Field of the invention The present invention relates to a method and/or system for determining portal hemodynamics of a subject. The method and/or system may further determine splenic and splanchnic hemodynamics of the subject.

Background of the Invention

In a human body, the portal vein receives blood from the spleen and the gastrointestinal tract. Both splenic and splanchnic blood flow and their contributions to portal venous blood flow are important factors involved in disorders such as liver cirrhosis, splenomegaly, portal hypertension and their complications [1]. The ability to assess splenic and splanchnic blood flows and their relative contributions to portal venous blood flow thus have important implications in the treatment and management of several liver disorders. A noninvasive imaging method which allows for in-vivo assessment of splenic and portal hemodynamics would be a valuable clinical tool to aid in the understanding and management of these disorders.

Quantitative assessment of blood transport within organs and tissues using tracer techniques are typically performed by two approaches (i) arterial-venous sampling approach and (ii) residual tracer analysis approach (or dynamic imaging approach). The arterial-venous sampling approach involves administering one or more tracers (possibly with different transport characteristics) to a subject at an organ inlet, and subsequent sampling at a venous effluent of the organ to analyze outflow curves of the one or more tracers [2]. The residual tracer analysis approach involves external monitoring of tissue residual tracer content using dynamic imaging modalities. In particular, the residual tracer analysis approach involves administering one or more tracers into an inlet of a tissue of interest in a subject, and subsequently monitoring the concentration of the one or more tracers remaining within the tissue of interest as a function of time. Therefore, the residual tracer analysis approach allows for in-vivo assessment of blood flow in a relatively non-invasive manner. The imaging modalities used for both approaches may comprise dynamic contrast-enhanced computed tomography (DCE CT), dynamic contrast-enhanced magnetic resonance imaging (DCE MRI) and nuclear medicine techniques such as dynamic scintigraphy and dynamic positron emission tomography (PET) [3 - 6]. However since the arterial-venous sampling approach is invasive, this may be less desirable.

Summary of the invention The present invention aims to provide a new and useful method and/or system for determining portal hemodynamics of a subject. The method and/or system may further determine splenic and splanchnic hemodynamics of the subject.

In general terms, the present invention proposes modifying the arterial-venous sampling approach to provide the splanchnic hemodynamics in a non-invasive manner. The modified arterial-venous sampling approach may be based on external data imaging of a tracer. For example the residual tracer analysis approach may in turn be used in the modified arterial-venous sampling approach together with the tracer data without invasive blood sampling. Initially the subject is administered with a tracer, and the residual tracer analysis approach determines the proportion of the tracer remaining in the spleen and the splenic blood flow. Then the arterial-venous sampling approach determines the splanchnic blood flow in the portal vein and the splenic and splanchnic contributions to the portal venous blood flow. A non invasive procedure may have the advantage of reduced risk, reduced cost, faster test procedure, lower chance of infection and/or lower recuperation time. Specifically, a first aspect of the present invention is a method for determining portal hemodynamics of a subject administered with a tracer, the method comprising the steps of: (a) determining tracer concentrations in an aorta, spleen and portal vein of the subject over time; (b) fitting a first model to the tracer concentrations in the spleen and aorta over time, wherein the first model relates the tracer concentrations in the spleen and aorta over time and a proportion of the tracer remaining in the spleen; and (c) determining portal hemodynamics of the subject by fitting a second model to the tracer concentrations in the portal vein and aorta over time, wherein the second model relates the tracer concentrations in the portal vein and aorta over time and a tracer concentration emerging from the portal vein, and wherein the fitting of the second model is based on the fitting of the first model.

The invention may alternatively be expressed as a computer system for performing such a method. This computer system may be integrated with a device for capturing input images indicating tracer concentrations in a subject, for example, DCE CT images, DCE MRI images and images from nuclear medicine techniques such as dynamic scintigraphy and dynamic PET. The invention may also be expressed as a computer program product, such as one recorded on a tangible computer medium, containing program instructions operable by a computer system to perform the steps of the method.

Brief Description of the Figures An embodiment of the invention will now be illustrated for the sake of example only with reference to the following drawings, in which:

Fig. 1 illustrates a flow diagram of a method for determining portal hemodynamics of a subject in an embodiment of the present invention;

Fig. 2 illustrates a schematic diagram of portal circulation;

Figs. 3(a) and 3(b) illustrate a compartmental model of portal venous blood flow the method of Fig. 1 is based on; Fig. 4 illustrates a block diagram showing examples of the arterial- venous sampling approach and the residual tracer analysis approach of observing an organ or tissue system during a tracer experiment;

Fig. 5 illustrates a table tabulating characteristics of patients in a study evaluating the method of Fig. 1 ;

Figs. 6(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a first patient;

Figs.7(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a second patient;

Figs. 8(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a third patient;

Figs. 9(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a fourth patient;

Figs. 10(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a fifth patient;

Figs. 11 (a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a sixth patient;

Figs. 12(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for a seventh patient;

Figs. 13(a) - (c) respectively illustrate a slice of one input image showing outlines of identified regions of interests, tracer concentration-time curves obtained with the method of Fig. 1 , and impulse residue and outflow functions obtained with the method of Fig. 1 for an eighth patient; and

Fig. 14 illustrates a table tabulating the splenic and splanchnic hemodynamic parameters and blood flow rates, as well as the portal venous parameters and blood flow rate of the patients in the study for evaluating the method of Fig. 1.

Detailed Description of the Embodiments

Referring to Fig. 1 , the steps are illustrated of a method 100 which is an embodiment of the present invention, and which determines portal hemodynamics of a subject administered with a tracer. Method 100 further determines splenic and splanchnic hemodynamics of the subject.

The portal hemodynamics of the subject refers to the dynamics of blood flow through the portal vein of the subject. This may comprise the splenic and splanchnic contributions to the portal venous blood flow (i.e. proportion of portal venous blood flow contributed by the splenic and splanchnic circulations) and the portal venous blood flow rate (i.e. rate of blood flow through the portal vein). Similarly, the splenic and splanchnic hemodynamics of the subject refers to the dynamics of blood flow through the splenic and splanchnic circulations of the subject respectively. The splenic and splanchnic hemodynamics may comprise splenic and splanchnic hemodynamic parameters, and blood flow rates (i.e. rates of blood flow through the splenic and splanchnic circulations). The splenic and splanchnic hemodynamic parameters may in turn comprise splenic and splanchnic mean transit times (i.e. average time taken by blood to traverse the splenic and splanchnic circulations respectively). The hemodynamic parameters for each circulation may also comprise exchange rate constants indicating rates at which blood between a vascular space and an interstitial space of the circulation is exchanged - see Figs. 3(a) and (b). The input to method 100 is a plurality of input images acquired from the subject over time. The input images are preferably acquired from one or more sections of the subject comprising both the spleen and aorta. Each input dataset can be a two-(2D) or three-dimensional (3D) image dataset, with each image comprising a plurality of voxels with respective signal values from which tracer concentrations in the subject at each point in time can be deduced. Each input image may be a DCE CT image, DCE MRI image or an image derived from nuclear medicine techniques such as dynamic scintigraphy and dynamic PET. For example, in the case that CT is used, the intensity values of the voxels in each input image may comprise CT numbers with Hounsfield units (HU).

Method 100 is based on a model of portal venous blood flow with an analysis of tracer arterial-venous and residual imaging data according to Equations (A.1) - (A.7) as follows. Model of portal venous blood flow

Fig. 2 illustrates a schematic diagram of portal circulation. In particular, Fig. 2 illustrates the schematic representation of the relative organ positions and the relationship between portal venous, splenic and splanchnic circulations.

The splenic blood flow or splenic contribution to the portal venous blood flow accounts for the venous blood supply to the portal vein from the spleen. Note that although the inferior mesenteric vein joins the splenic vein before reaching the portal vein (see Fig. 2), in this document, the "splenic blood flow" or "splenic contribution to the portal venous blood flow" refers to the portion of the portal venous blood flow that is derived from the spleen alone, i.e. the blood flow through the splenic vein before it mixes with the blood flow from the inferior mesenteric vein. The rest of the portal venous blood flow is accounted for by the splanchnic contribution. Referring to Fig. 2, the venous blood flow to the portal vein from the gastrointestinal tract forms part of the splanchnic blood flow or splanchnic contribution to the portal blood supply. This includes blood supply through the superior and inferior mesenteric veins.

Figs. 3(a) and 3(b) illustrate a compartmental model of portal venous blood flow. Method 100 is based on this compartmental model. In particular, Fig. 3(a) illustrates a block diagram showing splenic and splanchnic contributions to the portal venous blood flow. As illustrated in Fig. 3(a), by specifying a splenic fraction β (note that β need not be a fraction and may be any other measure of a proportion), portal venous blood flow may be resolved into two components represented by a splenic block 302 and a splanchnic block 304. In particular, the splenic contribution to portal venous blood flow may be represented by the splenic fraction β whereas the splanchnic contribution to the portal venous blood flow may be represented by a fraction given by 1— β . Both the splenic and splanchnic blocks 302, 304 derive their blood supply from the aorta through their respective arteries, namely the splenic artery and the superior mesenteric artery.

Fig. 3(b) illustrates a block diagram of a two-compartment exchange model describing each of the splenic and splanchnic blocks 302, 304 of Fig. 3(a). The two-compartment exchange model includes a vascular compartment representing the vascular space and an interstitial compartment representing the interstitial space, with individual blood influx and efflux rates ki, k ₂ . In Fig. 3(b), F denotes the rate of blood flow that supplies the vascular compartment and k ₁ , k ₂ denote the exchange rates constants indicating rates at which blood between the vascular and interstitial spaces is exchanged. In particular, ki denotes the rate of efflux (backflux) of blood from the vascular space which is assumed to be equal to the rate of influx of blood into the interstitial space whereas k ₂ denotes the rate of efflux of blood from the interstitial space which is assumed to be equal to the rate of influx of blood into the vascular space.

Each of the splenic and splanchnic blocks 302, 304 of Fig. 3(a) is associated with tracer kinetics equations and these equations can be solved to yield (i) an impulse outflow function h(t) for analysis of the organ arterial-venous tracer data, or (ii) an impulse residue function R(t) for analysis of residual tracer data (to be elaborated below). Explicit forms of h(t) and R{t) for the two- compartment exchange model are also given below. Note that h{t) and R(t) are two sides of the same coin (or tracer kinetics model). More specifically, both h(t) and R{t) allow for the estimation of hemodynamic parameters such as the vascular mean transit time MTT (i.e. average time taken by blood to traverse the vascular space), and the vascular-interstitial exchange rate constants, ki and k ₂ .

Analysis of tracer arterial-venous and residual imaging data

Fig. 4 illustrates a block diagram showing the two above-mentioned approaches of observing an organ or tissue system during a tracer experiment: (i) the arterial-venous sampling approach and (ii) the residual tracer analysis approach.

The arterial-venous sampling approach monitors the tracer arterial inflow and venous outflow concentrations over time. Referring to Fig. 4, considering a hypothetical unit tracer impulse input S(t) to the system 406 at the arterial inlet 402, the function representing a tracer concentration that emerges at the venous exit 404 may be referred to as the impulse outflow response h{t) since this function represents the system's 406 output response to an impulse input S{t) . Assuming the conservation of tracer mass for this system 406, the area under h(t) is unity (i.e. h(t) is normalized). Statistically, h(t) indicates a probability of the tracer taking time t to traverse the system 406, and can be viewed as a probability density function for traversal times such that the proportion of tracer emerging at the venous exit 404 in an infinitesimal time interval dt is given by h{t)dt (see Zierler [23]). The dynamic imaging approach monitors the tracer concentration remaining in the organ or tissue of interest as a function of time. Taking the system 406 as the organ or tissue of interest, and following the unit impulse input S{t) to the system 406, the function that denotes the proportion of tracer remaining in the system 406 may be referred to as the impulse residue response R{t) since this function is the system residual response to an impulse input δ(ή .

The relationship between R(t) and h(t) is as follows. Consider a hypothetical container 408 placed at the venous end 404 of the system 406 to collect tracer output during the experiment, the amount of tracer collected in the container 408 at any time t would be the cumulative output J' h(x) dx (here x replaces t as the integration variable to avoid confusion) and the proportion of tracer R(t) remaining in the system 406 can be calculated using Equation (A.1 ) as follows.

R(t) = 1 - [ h{x) dx (A.1 )

Differentiating Equation (A.1 ), the alternative relation between R(t) and h{t) shown in Equation (A.2) is obtained [23].

h(t) = - R(t) . (A.2) dt

Note that in Equation (A.1 ), R(t) is dimensionless and R(t)≤l . Furthermore h(t) is associated with units of time ^"1 . However, an impulse tracer input S(t) ^' \s not possible to achieve in practice. For an arbitrary input concentration-time curve C _Art (f) at the feeding arterial inlet 402, the corresponding venous outflow C _v (f) can be given by Equation (A.3) as follows.

C _v (f) = C _M (t) ® (t) = _Q ' C _M (x) h(t - x) dx (A.3)

Convolution, as denoted by ® , is a mathematical operation that treats the input C _M (t) as a series of impulses of various strengths and computes the repetitive summation of the corresponding h(t) . Inherent within Equation (A.3) is the assumption of a linear time-invariant system. The assumption of time-invariance (stationarity) implies that each impulse input at a later time would yield the same system response h{t) , except that the system response h{t) would be delayed accordingly in time. The assumption of linearity allows the superposition of all the system responses h{t) , such that the overall output C _v (r) is the summation of the individual outputs corresponding to impulse inputs weighted in height and time by C _M (t) .

Similarly, the system residual tracer concentration C _tlss (f) following an arbitrary input of C _Art (f) can be given by a convolution integral of the impulse residue response as shown in Equation (A.4).

C _tss (t) = F C _M .(t) ® R(t) . (A.4) In Equation (A.4), the quantity F denotes specific tissue blood flow (i.e. rate of blood flow through the tissue). Since C _liss (f) has units of tracer mass per volume of tissue and C _Art (f) has units of tracer mass per volume of blood, the quantity F has units of volume of blood (ml) per time (min) per volume of tissue (ml) i.e. ml/min/ml. For simplicity, in formulating Equation (A.4), it is assumed that blood in the tissue consists of only plasma without blood cells i.e. all blood concentration curves are taken to be identical to plasma concentration curves. However, hematocrit corrections may be incorporated into Equation (A.4) if necessary (see Equation (1 ) later).

Given C _M (t) and C _v (f) , it is possible to estimate h(t) in Equation (A.3) by deconvolution. Similarly, it is possible to estimate F, R(t) in Equation (A.4) given C _M (t) and C _tiss (f) . Impulse response functions of the two-compartment exchange model

Referring to Fig. 3(b), the two-compartment blood-tissue exchange model comprises a vascular compartment and an interstitial compartment, with the vascular compartment supplied by blood at a flow rate F. The tracer kinetics of this two-compartment exchange model can be described by the following pair of mass balance equations (A.5a) and (A.5b). dC, (t)

= - F C, (t) - K& (t) + K ₂ C ₂ {t) + S(t) (A.5a) dt dC ₂ (t)

= K& {t) - K ₂ C ₂ {t) (A.5b) dt

In Equations (A.5a) and (A.5b), S(t) is an unit impulse input at t = 0 , C _{ and C ₂ respectively denote the tracer concentrations within the vascular and interstitial compartments, and v _l and v ₂ denote the respective fractional volumes. Κ and K ₂ respectively denote the transfer constants for influx of blood into the interstitial compartment (assumed to be equal to the efflux of blood out of the vascular compartment) and efflux of blood out of the interstitial compartment (assumed to be equal to the influx of blood into the vascular compartment). These transfer constants i and K ₂ are related to the exchange rate constants, k ₁ and k ₂ by Equation (A.5c). The exchange rate constants and k ₂ have units of time ^"1 (min ¹ ) whereas the transfer constants Κ and K ₂ have units of volume of blood (ml) per time (min).

The impulse residue response f?(i)for each of the two-compartment systems 302, 304 in Fig. 3(a) can be expressed as a bi-exponential function as shown in Equation (A.6a) [5].

R{t ) = A exp(<z, t) + (l - A) exp(ar ₂ t) , (A.6a) where

a ₂ (A.6b)

and

A = ^{ai + kl + l<2} (A.6c)

Since the vascular mean transit time for each two-compartment system 302, 304 can be expressed as MTT =— , R{t) for the two-compartment system can be completely specified by the parameters MTT, k _{ and k ₂ of the two- compartment system.

Using Equation (A.2) and Equation (A.6a), the corresponding impulse outflow response h(t) may be derived as shown in Equation (A.7). h{t) = - _x A expfo f) - (l - A) ₂ exp(a ₂ t) (A.7)

Steps 102 - 110 of method 100

Method 100 comprises steps 102 - 1 10.

In step 102, aorta and splenic tracer concentrations (i.e. concentrations of the tracer in the aorta and the spleen respectively) over time are determined. In step 104, splenic hemodynamic parameters and splenic blood flow rate are derived using the aorta and splenic tracer concentrations over time. Next, in step 106, portal venous tracer concentrations (i.e. concentrations of the tracer in the portal vein) over time are determined. In step 108, splanchnic hemodynamic parameters, and splenic and splanchnic contributions to portal venous blood flow are derived using the portal venous and aorta tracer concentrations over time. Further in step 110, portal venous blood flow rate and splanchnic blood flow rate are derived using the splenic and splanchnic contributions to portal venous blood flow.

These steps 102 - 1 10 will now be described in more detail.

Step 102: Determine aorta and splenic tracer concentrations over time In step 102, aorta and splenic tracer concentrations in the subject over time are determined.

In one example, in step 102, the following sub-steps are performed for each input image. As mentioned before, each input image comprises voxels with intensity values indicating tracer concentrations in the subject at one point in time.

In the first sub-step, a region of interest comprising voxels corresponding to the spleen of the subject (i.e. splenic region of interest ROI _sp ieen) and a region of interest comprising voxels corresponding to the aorta of the subject (i.e. aortic region of interest ROI _a0 rta) are identified in the input image. This may be performed manually. For example, a region of interest (ROI) may be manually drawn in each slice of the 3D input image and the regions of interest in all the slices may then be combined to form the final ROI. Alternatively, the identification of the regions of interest (ROIs) may be performed automatically using imaging techniques. The identified ROIs usually do not differ by much across the plurality of input images. In the next sub-step, the tracer concentrations in the spleen and aorta of the subject at the one point in time corresponding to the input image are determined. In particular, the tracer concentration in the spleen is determined based on the intensity values of the voxels in the splenic region of interest ROI _sp ieen whereas the tracer concentration in the aorta is determined based on the intensity values of the voxels in the aortic region of interest ROI _a0 rta- In one example, the tracer concentrations may be determined as the average intensity value of the voxels in the respective ROIs. In another example, the tracer concentrations may be determined as the median intensity value of the voxels in the respective ROIs. The average or median of the intensity values of the voxels within each ROI is assumed to be robust to the (usually slight) differences across the ROIs identified in different input images. Therefore, by repeating the above sub-steps for each input image in step 104, tracer concentrations in the spleen of the subject at different points in time (i.e. splenic tracer concentration-time points) and tracer concentrations in the aorta of the subject at different points in time (i.e. aorta tracer concentration-time points) are obtained. These tracer concentration-time points may be viewed as points obtained by sampling the aorta (or splenic) concentration-time curves C _Art (f) (or C _spleen (f) ).

Step 104: Derive splenic hemodynamic parameters and splenic blood flow rate using the aorta and splenic tracer concentrations over time

In step 104, splenic hemodynamic parameters MTT _spleen , k _{1 spleen} and k _{2 spleen} and splenic blood flow rate F _spleen are derived using the aorta and splenic tracer concentrations over time determined in step 102.

Referring to Fig. 2, it can be seen that the arterial inlet of the spleen is the inlet of the splenic artery. Furthermore, the splenic artery receives blood from the aorta. Therefore, considering the spleen as the system 406 in Fig. 4 and using the residual tracer analysis approach, a first model relating the splenic and aorta tracer concentrations over time (in other words, the splenic and aorta tracer concentration-time curves C _sp , _een (i) , C _Art (f)) may be expressed in the form of Equation (1 ) (which corresponds to Equation (A.4)). The first model relates the tracer concentrations in the spleen and aorta over time and a proportion of the tracer remaining in the spleen.

^spleen (0 ⁼ ' ^" spleen.ROI ^ _ ® ^spleen (0 0)

As shown above, the first model comprises a residual term in the form of a splenic impulse residue function R _speen (t) describing the proportion of the tracer remaining in the spleen of the subject at time t . The residual term /? _spleen (f) is defined by splenic hemodynamic parameters which comprise a splenic mean transit time (MTT _spleen ), and exchange rates constants indicating rates at which blood between a vascular space and an interstitial space of the splenic circulation is exchanged (k _{1 spleen} and k _{2 spleen} )) (see Equations (A.6a) - (A.6c)).

The first model further comprises a splenic flow rate term F _{spleen ROI} describing a rate of flow through a part of the spleen corresponding to the splenic region of interest ROI _sp ieen- Here, "a part of the spleen" may include the entire spleen. In one example, F _{spleen R0I} is a specific quantity indicating the plasma flow through the part of the spleen corresponding to the ROI _sp ieen, with units in ml per min per ml of tissue.

As shown in Equation (1), the first model further implements a hematocrit correction for correcting the tracer concentrations in the aorta to account for red blood cells in the aorta. The hematocrit correction is represented by the constant Hct _A which denotes the fractional hematocrit in major blood vessels (which is assumed to be equal to the fraction of blood volume in the aorta occupied by red blood cells). In one example, Hct _A is 0.4.

In step 104, the first model is fitted to the tracer concentrations in the spleen and aorta over time (i.e. the splenic and aorta tracer concentration-time points derived from step 102). This fitting is performed by adjusting the residual term fl _spleen (f) and the splenic flow rate term F _{spleen ROI} . The adjusting of the residual term ft _sp i _een (0 is done by adjusting the splenic hemodynamic parameters

MTT _spleen , _spleen and k _{2 spleen} defining it.

Resulting residual term fl _sp i _een (f) and splenic flow rate term F _{spleen ROI} achieving the fit between the first model, and the splenic and aorta tracer concentration- time points are therefore achieved. In other words, the splenic hemodynamics of the subject comprising the splenic hemodynamic parameters MTT _spleen , ^k i,s _P ieen ^{and k} 2, _sp ieen defining the resulting residual term R _speen (t) is determined.

The splenic and aorta tracer concentration-time curves O _sp , _een ( i) , C _Art (f) satisfying Equation (1 ) and comprising the splenic and aorta tracer concentration-time points are also derived through the above fitting.

The first model may further comprise an additional delay parameter i ^" _sp i _{een aorta} to account for a difference in tracer arrival times to the spleen and the aorta. The delay parameter T _{spleen aorta} may be adjusted together with the residual term ft _spteen (?) and the splenic flow rate term F _{spleen ROI} during the fitting of the first model to the aorta and splenic tracer concentration-time points. The delay parameter r _{spleen aorta} achieving the fit between the first model and the tracer concentration-time points is generally dependent on the relative locations in the input image where the tracer concentration-time points are sampled. This value is not likely to be a characteristic of the spleen two-compartment exchange model shown in Fig. 3(b).

The splenic hemodynamics may further comprise a total splenic blood flow rate F _spleen (for whole venous blood) that emerges at the splenic vein i.e. a rate of blood flow out of the spleen. F _spleen can be calculated based on the resulting splenic flow rate term F _{spleen ROI} (derived from fitting the first model earlier) using

Equation (2). p _ ^spleen.ROI

spleen ^ Hd ) ^s P' ^een ' ' '

As shown in Equation (2), the splenic flow rate term F _{spleen ROI} is corrected with a hematocrit correction to account for red blood cells in the splenic vein emerging from the spleen. In particular, this hematocrit correction is represented by the constant Hct _v which denotes the fractional hematocrit in the venous blood (which is assumed to be equal to the fraction of blood volume in the splenic vein occupied by red blood cells). In Equation (2), V _spleen denotes the volume of the spleen. In one example, l/ _spleen is estimated from separate clinical diagnostic scans comprising the entire spleen of the subject.

Step 106: Derive portal venous tracer concentrations over time In step 106, portal venous tracer concentrations in the subject over time are determined.

In one example, in step 106, the following sub-steps are performed for each input image. As mentioned before, each input image comprises voxels with intensity values indicating tracer concentrations in the subject at one point in time.

In the first sub-step, a region of interest comprising voxels corresponding to the portal vein of the subject (i.e. portal venous region of interest ROW) is identified in the input image. This may be performed manually (for example, a region of interest (ROI) may be manually drawn in each slice of the 3D input image and the regions of interest in all the slices may then be combined to form the final ROIPV). Alternatively, the identification of ROIpv may be performed automatically using imaging techniques.

In the next sub-step, the tracer concentration in the portal vein at the one point in time corresponding to the input image is determined based on the intensity values of the voxels in the portal venous region of interest ROIpv. For example, the tracer concentration may be determined as the average intensity value of the voxels in the ROIPV. Therefore, by repeating the above sub-steps for each input image in step 106, tracer concentrations in the portal vein of the subject at different points in time (i.e. portal venous tracer concentration-time points) are obtained. These tracer concentration-time points may be viewed as points obtained by sampling the portal venous concentration-time curve C _PV (?) .

In one example, only a portion of the portal vein is visible on certain slices in an input image and the ROIpv is identified in the input image using this portion of the portal vein only. Depending on the size and orientation of the portal vein relative to the imaged section, the ROIPV might not contain the entire portal vein and C _PV (f) comprising the portal venous tracer concentration-time points could be underestimated due to partial-volume averaging effect. This partial-volume effect may be compensated during the deconvolution fitting of the portal venous tracer concentration-time points in step 108.

Note that step 106 may be performed prior to step 104. For example, the portal venous tracer concentrations over time may be determined together with the aorta and splenic tracer concentrations over time in step 102. Step 108: Derive splanchnic hemodynamic parameters, and splenic and splanchnic contributions to portal venous blood flow using the portal venous and aorta tracer concentrations over time

In step 108, splanchnic hemodynamic parameters MTT _splanchnic , k _{1 sp|anchnic} , k ^ ₂ .sp .lanc .hn .ic , 'and the splenic and sp rlanchnic contributions to p rortal venous blood flow represented by and 1 - β respectively are derived using the aorta and portal venous tracer concentrations over time as determined in steps 102 and 106.

Using the arterial-venous analysis approach [2], a second model relating portal venous and aorta tracer concentrations over time (in other words, the portal venous and aorta tracer concentration-time curves C _PV (f) and C _Art (f)) may be expressed in the form of Equation (3a) (which corresponds to Equation (A.3)). The portal vein concentration-time curve C _PV (f) refers to the tracer concentration of the combined output from the splenic and splanchnic blocks 302, 304 (or splenic and splanchnic two-compartment systems 302, 304) as shown in Fig. 3(a). The second model relates the tracer concentrations in the portal vein and aorta over time and the tracer concentration emerging from the portal vein. pC _PV (f) = C _An (t) ® h _pw (t) (3a)

As shown above, the second model comprises an outflow term in the form of a portal impulse outflow function /7 _PV (f) describing the combined impulse outflow response of the splenic and splanchnic blocks 302, 304 in Fig. 3(a), in other words, the tracer concentration emerging from the portal vein at time t .

Furthermore, the second model implements a partial volume correction for correcting the tracer concentrations in the portal vein to account for partial volume effects in the input images from which the portal venous regions of interest are identified. In Equation (3a), the partial volume correction is in the form of p(> l) which is a scaling factor to correct for partial-volume effects affecting the estimation of the points in C _PV (f) (i.e. the portal venous concentration-time points). The portal impulse outflow function ? _pv (f) in Equation (3a) is defined by splenic hemodynamics and splanchnic hemodynamics of the subject. The portal impulse outflow function Λ _ρν (ί) may be further defined by a weight factor weighting the splenic and splanchnic hemodynamics whereby the weight factor indicates the splenic contribution to portal venous blood flow. In one example, the portal impulse outflow function /7 _pv (f) may be derived using Equation (3b) as follows. hpv (t) = β Λ- _ρΐ8Θη (ί) + (1 - β) ^splanchnic (t) . (3b)

As shown in Equation (3b), the portal impulse outflow function h _pv (t) encompasses both splenic and splanchnic components, denoted by and /? _splanchnic (f) _> respectively. These splenic and splanchnic components are weighted by the weight factor in the form of the splenic fraction β . The splenic fraction β represents the fraction of portal venous blood flow contributed by the splenic circulation. 7 _spleen (f) comprises the splenic hemodynamic parameters MTT _spleen , k, _,spleen , k _{2 sp|een} which have been determined in step 104. More specifically, these are the parameters defining the residual term R _spleen {t) which achieves the fit between the first model, and the aorta and splenic concentration-time points. The remaining parameters in Equation (3b) are to be determined and these include β and the splanchnic hemodynamic parameters comprised by

^splanchnic (0 0·®· ^" T ^" T ^" splanchnic , ^l, _sp | _anchnic > ^2, _S p| _ancnn j _C ) ^■

In step 108, the second model is fitted to the tracer concentrations in the portal vein and aorta over time (i.e. the portal venous and aorta tracer concentration- time points). This fitting is performed by adjusting the outflow term (i.e. the portal impulse outflow function h _pv ( t) ).

As mentioned above, the outflow term is defined by h _{sp een} ( t) comprising the splenic hemodynamic parameters, ft _sp i _anchnic (f) comprising the splanchnic hemodynamic parameters and the splenic fraction β . During the fitting of the second model, the splenic hemodynamic parameters MTT _spleen , k _{1 sp|een} , k _{2 n}

(determined in step 104) are kept constant. In other words, the fitting of the second model is based on the fitting of the first model, more specifically, based on the splenic hemodynamics of the subject derived from the fitting of the first model. The adjusting of the outflow term is done by adjusting β and the splanchnic hemodynamics parameters MTT _splancnnic , k _1isplanchnlc , k _2,sp|anchnic . Note that p , the scaling factor to correct for partial-volume effects as shown in Equation (3a), may also be adjusted. Resulting splenic fraction β and splanchnic hemodynamics parameters MTT- s _n p _l l_a _n nc _h h _n n _i i ₍ c. ,' k, i. sp ,lanc .hn .ic ,' k ₂ z. sp ,lanc .hn .ic defining ⁵³ the outflow term which achieves the fit between the second model and the portal venous and aorta tracer concentration-time points are thus determined. In other words, the portal hemodynamics of the subject comprising the resulting splenic fraction β is determined. The splanchnic contribution (which is also part of the portal hemodynamics) may be obtained based on the resulting splenic fraction β , in particular, it is calculated as 1 - β . Furthermore, the splanchnic hemodynamics of the subject comprising the resulting splanchnic hemodynamics parameters MTT _splanchnic , k _{1 sp|anchnic} , k _2,splanchnic are also determined.

From the above fitting, the portal venous tracer concentration-time curve C _PV (f) satisfying Equation (3a) and comprising the portal venous tracer concentration- time points is also derived. The scaling factor p derived from the fitting can be used to correct for partial-volume effects affecting C _pv (f) . The corrected portal venous concentration-time curve is given by Equation (4).

C _PV,corr (i) = pCp _V (f) (4) The tracer from the splenic pathway usually arrives earlier at the portal vein, as compared to the tracer from the splanchnic pathway i.e. there is usually a difference in tracer arrival times to the portal vein from the splenic and splanchnic circulations. The second model may further comprise two additional delay parameters r _{spleen PV} and i- _{splanchnic PV} incorporated into /7 _spleen (f) and

Splanchnic (0 ^to account for this difference. The delay parameters r _{spleen pv} and r _splanchnic p _V are adjusted with the outflow term h _{P J} {t) during the fitting of the second model to the aorta and portal venous tracer concentration-time points. In other words, the adjustable parameters during the fitting of the second model may comprise p , β , MTT _splanchnic , _ic , k _{2 nic} , r _spleer , _PV and t- _{splanchniCiPV} .

Step 110: Derive portal venous blood flow rate and splanchnic blood flow rate using the splenic and splanchnic contributions to portal venous blood flow The portal hemodynamics of the subject may further comprise a rate of blood flow through the portal vein of the subject i.e. portal venous blood flow rate F _pv whereas the splanchnic hemodynamics of the subject may further comprise a rate of blood flow through the splanchnic circulation of the subject i.e. splanchnic blood flow rate F _splancnnic .

In step 110, the portal venous blood flow rate F _pv and the splanchnic blood flow rate F _splanchnic are derived.

Since the splenic blood flow contributes to a fraction of the portal venous blood flow given by the splenic fraction β and the remaining of the portal venous blood flow is contributed by the splanchnic blood flow, the portal venous blood flow rate F _pv and the splanchnic blood flow rate F _splanchnic may be calculated based on the splenic fraction β (derived from the fitting in step 108) and the total splenic blood flow rate F _leen obtained in step 104 . The total splenic blood flow rate F _spleen obtained in step 104 is in turn based on the splenic flow rate term ^F s _P ieen,Roi derived from the fitting in step 104.

More specifically, the portal venous blood flow rate F _pv and the splanchnic blood flow rate F _splancnnic may be calculated using Equations (5a) and (5b).

]_

F _PV — n spleen ' (5a) β

^splanchnic n ^spleen ^■ (^^)

Clinical Feasibility Study

Patients

To evaluate method 100, DCE CT was implemented as part of a trial involving the use of a combination of anti-angiogenic agents for unresectable or metastatic hepatocellular carcinomas (HCCs). DCE CT was performed at baseline and Day 8 or Day 29 of anti-angiogenic therapy to assess the degree of inhibition of angiogenesis. Only the baseline DCE CT scans before therapy were retrospectively analyzed by the current study.

Images from twenty seven patients 18 years or older with histologically confirmed unresectable HCC were accrued for the trial. Only images satisfying the following criteria are included in the current study: (i) the liver and portal vein are included in the images and (ii) the images show a satisfactory scan quality as evaluated based on the aortic enhancement curves and a lack of severe motion artifacts.

Six patients did not undergo DCE CT and were excluded from this study. DCE CT was not performed for the liver in eight cases and these were excluded from this study as well. The portal vein was not included in one patient's acquired images and this case was also excluded. Of the remaining patients whose images include the liver and portal vein, the scan quality of the images of 4 patients was unsatisfactory due to severe respiratory artifacts and these patients were hence also excluded from this study. Only the images of eight patients satisfied the inclusion criteria. These patients thus formed the study population. All eight patients had HCC previously confirmed by histology. Two of the eight patients were diagnosed with cirrhosis based on histology whereas the remaining six patients were diagnosed with cirrhosis based on CT findings. Fig. 5 shows a table tabulating the characteristics such as the patient demographics, method for diagnosing cirrhosis and the clinical parameters (e.g. Child's score, and presence of collaterals) of the eight patients.

DCE CT protocol In this study, DCE CT was performed using a 64-detector row CT scanner (Lightspeed; General Electric Medical Systems, Milwaukee, Wisconsin). The dynamic CT protocol comprised 27 acquisitions (1 00 kV, 80 mAs, Cine mode with 8 rows of 5 mm collimation, 1 -sec gantry rotation, Field of View 50 x50 cm, Matrix 51 2x51 2) at the following scan and breath-hold timings: 0 (Start of injection at 0 sec), (instruction to breathe and hold, BH) 8, 1 0, 1 2, 1 4, 1 6, 1 8, 20, 22, 24, 26, 28, 32, 36, (BH), 40, 44, 48, 52, 56, (BH), 64, (BH) 76, (BH), 88, (BH), 1 00, (BH), 1 1 2, (BH), 1 24, (BH), 1 36, (BH), and 148 sec. Combined radiation dosage of the scouts and the 27 dynamic scans was estimated to be 62.1 mSv, using an anthropomorphic phantom. A bolus infusion of 70 ml of contrast agent (Omnipaque; General Electric Healthcare, Princeton, NJ) was administered to each patient intravenously at 4 ml/sec using an automatic injector via an antecubital vein. The contrast agent was immediately followed by 30 ml of saline solution at the same flow rate. For each DCE CT scan image, the ROIs (i.e. ROI _a0 rta and ROIPV) were manually drawn over the aorta and portal vein in the image. An ROI including the whole spleen (ROI _sp ieen) as seen on each scan image was also drawn. The ROIs were drawn by a radiologist (CHT with more than 10 years of experience). Intensity values in the form of CT numbers (Hounsfield units HU) of voxels within each ROI were averaged to yield the tracer concentration-time points. The linear relationship between tracer concentration and CT numbers were separately validated using phantom experiments.

Spleen volume measurement

Routine clinical abdominal CT examinations were performed 2 to 25 days before the DCE CT examinations. Splenic ROIs were manually drawn on all CT sections of the 3D image obtained via the abdominal examination. The cross- sectional areas of these ROIs were computed. Splenic volume was then calculated by summing the consecutive splenic ROIs areas (taking into account the slice thickness as well).

Results

For all the eight patients, the splenic and portal vein tracer concentration-time curves C _PV (f) derived from the DCE CT images by method 100 can be appropriately described by the portal venous circulatory model.

Figs. 6 - 13 show the tracer concentration-time curves C _pv (f) ,

C _spleen (f) obtained for the eight patients using method 100. In particular, for each of Figs. 6 - 13, part (a) illustrates a slice of one of the input images showing the outlines of the various ROIs identified for obtaining the tracer concentration-time points. In particular, ROIs 602, 702, 802, 902, 1002 are the ROIs comprising voxels corresponding to the aorta i.e. ROI _a0 rta, ROIs 604, 704, 804, 904, 1004 are the ROIs comprising voxels corresponding to the portal vein i.e. ROIPV and ROIs 606, 706, 806, 906, 1006 are the ROIs comprising voxels corresponding to the spleen i.e. ROI _sp i _e en- Part (b) of Figs. 6 - 13 illustrate the various tracer concentration-time curves obtained from fitting the first and second models to the average intensity values in the ROIs identified in the DCE CT images. Part (c) of Figs. 6 - 13 show the impulse residue function and impulse outflow functions derived from the fittings of the first and second models to the respective tracer concentration-time points.

Fig. 14 shows a table tabulating the splenic and splanchnic hemodynamic parameters and blood flow rates, as well as the portal venous parameters and blood flow rate derived in this study. As mentioned above, these parameters are derived from parametric deconvolution analysis. In particular, the splenic hemodynamics parameters are derived by fitting the first model to the splenic and aorta tracer concentration-time points whereas the splanchnic and portal vein (PV) parameters are derived by fitting the second model to the portal venous and aorta tracer concentration-time points. In normal subjects, the splenic component of portal venous blood flow is about 40% (i.e. β ~ 0.4), whereas in subjects with cirrhosis, the splenic share of portal inflow was previously found to increase markedly, exceeding 50% [1]. In patients with portal hypertension, splanchnic blood flow may be largely shunted from the portal to the systemic circulation through portosystemic collateral vessels, while the spleen actively congests the portal system, contributing to the portal hypertension [1]. In the above clinical feasibility study of cirrhotic patients involving method 100, the mean splenic fraction was also found to be elevated (mean=0.75, std=0.22) with values ranging from 0.42 to 1.0. From Figs. 5 and 14, it can be seen that all patients with elevated splenic fraction β>0.7 except Patient 1 with β =0.77 (i.e. Patients 2, 4, 7 and 8) were previously diagnosed with para-esophageal collaterals. On the other hand, Patients 5 and 6 with relatively lower splenic fraction, β =0.42 and 0.56 respectively, were not previously diagnosed with para-esophageal collaterals. However, Patient 3 who also has a relatively lower splenic fraction β =0.53 was also previously diagnosed with para-esophageal collaterals. Splenic volumes of these eight patients, as estimated using routine abdominal CT scans, varied widely between 48 to 529 ml (see Fig. 5).

Also, as shown in Fig. 14, for Patients 4 and 8, the splenic fraction β which specifies the splenic contribution to portal venous blood flow was found to be very close to 1 (i.e. very close to 100%, with negligible splanchnic contribution to portal venous blood flow). In other words, the portal venous concentration- time curves C _pv (f) for these patients may be predominantly described using splenic parameters. In particular, it was found that for each of Patients 4 and 8, the portal venous concentration-time curve C _pv (f) may be completely specified using only the splenic parameters derived from fitting the first model to the splenic and aorta tracer concentration-time points and any adjustment of the splanchnic parameters had no effect on improving the fitting of the second model to the portal venous and aorta tracer concentration-time points. The splenic and portal venous tracer concentration-time curves C _spleen (f) and C _PV (f) for Patients 4 and 8 are respectively shown in Figs. 9 and 13.

Furthermore, para-esophageal collaterals were observed in Patients 4 and 8, implying that the porto-systemic shunting in these patients may be larger than their splanchnic inflow, with the significant efflux via the porto-systemic shunt. This is likely to result in lower than expected values for splanchnic flow. The portal vein concentration-time curves for these patients are thus relatively independent of the splanchnic parameters and therefore it is hard to estimate the splanchnic parameters accurately using method 100. Hence in Fig. 14, splanchnic parameters for Patients 4 and 8 are not included. Note that these cases were not included in the computation of the mean and standard deviation (std) of the splanchnic parameters in Fig. 14.

Using duplex Doppler ultrasound for blood flow measurement, Zwiebel et al [8] estimated splenic artery blood flow rate in 17 patients with cirrhosis and portal hypertension to be 599 ± 340 ml/min. This was significantly higher than that in healthy subjects whose estimated splenic artery blood flow rate was found to be about 413 ± 1 10 ml/min. According to Zwiebel et al [8], splenic artery blood flow rate was particularly increased in patients with splenomegaly. The splenic blood flow rate in cirrhotic patients derived using method 100 was 624.41 ± 466.65 ml/min which is similar to the results of Zwiebel et al [8].

Zwiebel et al [8] also reported an increase in blood flow rate in the superior mesentery artery (SMA) for patients with cirrhosis and portal hypertension. In particular, the blood flow rate of these patients with cirrhosis and portal hypertension is approximately 574± 220 ml/min whereas the blood flow rate of healthy subjects is approximately 445± 63 ml/min. However, it was not indicated in Zwiebel et al [8] whether porto-systemic collaterals were present and thus, whether the estimated superior mesenteric arterial blood flow was likely to be largely channeled to the portal vein through the mesenteric veins. On the other hand, using method 100 in the above study, the portion of splanchnic blood flow that contributes directly to portal venous flow is calculated. Using method 100, the splanchnic blood flow rate that channels into portal venous flow is found to be 139.4 ± 120.2 ml/min, which is much lower than estimates of blood flow rates in the superior mesenteric artery. This may be due to the presence of portosystemic shunts in some of the patients such that in these patients, only a portion of blood flow in the mesenteric arteries was channeled into the portal vein (note that para-esophageal collaterals were observed in 5 out of the 8 patients examined in the clinical feasibility study). Using dynamic scintigraphy, Fine et al [6] studied splenic and splanchnic transit times with tracer kinetics models formulated by a combination of gamma density functions. Their estimates for splenic mean transit time was 5.07 ± 0.701 sec for normal subjects, which is significantly lower than 1 1 .3sec and 29.8 sec for two of their subjects with portal hypertension. Their estimates for blood mean transit time through the gastrointestinal tract was 21 .93 ± 2.88 sec for normal subjects, and 29.0 sec and 17.0 sec for the two subjects with portal hypertension. Referring to Fig. 14, the splenic and splanchnic mean transit times for cirrhotic patients derived using method 100 from the above study are respectively, 15.3± 10.1 sec and 23.6± 12.1 sec, which are in good agreement with those estimated by Fine et al [6]. Partial-volume correction factors p were close to unity (between 1 and 1.04) in 4 cases (Patients 1 , 2, 4, and 8), suggesting that the portal venous concentration-time curve C _pv (f) was appropriately sampled in these cases (i.e. the portal venous tracer concentration-time points obtained in step 106 were relatively accurate), ranged between 1.1 and 1 .3 in the other 4 cases. Although these values are not exceedingly large, their effect on obtaining an accurate fitting of the second model to the tracer concentration-time points, and hence an accurate C _PV (f) is not negligible. This is especially since none of the other adjustable parameters can result in the same effect as p in the overall scaling of C _PV (i) . Note that in Figs. 9, 1 1 , and 12, the decreasing portion of the partial-volume corrected portal venous concentration-time curve C _{PV corr} (f) is initially above the aorta curve C _Art (i) (at about 40 - 50sec for the injection protocol in the above study) and approaches C _Art (f) at a later time (about 150 sec for the injection protocol in the above study). This shows that the C _{PV corr} (f) is more accurate since the tracer concentration in the portal vein should, in general, eventually approach that in the artery after a few cardiac cycles of circulatory mixing. However, if the sampled C _PV (f) (Le. the portal venous tracer concentration-time points) is affected by partial-volume effects, then the sampled C _pv (f) may be underestimated and a large portion of the sampled C _pv (f) will be lower than C _Art (f) (see "C _PV (f) " and "Fit using Eq. 3" in Fig. 1 1 (b)).

The above study may further include normal subjects as control subjects. The above study may further implement steps to validate the various parameters obtained. Note that although DCE CT datasets were used to evaluate method 100 in the above study, method 100 is not limited to using DCE CT images and can similarly be applied on other types of images such as DCE MRI images. However, it is preferable not to use method 100 on images with motion or breathing artifacts or images from techniques which are unable to capture the aorta, portal vein and spleen on a single scan plane.

Advantages

The advantages of method 100 are as follows. Method 100 employs a combination of deconvolution analysis and portal venous circulatory modeling and allows for separate estimation of splenic and splanchnic components to portal venous blood flow using dynamic contrast- enhanced CT or MR imaging. Method 100 exploits the inventors' observations that major blood vessels such as the aorta or portal vein are usually visible on DCE CT scans and thus, allow for in-vivo monitoring of inlet and outflow tracer concentration-time curves. In particular, method 100 uses a novel combination of both arterial-venous and residual tracer analysis approaches to derive quantitative estimates for portal blood flow and to resolve the relative contributions to the portal blood flow from splenic and splanchnic circulation. More specifically, method 100 first employs the residual tracer analysis approach to determine splenic hemodynamics of the subject, and then by coupling with the arterial-venous approach, further allow the derivation of the splenic fraction β (i.e. fraction of the portal venous blood flow contributed by the splenic circulation) and other portal hemodynamics parameters.

Method 100 is a deconvolution method that can be used to resolve the splenic and splanchnic contributions to portal venous blood flow and derive quantitative estimates describing splenic and portal blood flow. In particular, in method 100, a parametric deconvolution approach is adopted, by first assuming the functional forms of h(t) and R(t) through tracer kinetics modeling, and subsequently fitting models comprising these functional forms by adjusting the model parameters. The method 100 can be implemented using most types of medical images such as DCE CT or MR images. As shown in the above study using DCE CT datasets of 8 cirrhotic patients, method 100 can accurately estimate several portal parameters, and splenic and splanchnic hemodynamic parameters, including splenic and splanchnic mean vascular transit times.

Portal venous return from the bowel can take several different routes of which the superior mesenteric vein and the inferior mesenteric vein are the major channels. However, there are also smaller veins which may drain directly into the portal or splenic veins, such as the short gastric veins, the right and left gastroepiploic veins or pancreaticoduodenal veins. Method 100 is able to account for the blood flow from these smaller veins by simply subtracting the calculated splenic blood flow from the total portal venous blood flow. It does not matter if these smaller veins drain into the splenic vein or the main portal vein branches because they would have been accounted for in method 100 by subtracting the calculated splenic flow from the total portal venous blood flow.

Method 100 can be applied on the same DCE imaging dataset for both spleen and portal hemodynamics analysis. Hence, both liver parenchyma perfusion and portal hemodynamics can be concurrently studied using the same set of DCE scans.

Furthermore, an accurate C _pv (f) is important in liver perfusion assessment using DCE CT or MR imaging. Blood is supplied to the liver by both the hepatic artery and the portal vein, and the hepatic perfusion ratio between the hepatic artery and portal vein has been found to vary in patients with liver tumors and cirrhosis. Reliable assessment of hepatic perfusion and the hepatic perfusion ratio would depend on the accuracy of both input curves, C _M (t) and C _pv (f) . If C _pv (f) was underestimated due to partial-volume effects, the liver parenchyma perfusion parameters subsequently estimated could also be affected. Method 100 corrects for partial-volume effects in C _pv (f) before performing liver perfusion analysis. Thus, it can achieve more accurate results.

Also, the portal venous impulse outflow response model (which method 100 is based on) can be used in situations where the portal vein cannot be captured during imaging (i.e. when only the aorta tracer concentration-time curve C _M (t) can be sampled). If an estimate of C _PV (f) is required for further analysis, an approximate C _pv (f) function can be derived by convolving the sampled C _M {t) with a model hp _V (t) using typical values of splenic and splanchnic parameters pertaining to the particular patient's demographic profile. In addition, quantifying portal venous blood flow and separately identifying the splenic and splanchnic components has potential clinical applications. These include assessing patients with small-for-size liver graft, monitoring the activity of Crohn's disease and monitoring the efficacy of medical therapies for portal hypertension as elaborated below.

Small-for-size liver graft is a complication that may occur in liver transplantation [9]. More specifically, small-for-size liver graft refers to the situation in which the transplanted liver is too small to receive the patient's portal blood flow. Barotrauma occurs to the graft and the patient suffers deterioration in liver function. Splenectomy is one possible treatment for this condition. In splenectomy, the portal blood flow from the spleen is reduced by removing the spleen [10-14]. Other strategies for decompressing the portal circulation by shunts have also been considered [15, 16]. Currently, the diagnosis of small- for-size graft is clinical and relies only on portal pressure measurements or clinical effects of back-pressure such as splenic enlargement. Method 100 is advantageous as it is able to yield information on the proportion of portal venous blood flow contributed by the splenic and the splanchnic circulation. With this information, a more rational decision on whether to perform splenectomy or a portosystemic shunting procedure may be made. Similar use of method 100 in patients with portal hypertension may also facilitate the selection of patients for splenectomy or shunting procedures.

In addition, there is currently a need in diagnostics to non-invasively measure portal pressure. This is important in monitoring therapy for portal hypertension and for chronic hepatitis C, as well as for prognostication [17]. Deriving hepatic venous pressure gradient is currently a popular way of measuring portal pressure. In the normal human liver, there is to date no known relationship between portal venous blood flow and portal pressure [18]. However, animal experiments suggest that in a state of increased hepatic resistance, such as cirrhosis, there is an increase in portal venous blood flow which results in an increase in portal pressure [19]. Therefore, method 100 is advantageous as it quantifies portal venous blood flow which may serve as a biomarker for efficacy of therapy for portal hypertension. Furthermore, current concepts of the pathophysiology of cirrhosis and portal hypertension suggest that there is a reversible element of hepatic resistance resulting from contraction of the stellate cell which results in decreased portal venous blood flow. This reversible element can potentially be modulated by pharmacological therapy [20, 21]. It is also known that increased mesenteric blood flow contributes to portal hypertension and there are also potential pharmacological interventions to modulate this effect. Using method 100 to quantify portal venous blood flow, the efficacy of the pharmacological therapies or interventions may also be evaluated. Also, information on splanchnic blood flow is potentially useful in assessing the activity of Crohn's disease. A weak negative correlation has been shown between splanchnic blood flow transit time and disease activity [22]. In general, an increase in splanchnic blood flow correlates with a decrease in splanchnic transit time. Hence, method 100 which derives both splanchnic blood flow and splanchnic transit time is potentially useful for monitoring the activity of the Crohn's disease.

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