (ETK) model [16], two-compartment exchange (2CX) model [17], adiabatic approximation to the tissue homogeneity (AATH) model [18], and distributed parameter (DP) model [19]. The Q P ðþand t Q I ðþfor t the five models are given by Q I;TK ðþ¼ t v P EF V P e v P EF vi V t P ; ð4þ Q P;ETK ðþ¼d t ðþand t Q I;ETK ðþ¼ t v P EF V P e v P EF vi V t P ; Q P;2CX ðþ¼ t F Be at þ ð1 BÞe bt V P and Q I;2CX ðþ¼ t v P F ða BÞ e at e bt V P a þ 1 þ v P PS PS vi V P V with A ¼ and B ¼ A P a b a b ; 2 a where ¼ 1 b 2 F þ 1 þ v sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 P PS F þ 1 þ v P PS v P F PS 5; V P V P V P V P V P V P Q P;AATH ðþ¼ t F V P and Q I;AATH ðþ¼ t v P EF u t V P V P F Q P;DP ðþ¼ t F ut ðþu t V P V P F and Q I;DP ðþffi t v P F 1 e PS F V P ð5þ ð6þ ut ðþu t V P F ð7þ ð Þ ; 1 þ v P PS PS V P F e v PEF vi V P t V P F t V P F u t V P F where Q P;ETK ðþ, t Q P;2CX ðþ, t Q P;AATH ðþ, t and Q P;DP ðþ t represent Q P ðþ t for the ETK, 2CX, AATH, and DP models, and Q I;TK ðþ, t Q I;ETK ðþ, t Q I;2CX ðþ, t Q I;AATH ðþ, t and Q I;DP ðþrepresent t Q I ðþfor t the TK, ETK, 2CX, AATH, and DP models, respectively. Note that Q P ðþand t C P for the TK model do not apply because of the assumption that v P in the TK model [16], and that Q I;DP ðþis t approximated using the first two ; ð8þ

5 Parameter Comparison Between Fast-Water-Exchange-Limit 37 terms of the Taylor series solution for the parenchyma phase [19]. Here, dðþ, t V P, PS, and E ¼ 1 e PS=F denote the Dirac delta function, plasma volume (in ml), capillary wall permeability-surface area product (in ml/min), and extraction fraction, respectively. C P ðþ, t C I ðþ, t and C T ðþfor t each model can be derived as fully continuous-time functional forms by incorporating the dual-input functions, C A ðþ t and C PV ðþ t in Eqs. (1) and (2). 2.3 Water Exchange Modeling and MR Signal Intensity To incorporate water exchange with each kinetic model, an intracellular pool is added as a third compartment, where the transcytolemmal water exchange is described by the mean intracellular water molecule lifetime s C (in sec). The effect of water exchange on the estimation of kinetic parameters is assessed based on a full 2SX model for the WX- TK model or a full 3S2X model for the WX-ETK, WX-2CX, WX-AATH, WX-DP models. Because the transendothelial water exchange is related to PS or extraction-flow product EF (in ml/min) depending on a kinetic model used, use of a fixed or predetermined water exchange rate constant would be to assume a limited value for PS (or EF) [11]. As an alternative, we assume that the transendothelial water exchange behavior is much like the tracer exchange behavior between the plasma and interstitial compartment. Therefore, the dependence of the transendothelial water exchange on PS (or EF) and that of the transcytolemmal water exchange on s C are specified mathematically, then they are constrained during fitting each kinetic model. The decay of longitudinal magnetization M q in the whole blood, interstitial space, and parenchyma cells (with q = B, I, and C, respectively) can be described by the following coupled Bloch-McConnell equations [20]: dm dt ¼ XM þ C; ð9þ where M ¼ ½M B ðþ; t M I ðþ; t M C ðþ t Š T ; C ¼ ½R 10B M 0B ; R 10I M 0I ; R 10C M 0C Š T, and 2 6 X ¼ 4 ðr 10B þ K BI Þ K IB 0 K BI ðr 10I þ K IB þ K IC Þ K CI 0 K IC ðr 10C þ K CI Þ 3 7 5; ð10þ where X is the exchange matrix of the 3S2X model, and K qr denotes the rate of transfer of magnetization from compartment q to compartment r. The M 0q is the equilibrium magnetization in compartment q, andr 10q (¼ 1=T 10q ) denotes the native longitudinal relaxation rate. Here it is assumed that the direct exchange of water between blood and parenchyma cells is negligible. The 3S2X of water between compartment q and r requires that K qr M 0q ¼ K rq M 0r [20]. The K qr can be also expressed in terms of water mean lifetimes (s B, s I, and s C (in sec)) and volume fractions of the three compartments by keeping mass balance K BI ¼ 1=s B, K IC ¼ 1=s I ðv B = Þ=s B, K IB ¼ 1=s I ðv C = Þ=s C, and K CI ¼ 1=s C, where v B ¼ v P = ð1 H SV Þ is the fractional blood

6 38 S.H. Lee et al. volume, and H SV is the fractional blood volume, and H SV is the hematocrit in small vessels (ffi 0.25) [14]. The three mean lifetimes are related by =s I ¼ v B =s B þ v C =s C [6]. Here we assume that the water fraction in each compartment is 1 for simplicity [21, 22]. The longitudinal magnetization evolving from a 3S2X model can be expressed as a linear sum of the three compartmental longitudinal magnetizations (i.e., Mt ðþ¼m B ðþþm t I ðþþm t C ðþ). t The transcytolemmal water exchange rate is related to s C, which is the ratio of the intracellular volume V C (in ml) to the cell membrane permeability-surface area product PS C (in ml/min). The cell to interstitium water transfer rate, K CI, is given by [9] K CI ¼ 1 ¼ 60 PS C ¼ 60 PS C ; s C V C v C V T ð11þ where V B =V T þ V I =V T þ V C =V T ¼ v B þ þ v C ¼ 1, V T is the tissue volume (in ml), V B is the blood volume (in ml), V I is the interstitial volume (in ml), and v C is the fractional intracellular volume, respectively. The constant 60 is used to convert the time-scale from minutes to seconds. On the other hand, the transendothelial water exchange rate is related to PS (or EF). According to the physiologic assumption of each kinetic model, the CA is exchanged between the plasma and interstitial compartments by EF in the ETK and AATH models, whereas it is exchanged by PS in the 2CX and DP models. Thus, the blood to interstitium water transfer rate, K BI, is constrained with the parameters to take into account the transendothelial tracer exchange for the 3S2X model: K BI ¼ 1 s B ¼ ( 60 PS V B 60 EF V B for WX - 2CX and WX - DP models for WX - ETK and WX - AATH models ; ð12þ Note that K BI (or K IB ) does not apply to the WX-TK model because it assumes that v P in the estimate of C T ðþ[23]. t Like the formalism presented in Eqs. (11) and (12), the interstitium to cell water transfer K IC and the interstitium to blood water transfer K IB can be given by K IB ¼ 1 s I v C 1 s C ¼ K IC ¼ 1 v B 1 ¼ 60 PS C ¼ 60 PS C ; s I s B V I V T ( 60 PS V I 60 EF V I ð13þ for WX - 2CX and WX - DP models : ð14þ for WX - ETK and WX - AATH models In the absence of CA, it is assumed that the water exchange system is in the FXL [23]. The FXL condition is also maintained to estimate the postcontrast relaxation rate R 1 ðþonly t in the dual feeding vessels during CA passage because they both consist of a single blood pool. After administration of CA, T1 can be replaced under the FXL condition by: R 1 ðþ¼1=t t 1 ðþ¼r t 10 þ r 1 C T ðþ¼1=t t 10 þ r 1 C T ðþ, t where r 1 is the spin-lattice relaxivity, R 1 ðþ t and R 10 are the post- and precontrast relaxation rates (in sec 1 ), and T 1 ðþ t and T 10 are the post- and precontrast T1 values (in sec),

7 Parameter Comparison Between Fast-Water-Exchange-Limit 39 respectively. The relaxivities in tissue are assumed to be equal to those in aqueous solution (r 1 = 4.5 s 1 mm 1,r 2 = 5.5 s 1 mm 1 at 21 C and 1.5 T, where r 2 is the spin-spin relaxivity) [24]. The signal intensity obtained from a spoiled gradient echo sequence in the FXL as given by the Ernst-Anderson equation is [24] n o S T ðþ¼g t PD e TE 1 T 20 þr 2 C T ðþ t 1 e TRR 1ðÞ t sinðhþ 1 cosðhþe ; ð15þ TRR 1ðÞ t where g is the machine gain, PD is the proton density, T20 is the precontrast effective T2 value, h is the flip angle, and S T ðþis t the MR signal intensity in the tissue. In the FXL, the entire tissue relaxes with a single effective R 1 ðþrepresenting t the weighted average of the three compartmental R 1 s, i.e., R 1 ðþ¼v t B R 1B ðþþv t I R 1I ðþþv t C R 10C, where R 1B ðþand t R 1I ðþdenote t the postcontrast longitudinal relaxation rates within the blood and interstitial spaces, respectively. Similarly, in the absence of CA, R 10C for the water exchange model is calculated by: R 10C ¼ ðr 10 R 10I Þ=v C for the 2SX model [23], and R 10C ¼ ðr 10 v B R 10B R 10I Þ=v C for the 3S2X model [25], where R 10B and R 10I are assumed to be 0.74 and 0.5 s 1, respectively [21, 25]. The effect of CA in the blood and interstitial spaces can be incorporated into the exchange matrix X by replacing R 10B and R 10I in Eq. (10) with R 1B ðþ¼r t 1B ð1 H SV ÞC P ðþþr t 10B and R 1I ðþ¼r t 1I C I ðþþr t 10I, where r 1B and r 1I are the respective relaxivities which are held constant as r 1B ¼ r 1I ¼ r 1. For a spoiled gradient echo acquisition, the Ernst-Anderson equation using X from Eq. (10) is applied to find the signal in each compartment [6, 25]: n o S ¼ g PD e TE 1 T 20 þr 2 C T ðþ t sinðhþ I cosðhþe TRX 1 I e TRX V; ð16þ where S ¼ ½S B ðþ; t S I ðþ; t S C ðþ t Š T, V ¼ ½v B ; ; v C Š T, I is the 3 3 identity matrix, and e TRX is a matrix exponential, which can be calculated based on a scaling and squaring algorithm with a Pade approximation method [26]. The transverse relaxation rate, R 2 ðþ¼1=t t 20 þ r 2C T ðþ, t is assumed to be under the FXL condition for simplicity because the T1 effects are of primary concern in this study. For no dependence on T20, the relative signal enhancement in the tissue, E T ðþ, t can be used as an objective function for curve-fitting of DCE-MRI data, i.e., E T ðþ¼s t T ðþ=s t T ð0þ1, where S T ðþ¼s t B ðþþs t I ðþþs t C ðþ. t Therefore, E T ðþ t is fitted using Eq. (16) with C P ðþ, t C I ðþ, t and C T ðþfor t the 3S2X model (i.e., WX-ETK, WX-2CX, WX-AATH, and WX- DP models). When CA extravasation is high, the 3S2X model can be simplified to ignore a distinct blood volume contribution, and thus the 2SX model can be used. This system can be described using a two-pool exchange formalism [27]. The solution has a bi-exponential form with the T1 relaxation of the system described by two rate constants, R 1S and R 1L, where R 1S and R 1L are the rate constants for the component with the smaller and larger T1 s, and their respective fractional apparent populations, a L and a S, where a S þ a L ¼ 1. For the 2SX model, a closed-form expression of MR signal intensity is given by [23]

8 40 S.H. Lee et al. n o S T ðþ¼g t PD e TE 1 T 20 þr 2 C T ðþ t 1 e TRR 1SðÞ t sinðhþ a S 1 cosðhþe TRR 1SðÞ t 1 e TRR 1LðÞ t þ a L with ðr 1 cosðhþe TRR 1LðÞ t 1S ðþ; t R 1L ðþ t Þ ¼ 1 2 2R 10C þ r 1I C I ðþ t s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ R 10 R 10C þ K CI 2K CI r 1I C I ðþ t R 9 10 R 10C þ K 2 = CI þ 4K CIK IC ; 8 9 and a S ðþ¼ t >< R 10C R 10 r 1I C I ðþ t ð v C Þþ K CI >= r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 : 2K CI r 1I C I ðþ t R 10R 10C þk 2þ >: CI 4KCI K IC >; The E T ðþ t for the FXL standard models and the 2SX model is given by E T ðþ¼s t T ðþ=s t T ð0þ1. Therefore, E T ðþis t fitted using Eq. (15) with C T ðþfor t the FXL standard model, and using Eq. (17) with C I ðþand t C T ðþfor t the WX-TK model. An example of fitting the five different dual-input FXL standard models and their corresponding WX models to a voxel-level tissue enhancement curve in HCC is provided in Fig. 1. ð17þ (a) (b) Fig. 1. Graphs illustrating examples of fitting (a) five different FXL standard dual-input tracer kinetic models and (b) their corresponding WX models to a voxel-level tissue enhancement curve which was sampled from the HCC in DCE-MRI data. 2.4 Kinetic Parameter Calculation The parameters that can be directly estimated by parametric fitting are {F=V P, c, PS=V P, v P,, t Lag;T } for the FXL standard models, and {F=V P, c, PS=V P, v P,, s C, t Lag;T } for the WX models. Thus, the total hepatic blood flow (BF), arterial blood flow (BF A ), portal blood flow (BF PV ), blood volume (BV), mean transit time (MTT) and PS

9 Parameter Comparison Between Fast-Water-Exchange-Limit 41 can further be computed for the FXL standard and WX models according to: BV ¼ 100 V P = fð1 H SV Þmg ¼ 100 v P = fð1 H SV Þq T g (in ml/100 g), where m ¼ q T V T is the mass of the tissue with density q T (= 1.04 g/cm 3 in the case of soft tissues), BF ¼ BV F=V P (in ml/min/100 g), BF A ¼ cbf (in ml/min/100 g), BF PV ¼ ð1 cþbf (in ml/min/100 g), MTT ¼ ðv P þ V I Þ=F (in min) (MTT ¼ V I =F for the TK and WX-TK models), PS ¼ ð1 H SV ÞBV PS=V P (in ml/min/100 g). For the WX models, PS C can additionally be calculated according to PS C ¼ ð100=q T Þ fðv C =s C Þ=60g (in ml/min/100 g). 2.5 Patients and DCE-MRI Protocol A total of 20 patients (gender, 18 men and 2 women; age range, years; mean age, years) with advanced HCC were included in this study. DCE-MRI of the liver was performed using a phased array body coil on a 1.5-T MRI system (Avanto; Siemens, New York, NY). First, three-dimensional (3D) volume interpolated excitation coronal T1-weighted sequence of varying flip angles of 10, 15, 30, 60, and 90 degrees were obtained in a breath hold before CA injection. Second, through the 20-gauge peripheral intravenous line in the arm, 0.1 mmol/kg bodyweight of Gd-DTPA contrast was power injected at 2 ml/s. Third, a series of coronal T1-weighted DCE-MR images were obtained using a 15-degree flip angle after 5-second delay after the initiation of CA injection, and the scanning continued for up to 4 min and 30 s. The acquisition parameters included: TR = 5 ms, TE = 1.58 ms, 5-mm slice thickness, 0-mm interslice gap, 20 slices, matrix, and field of view of mm. Two consecutive 7-second acquisitions forming two different time points were repeated 10 times with a delay of 21 s between them. The scanning time in every acquisition was 14 s with a break of 21 s, and the patients were asked to hold their breath during acquisition. 2.6 Image and Statistical Analysis Image registration was performed initially before further kinetic analysis. To reduce movement-induced artifacts, we coregistered each set of dynamic series relative to the first precontrast image as a template by using the Insight Segmentation and Registration Toolkit (ITK) [28], which was conducted based on the serial procedures of 3D rigid, affine, and B-spline deformable registration methods. The native T1 of each voxel was estimated by using the precontrast images acquired with the five flip angles (10, 15, 30, 60, and 90 ) [29]. The four sets of preconstrast images with flip angles, 10, 30, 60, and 90, were also coregistered to the first set of DCE-MR images (i.e., the precontrast image acquired with the flip angle 15 ), respectively. Region of interest (ROI) analysis was performed by an experienced gastrointestinal surgeon to derive arterial and portal-venous input curves and to delineate the tumor. To calculate kinetic parameters, the same dual-input curves were used among the models for each patient by placing ROIs within the abdominal aorta (size: 5.2 mm 2 ) and the major portal vein branch (size: 5.2 mm 2 ). The target lesions were outlined in the central partitions of the imaging volume. The tissue enhancement curve corresponding to each voxel within

10 42 S.H. Lee et al. tumor ROIs was separately fitted using the five FXL standard models and the five WX models. Statistical analysis was performed using SPSS version 20.0 (IBM SPSS statistics, version 20.0 for Windows; SPSS, Inc., Chicago, IL, USA, an IBM Company). Paired comparison of kinetic parameters (BF, c, BF A, BF PV, BV, MTT, PS,, and E) that have the same physiological meaning between the FXL standard and WX models was evaluated using Wilcoxon signed-rank test for each parameter and for each model pair. 3 Results The mean and standard deviation (SD) values for the different parameters for the different models, and the Wilcoxon signed-rank test results for each parameter for each model pair are summarized in Table 1. The BF was higher with the FXL standard TK, ETK, 2CX, and DP models than with their corresponding WX models, whereas it was lower with the FXL standard AATH model. The BF PV, PS, and were all higher with all FXL standard models than their corresponding WX models, whereas c was lower with all FXL standard models. The BF A was higher with the FXL standard TK, 2CX, and DP models than with their corresponding WX models, whereas it was lower with the FXL standard ETK and AATH models. The MTT was higher with the FXL standard TK and AATH models than with their corresponding WX models, whereas it was lower with the FXL standard ETK, 2CX, and DP models. The E was higher with the FXL standard TK and 2CX models than with their corresponding WX models, whereas it was lower with the FXL standard ETK, AATH, and DP models. All parameters except the TK-model-derived E, the ETK-model-derived BF A, MTT and E, the 2CX-model-derived c and E, the AATH-model-derived BF, c, BV, MTT, PS and E, and the DP-model-derived c were statistically significantly different for the pairwise comparison between the FXL standard and WX models. In other words, BF (TK vs. WX-TK: P < 0.001, ETK vs. WX-ETK: P = 0.002, 2CX vs. WX-2CX: P = 0.001, and DP vs. WX-DP: P < 0.001), BF PV (TK vs. WX-TK: P = 0.001, ETK vs. WX-ETK: P < 0.001, 2CX vs. WX-2CX: P = 0.004, and DP vs. WX-DP: P = 0.028), BV (TK vs. WX-TK: P < 0.001, ETK vs. WX-ETK: P < 0.001, 2CX vs. WX-2CX: P < 0.001, and DP vs. WX-DP: P < 0.001), and PS (TK vs. WX-TK: P < 0.001, ETK vs. WX-ETK: : P = 0.021, 2CX vs. WX-2CX: P < 0.001, and DP vs. WX-DP: P = 0.012) were statistically significantly different in the pairwise comparison with all models except the AATH model, c (TK vs. WX-TK:P = and ETK vs. WX-ETK: P = 0.004) with the TK and ETK models, BF A (TK vs. WX-TK: P = 0.001, 2CX vs. WX-2CX: P = 0.002, AATH vs. WX-AATH: P = 0.007, and DP vs. WX-DP: P = 0.001) with all models except the ETK model, MTT (TK vs. WX-TK: P = 0.014, 2CX vs. WX-2CX: P = 0.044, and DP vs. WX-DP: P = 0.028) with the TK, 2CX and DP models, (TK vs. WX-TK: P < 0.001, ETK vs. WX-ETK: P < 0.001, 2CX vs. WX-2CX: P = 0.011, AATH vs. WX-AATH: P = 0.001, and DP vs. WX-DP: P < 0.001) with all models, and E (DP vs. WX-DP: P = 0.021) with only the DP model, respectively. An example of parametric maps in HCC for several selected parameters that were statistically significantly different for each model pair is provided in Fig. 2.

11 Parameter Comparison Between Fast-Water-Exchange-Limit 43 Table 1. Statistics (mean ± SD) for ROI analysis of each parameter in HCC, and the Wilcoxon signed-rank test results to compare each model pair (FXL vs. WX) for each parameter. Parameter Model Mean ± SD P-value FXL WX BF (ml/min/100 g) TK ± ± <0.001 ETK ± ± CX ± ± AATH ± ± DP ± ± <0.001 c TK ± ± ETK ± ± CX ± ± AATH ± ± DP ± ± BF A (ml/min/100 g) TK ± ± ETK ± ± CX ± ± AATH ± ± DP ± ± BF PV (ml/min/100 g) TK ± ± ETK ± ± < CX ± ± AATH ± ± DP ± ± BV (ml/100 g) TK ± ± <0.001 ETK ± ± < CX ± ± <0.001 AATH ± ± DP ± ± <0.001 MTT (min) TK ± ± ETK ± ± CX ± ± AATH ± ± DP ± ± PS (ml/min/100 g) TK ± ± <0.001 ETK ± ± CX ± ± <0.001 AATH ± ± DP ± ± TK ± ± <0.001 ETK ± ± < CX ± ± AATH ± ± DP ± ± <0.001 E TK ± ± ETK ± ± CX ± ± AATH ± ± DP ± ± Note Bold numbers indicate statistical significance in the Wilcoxon signed-rank test (two-tailed P < 0.05).

12 44 S.H. Lee et al. Fig. 2. Parametric maps obtained with five FXL standard models (TK, ETK, 2CX, AATH, and DP) and their corresponding WX versions (WX-TK, WX-ETK, WX-2CX, WX-AATH, and WX-DP) in HCC. Each model pair except for the pair of the AATH and WX-AATH models displays four kinetic parameters that were most significantly different between the FXL standard and WX models. Note that only two kinetic parameters were statistically significantly different between the AATH vs. WX-AATH models (see Table 1). 4 Discussion On the whole, the AATH model was relatively less influenced by intercompartmental water exchange as compared to other models, although the AATH-model-derived BFA and vi were significantly different between the FXL standard and WX models. Of the kinetic parameters investigated, E was relatively consistent between the FXL standard and WX models; only the DP-model-derived E was different between them. However, no parameters were consistent over all pairs between the FXL standard and WX models. In the present study, although we focused on the comparison of kinetic parameters that have the same physiological meaning between the FXL standard and WX models, we could obtain additional parameters such as sc, PSC and vc by using the WX models as shown in Fig. 3, which may provide valuable information relating to tumor cell characteristics in addition to tumor microvascular characteristics. Therefore, further investigations are warranted to prove whether it is useful for the prediction of clinical outcome.

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