WO2011056122A1

WO2011056122A1 - A method and an apparatus for determining body vessel characteristics using pc-mri imaging

Info

Publication number: WO2011056122A1
Application number: PCT/SE2010/051146
Authority: WO
Inventors: Anders WÅHLIN; Anders Garpebring; Khalid Ambarki; Anders Eklund
Original assignee: Individual
Current assignee: Individual
Priority date: 2009-11-03
Filing date: 2010-10-21
Publication date: 2011-05-12
Anticipated expiration: 2012-05-03

Abstract

A method for determining body vessel characteristics from PC-MRI imaging data of a PC- MRI image sequence comprising said body vessel, wherein the PC-MRI imaging data is arranged to digitally represent a volume of space as a plurality of voxels, each voxel being assigned a complex value comprising a signal magnitude registered for a portion of the volume of space corresponding to said voxel and a signal phase registered for said portion of the volume of space corresponding to said voxel, and wherein each voxel is associated with a pixel in the PC-MRI images of the PC-MRI image sequence. The method is characterised in that it comprises the steps of: determining complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in a region of interest comprising the body vessel in the PC-MRI images of the PC-MRI image sequence; and determining at least one body vessel characteristic based on the determined complex summation values. The invention further relates to an apparatus for determining body vessel characteristics in PC-MRI imaging and a computer program product for use in such an apparatus.

Description

A method and an apparatus for determining body vessel characteristics using PC-MRI imaging

Technical field

The invention relates in general to phase contrast magnetic resonance imaging (PC-MRI), and in particular to an apparatus and a method for determining body vessel characteristics using PC-MRI imaging. The invention also relates to a computer program product.

Background

Magnetic Resonance Imaging (MRI) is primarily a medical imaging technique most commonly used in radiology to visualize the internal structure and function of the human body. MRI uses a powerful magnetic field to align the nuclear magnetization of, for example, hydrogen atoms of water in the human body. Radio frequency (RF) fields are used to systematically alter the alignment of this magnetization, causing the hydrogen nuclei to produce a rotating magnetic field detectable by the MRI scanner. These alignment changes create an MRI signal which can be manipulated by additional magnetic fields to build up enough information to construct an internal image of the human body.

PC-MRI is an MRI measuring sequence or technique that further is able to encode velocity information into the phase of an MRI image. This may be performed by manipulating the phase of the MRI signal using varying magnetic fields in such a way that it is directly proportional to velocity. Thus, PC-MRI imaging may be used to achieve quantitative measurements of, for example, blood flow or the flow of other fluids in the human body. These quantitative measurements may then for example be used in cardiovascular diagnostics or in characterising the cerebrospinal system of the central nerve system. In PC-MRI, the measurement signal outputted by a PC-MRI scanner may comprise a plurality of signal magnitude values and signal phase values corresponding to a particular volume of space inside a human body being scanned. This plurality of signal magnitude values and signal phase values can be said to correspond to small volume elements that spans the volume of space. These volume elements may be digitally represented by voxels in the PC-MRI imaging data. Each voxel may be assigned a complex value relating to its corresponding volume element. The complex value may comprise the signal magnitude value registered for the corresponding volume element and the signal phase value registered for the same corresponding volume element. Each voxel may also be associated with a pixel in the PC-MRI images. One example of a PCI-MRI image is shown by Figs. 1 A and IB, which depicts a cross section of a human skull. Fig. 1 A shows the signal magnitude of the voxels associated with the pixels, and Fig. IB shows the signal phase of the voxels associated with the pixels.

In accordance with conventional methods for measuring body vessel characteristics in PC- MRI images, by using the signal phase values for the voxels associated with the pixels in the PC-MRI images that represents a flow, and thus also comprise a velocity, a value of the flow or the velocity of a fluid flowing in the body vessel may be estimated. However, this requires that the PC-MRI phase image is first segmented into a first set of pixels that represent the flow (i.e. the body vessel) and a second set of pixels that represent the surrounding stationary tissue. This segmentation is a difficult and time consuming task since it requires an accurate delineation of the body vessel in the signal phase image in the PC- MRI images. Furthermore, the accuracy of the delineation of the body vessel may be limited by the pixel resolution of the PC-MRI images and/or the performance of an operator or software performing the delineation of the body vessel.

Because the area of the body vessel in the PC-MRI images normally is small in comparison to the resolution of the PC-MRI images, the delineation of the body vessel in the PC-MRI images will lead to partial volume effects from voxels (or pixels) that comprise both flowing and stationary medium. Thus, including or excluding such voxels (or pixels) from the phase value summation when performing the delineation will inevitably lead to errors in the estimation of the body vessel characteristics. It follows that conventional methods for determining body vessel characteristics using PC-MRI imaging are not particularly accurate or robust. EP 0 638 816 A2 describe a method attempting to correct for partial volume effects in phase contrast magnetic resonance imaging (PC-MRI) by estimating a mean velocity per area for each voxel (represented as a pixel). This is performed by recalculating voxel phase and velocity values using calibration voxels that are selected centrally within the vessel lumen. The velocity value for the voxel is then multiplied with the area of the voxel. In this manner, an estimate of the flow or velocity may be obtained on a voxel-by-voxel basis. The voxel estimates may then be summed for all voxels determined to be part of the body vessel in order to provide an estimated value of the flow in the body vessel. Summary

Accordingly, there is a need to provide a robust method for determining a body vessel characteristic using PC-MRI imaging.

According to the teachings presented herein, a method for determining body vessel characteristics from PC-MRI imaging data of a PC-MRI image sequence comprising said body vessel is described, wherein the PC-MRI imaging data is arranged to digitally represent a volume of space as a plurality of voxels, each voxel being assigned a complex value comprising a signal magnitude registered for a portion of the volume of space corresponding to said voxel and a signal phase registered for said portion of the volume of space corresponding to said voxel, and wherein each voxel is associated with a pixel in the PC-MRI images of the PC-MRI image sequence. The method is characterised in that it comprises the steps of: determining complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in a region of interest comprising the body vessel in the PC-MRI images of the PC-MRI image sequence; and determining at least one body vessel characteristic based on the determined complex summation values.

By performing complex summation of the signal magnitude and signal phase information in each of the PC-MRI images in the PC-MRI image sequence such that a complex summation value is determined for each PC-MRI image in the PC-MRI image sequence, these complex summation values may be used in determining body vessel characteristics. This method is able to achieve more accurate results than conventional methods, since it is able to utilize both the signal magnitude and signal phase information in the PC-MRI images in the PC- MRI image sequence for determining characteristics of a fluid in the body vessel, while conventional methods only utilizes the signal phase information in the PC-MRI images in the PC-MRI image sequence when estimating, for example, the velocity or flow of a fluid in a body vessel. Advantageously, this may significantly reduce or substantially eliminates the partial volume effects from the voxels (or pixels) that comprise both flowing and stationary components on the estimation of the characteristics of a fluid in the body vessel comprised in the PC-MRI images in the PC-MRI image sequence. It can also be shown that the method is more robust than conventional methods since it does not require an accurate segmentation or delineation of the body vessel in the PC-MRI images in the PC-MRI image sequence.

Another advantage of the method is that it enables the use of low resolution PC-MRI images for determining body vessel characteristics in a PC-MRI image sequence. This may results in that the time required for a patient to be examined in the PC-MRI scanner can be reduced, whereby the duration of the examination of the patient can also be reduced.

The at least one body vessel characteristic may be the velocity of a fluid in the body vessel, the actual area of the body vessel and/or the flow of a fluid in the body vessel. More specifically, the velocity or flow of a fluid flowing through the body vessel, although in a strict meaning may be considered characteristics of the fluid, is herein defined as

characteristics of the imaged body vessel or body vessel characteristics.

A further advantage of the method is that no accurate segmentation or delineation of the body vessel and a less accurate setting of the sensitivity of the PC-MRI scanner is required by the operator of the PC-MRI-scanner. This result in a less complicated and more objective method (i.e. a less operator dependable method) to extract the information needed to perform the determination of the body vessel characteristics from the PC-MRI images in the PC-MRI image sequence than according to conventional methods. Also, it follows that the duration of the examination of the patient can be further reduced.

Another further advantage of the method is that since the determination of the actual area of the body vessel is performed without relying on an operator to draw an accurate delineation of the body vessel, the method provides for a simple and easy way to determine the actual area of a body vessel comprised in PC-MRI images in the PC-MRI image sequence. Using conventional methods for the determination of the actual area of the body vessel, that is, from the manual delineation of the body vessel in the PC-MRI images estimating the actual area of the body vessel, is difficult and provides unreliable results, since it relies on the performance and accuracy of the operator/software and on the pixel resolution of the PC- MRI images. However, according to the above, an objective and robust method for determining the actual area of the body vessel may be achieved, which is less dependent upon the performance of an operator or software performing the delineation, or on the pixel resolution of the PC-MRI images.

The method may further comprise the steps of: adapting a mathematical representation of a spiral-shaped curve in the complex plane based on the determined complex summation values; and determining the body vessel characteristics based on the characteristics of the adapted mathematical representation of the spiral-shaped curve in the complex plane. By performing complex summation of the signal magnitude and signal phase information in each of the PC-MRI images in the PC-MPJ image sequence such that a complex summation value is determined for each PC-MPJ image in the PC-MPJ image sequence and having these represent a position in the complex plane, a mathematical representation of a spiral- shaped curve may be adapted or fitted to the positions of the complex summation values in the complex plane. From the characteristics of this adapted mathematical representation of a spiral-shaped curve, the body vessel characteristics may be derived from the PC-MRI images in the PC-MRI image sequence. The characteristics of the adapted mathematical representation of the spiral-shaped curve that is used in the determination of body vessel characteristics comprised in the PC-MRI images in the PC-MRI image sequence, may comprise the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve, the point in the complex plane where the spiral-shaped curve of the adapted mathematical representation intersect with the real axis, and/or the vector angles of vectors going from the centre point to each of the points in the complex plane corresponding to the determined complex summation values. From these characteristics of the adapted mathematical representation of the spiral-shaped curve it is possible to determine the body vessel characteristics of the body vessel shown in the region of interest in the PC-MRI images of the PC-MRI image sequence.

Furthermore, the PC-MRI images of the PC-MRI image sequence may be a sequence of PC-MRI images wherein each represents a specific point in time over at least one cardiac cycle. A cardiac cycle is a term that may be used to refer to all or any of the events related to the flow or blood pressure that occurs from the beginning of one heartbeat to the beginning of the next heartbeat. This may allow an operator to establish a range of diagnoses of various conditions and illnesses.

The region of interest in the PC-MRI images of the PC-MRI image sequence may comprise the complete PC-MRI images or at least a part of the PC-MRI images. If the PC-MRI images of the PC-MRI image sequence only comprise pixels representing the flow in the body vessel and pixels comprising static or stationary tissue, the complete PC-MRI images may be used as the region of interest. Otherwise, the region of interest should comprise nothing but the part of the complete PC-MRI images comprising pixels representing the flow in the body vessel and pixels comprising static or stationary tissue. The method may thus further comprise the steps of: receiving information indicating the region of interest comprising the body vessel in each of the PC-MRI images of the PC-MRI image sequence; and determining the complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in the region of interest indicated by the received information. This allows the operator to perform a rough delineation or segmentation of the region of interest comprising the body vessel in the PC-MRI images of the PC-MRI image sequence. By reducing the number of pixels surrounding the body vessel in the region of interest, the accuracy of the determination of the body vessel characteristics may be further increased.

The mathematical representation of the spiral-shaped curve in the complex plane which is adapted to the complex summation values may be described by the following equation:

wherein I_ROi is the complex summation value in the region of interest in the PC-MRI images of the PC-MRI image sequence; is the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represent stationary tissue, I_B is the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represents the body vessel, A_A is the actual area of the stationary medium shown in the ROI in the PC-MRI image, A_B is the actual area of the body vessel shown in the ROI in the PC-MRI image, v_max is the maximum momentary velocity of the flow of a fluid in the body vessel; and v_enc is a known PC-MRI scanner setting that controls the sensitivity of the PC-MRI protocol. The flow of a fluid in the body vessel may here be approximated as a laminar flow, and the body vessel may be approximated as a circular or elliptically shaped body vessel.

According to a further aspect of the invention, an apparatus for determining body vessel characteristics from PC-MRI imaging data of a PC-MRI image sequence comprising the body vessel is provided, comprising: a processing unit arranged to receive PC-MRI imaging data of a PC-MRI image sequence and digitally represent a volume of space as a plurality of voxels, each voxel being assigned a complex value comprising a signal magnitude registered for a portion of the volume of space corresponding to said voxel and a signal phase registered for said portion of the volume of space corresponding to said voxel, and wherein each voxel is associated with a pixel in the PC-MRI images of the PC-MRI image sequence. The apparatus is characterized in that the processing unit is further arranged to: determine complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in a region of interest comprising the body vessel in the PC-MRI images of the PC-MRI image sequence, and determine at least one body vessel

characteristic based on the determined complex summation values.

According to yet a further aspect of the invention, a computer program product for use in an apparatus according to the above is provided, which comprises computer readable code means, which when run in a processing unit in the apparatus causes the apparatus to perform the steps of: determining complex summation values based on the signal magnitude and signal phase of voxels associated with the pixels in a region of interest comprising a body vessel in PC-MRI images of a PC-MRI image sequence; determining at least one body vessel characteristic based on the complex summation values.

Further advantageous embodiments of the method, the apparatus and the computer program product are set forth in the dependent claims, which correspondently describe further advantageous embodiments of the invention. Brief description of the drawings

The objects, advantages and effects as well as features of the invention will be more readily understood from the following detailed description of exemplary embodiments of the invention when read together with the accompanying drawings, in which:

Fig. 1A-1B shows the signal magnitude and signal phase of a PC-MRI image of a cross section of a human skull.

Figs. 2A-2B shows illustrations which describe principles used by the exemplary

embodiments of the invention.

Figs. 3A-3D and 4A-4B show illustrations which describe an operation according to an exemplary embodiment of the invention. Fig. 5 A shows a graph illustrating the result of an operation according to an exemplary embodiment of the invention.

Fig. 5B shows a graph illustrating a flow determined by the operation according to the exemplary embodiment of the invention described in Fig. 5A and a flow determined according to a convention method.

Fig. 6A shows four PC-MRI images comprising a body vessel in which four different regions of interests are indicated. Fig. 6B shows the flow determined by an operation according to the exemplary embodiment of the invention for the four different regions of interest indicated in Fig. 6A over 32 PC- MRI images representing one cardiac cycle.

Fig. 6C shows the flow determined by a conventional method according to the prior art for the four different regions of interest indicated in Fig. 6A over 32 PC-MRI images representing one cardiac cycle. Fig. 7 shows a flowchart illustrating a method according to an embodiment of the invention.

Fig. 8 shows a flowchart illustrating a method according to another embodiment of the invention.

Fig. 9 shows a flowchart illustrating a method according to a further embodiment of the invention.

Fig. 10 shows an apparatus and a computer program product according to an embodiment of the invention.

Detailed description

From a PC-MRI measurement sequence in a PC-MRI scanner, PC-MRI imaging data of a PC-MRI image sequence is obtained. The PC-MRI imaging data in the PC-MRI image sequence comprises a sequence of paired signal magnitude and signal phase images. One pair of the signal magnitude and signal phase images may also be referred to as a PC-MRI image. Each pair of the magnitude and phase images, that is, each PC-MRI image, represents a specific point in time of the duration of the PC-MRI measurement sequence.

In the PC-MRI imaging data of a PC-MRI image sequence, a volume of space in the body that is being scanned by the PC-MRI scanner may be digitally represented as a plurality of voxels. A voxel may be described as a volume element that represents a position in a grid of a three dimensional space. Thus, a voxel can be said to be analogous to a pixel, which for example may represent 2D image data in 2D image bitmaps. Each voxel in the PC-MRI imaging data is for each PC-MRI image in a PC-MRI image sequence assigned a value which represents the signal magnitude that is registered by the PC- MRI scanner for its corresponding portion of the volume of space that is scanned. Each voxel in the PC-MRI imaging data is also, for each PC-MRI image in the PC-MRI image sequence, assigned a value which represents the signal phase that is registered by the PC- MRI scanner for the same corresponding portion of the volume of space. The magnitude and phase for each PC- MRI image may be registered for each voxel in the PC-MRI imaging data as a complex value. The complex value thus comprises a signal magnitude value and a signal phase value. Each voxel is also associated with a specific pixel in the PC-MRI images of the PC-MRI image sequence. Thus, each specific pixel in the PC-MRI images of the PC-MPJ image sequence may correspond to a complex value the signal magnitude and the signal phase registered by the PC-MPJ scanner. This may be described according to the following equation, Eq. 1 :

I_J = A_Je"' (Eq. 1) wherein / . represents the complex value for the j :th pixel comprised in the signal magnitude and signal phase image pair of the PC-MPJ image that represents the specific point in time t, A _j corresponds to the signal magnitude of the j:th pixel, and θ_; corresponds to the signal phase of the j:th pixel.

Figs. 1 A and IB shows the signal magnitude and signal phase, respectively, of a PC-MRI image of a cross section of a human skull at a specific point in time of the duration of the PC-MRI measurement sequence. A pixel in the signal magnitude image of the PC-MRI image in Fig. 1 A corresponds to the same pixel in the signal phase image of the PC-MRI image in Fig. IB, that is, each pixel pair in the signal magnitude and signal phase images corresponds to the same single complex value. Furthermore, in the PC-MRI image shown in Figs. 1 A and IB, an example of a region of interest (ROI) is indicated. This ROI comprises a body vessel known as the aqueduct in the human brain in which cerebrospinal fluid (CSF) flows and oscillates during a cardiac cycle. For example, investigating changes in the flow of the cerebrospinal fluid (CSF) in the aqueduct in the human brain may be useful in diagnosing hydrocephalus patients. Other examples that illustrate the usefulness of PC-MRI quantitative measurements may comprise the quantification of velocity and/or flow in blood vessels which may aid in determining the blood supply to the brain and blood flow inside the brain, the velocity and/or flow of blood in the aorta or the velocity and/or flow of cerebrospinal fluid (CSF) in the ventricle system of the brain, etc. These are merely examples of areas of application for PC-MRI imaging, and should not be construed as limiting. Also, the term PC-MRI is used herein to denote any MRI sequence comprising velocity encoding based on the signal phase. Today, a PC-MRI image sequence for use in determining characteristics of a body vessel may normally comprise about 32 PC-MPJ images which each represent a specific point in time over a cardiac cycle. However, the term PC-MPJ image sequence is used herein to refer to a sequence of PC-MPJ images which may comprise any number or plurality of PC- MPJ images. The term plurality is herein used to denote any number from 2 to infinity.

Figs. 2 A and 2B show illustrations which describe principles used by exemplary

embodiments of the invention. In PC-MRI imaging, time-of-flight effects on the registered signals of the PC-MRI scanner caused by the physiology of the body will occur. These time- of- flight effects on the registered signals of the PC-MRI scanner will cause the signal magnitude registered or detected for a flowing medium in a PC-MRI image to be significantly higher than the signal magnitude registered or detected for a stationary medium, e.g. static or stationary tissue, in a PC-MRI image. It can also be shown that the signal phase registered or detected for a flowing medium in a PC-MRI image is directly proportional to the velocity of the flowing medium. As will become apparent in the following, because of the above mentioned facts and the fact that the signal magnitude registered or detected for a small volume element in a volume of space, e.g. a voxel, is substantially unaffected by the velocity of the flowing medium, a mathematical expression (see equation Eq. 2) for the complex value of a region of interest comprising pixels corresponding to both flowing medium and stationary medium may be established.

Fig. 2A shows an illustration of registered signals for pixels corresponding to flowing medium and stationary medium as a sum of complex vectors in the complex plane. The complex plane spans a two-dimensional space comprising a real valued axis and an imaginary valued axis. In Fig. 2A, the sum of the complex vectors of 5 pixels pi, p2, p3, p4, and p5 is shown. According to the above, it can be shown that the pixels pi, p2, and p3 correspond to a stationary medium, and that the pixels p4 and p5 correspond to a velocity of a flowing medium resulting in the phase shifts 0_j and θ₂ . It should be noted that it may be derived from the illustration that the pixels pi, p2, p3 does not correspond to a flowing medium, but that the pixels p4 and p5 may correspond either to only flowing medium or to a combination of flowing and stationary medium. On the left side in Fig. 2B, a PC-MRI image is shown wherein an example of a region of interest (ROI) comprising a body vessel is indicated. As in the previous example, the body vessel is here the aqueduct in the human brain in which cerebrospinal fluid (CSF) flows and oscillates during a cardiac cycle. The indicated ROI in the PC-MRI image comprising the body vessel may comprise N number of pixels. As seen on the left side in Fig. 2B, the N number of pixels in the ROI corresponds to both flowing medium and stationary medium. A complex summation value I_R0I for the complex values of the pixels in the ROI may be described according to the following equation, Eq. 2: i=N

I_R01 =∑A e^m' (Eq. 2)

i=\

The right side in Fig. 2B shows an illustration of a complex plane in which the location of the complex summation value of the ROI, I_R0I , is shown. The location is indicated in Fig.

2B by a vector corresponding to the complex summation value of the ROI, I_R0I .

Figs. 3A-3D and 4A-B shows illustrations which describe an operation or method according to an exemplary embodiment of the invention. It is assumed that the region of interest (ROI) in the PC-MRI images of a PC-MRI image sequence comprises pixels that represent a body vessel with an oscillating laminar flow having an elliptical or circular cross-section. It should also be noted that the pixels comprised in the ROI may also represent stationary tissue or represent both the body vessel and stationary tissue. An example of such a region of interest (ROI) in the PC-MRI images of a PC-MRI image sequence is shown to the left in Fig. 2B and in the signal magnitude and signal phase image of the PC-MRI image in Fig. 1 A and IB. The region of interest may, for example, be determined by performing a rough delineation or segmentation of the PC-MRI images in the PC-MRI image sequence or may be determined as the complete PC-MRI images in the PC-MRI image sequence. The latter, however, requires that there are no other pixels in the PC-MRI images that represent a flowing medium than the pixels representing the body vessel. First, a complex summation value may be determined based on the complex values associated with the pixels in the region of interest (ROI) according to equation Eq. 2 for each PC-MRI image in the PC-MRI image sequence. The PC-MRI image sequence is here assumed to comprise a plurality of PC-MRI images which each represent a specific point in time over a cardiac cycle. Thus, the resulting plurality of complex summation values is thus associated with the specific points in time over a cardiac cycle. Fig. 3A-3D shows illustrations of a complex plane wherein the locations of the points corresponding to the complex summation values for a region of interest in 3, 6, 9 and 16, respectively, PC-MRI images in a PC-MRI image sequence are shown.

Secondly, at least one characteristic of the body vessel comprised in the ROI in the PC-MRI images of the PC-MRI image sequence is determined based on the determined complex summation values. This may be performed by adapting or fitting a curve or function in the complex plane to the locations of the points corresponding to the complex summation values for the region of interest in the PC-MRI images in a PC-MRI image sequence. The term curve or function may herein used interchangeably to denote a representation in the complex plane. A mathematical representation of the curve in the complex plane may be derived in a manner described below:

Let I A denote the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represent stationary tissue,

Let I_B denote the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represents the body vessel,

Let A_A denote the actual area of the stationary medium shown in the ROI in the PC- MRI image,

Let A_B denote the actual area of the body vessel shown in the ROI in the PC-MRI image,

Letf(v) denote a function that describes the distribution of velocities v of the fluid in the body vessel (i.e. the flowing medium),

- LetG (v; v_enc ) denote the signal phase registered for a portion of a volume of space corresponding to a voxel associated with a pixel in the ROI. Thus, a mathematical representation or model of I_R0I may be derived by complex summation of the complex values of the pixels in the ROI and may be described according to the following equation, Eq. 3 :

I_R0I = I_AA_A + I_BA_B } (v)e^S(-"¾v (Eq. 3)

For a body vessel with a laminar flow having an elliptical or circular cross-section, a function that describes the distribution of velocities v of the fluid in the body vessel may be described according to the following equation, Eq. 4: l/v max , ' 0 <— v≤— v max (Eq

0, else wherein v_max is the maximum momentary velocity in the flowing medium (i.e. the fluid in the body vessel). For a body vessel with a laminar flow having an elliptical or circular cross- section, it may also be derived that the mean value of the velocity, v_mean in the flowing medium is substantially equal to half of the maximum momentary velocity in the flowing medium, that is, v_mean = .

In PC-MRI imaging, there is a known correlation between the velocity of the flowing medium and signal phase. This correlation may be described according to the following equation, Eq. 5 :

θ (ν;ν_) =— (Eq. 5)

wherein v_enc denotes a known PC-MRI scanner setting that controls the sensitivity of the PC-MRI protocol. By inserting the equations Eq. 4-5 in equation Eq. 3, the mathematical representation or model of I_R0I may be described according to the following equation, Eq. 6:

I Roi - (Eq. 6)

0 ^r max

This mathematical representation or model of I_R0I shown above in equation Eq. 6 describes a spiral-shaped curve in the complex plane. By adapting the mathematical representation or model of I_R0I to the plurality of complex summation values associated with specific points in time over a cardiac cycle previously obtained in the complex summation by fitting the spiral-shaped curve in the complex plane, the parameters I _A ^■ A_A , I_B ^■ A_B and in equation Eq. 6 may be determined.

Fig. 4A shows a spiral-shaped curve in the complex plane of the mathematical

representation or model of I_R0I as it has been fitted to the plurality of complex summation values shown in Fig. 3D associated with specific points in time over a cardiac cycle obtained in the complex summation. The mathematical representation or model of I_R0I may be adapted to the plurality of complex summation values shown in Fig. 3D associated with specific points in time over a cardiac cycle by using different mathematical curve fitting techniques, such as, for example, the method of least squares, regression analysis, etc. It should be noted that there are numerous known techniques or methods for fitting a curve to a set of data points and that the invention should not be construed as limited to any particular technique or method for doing so.

Fig. 4B shows how the characteristics of the spiral-shaped curve in the complex plane of the adapted mathematical representation or model of I_R0I correspond to the parameters I _A ^■ A_A ,

I_B ^■ A_B andv_^ . Thus, according to an exemplary embodiment of the invention, by determining the centre point in the complex plane of the adapted mathematical

representation of the spiral-shaped curve, and the vector angles (a ) of vectors going from the determined centre point in the complex plane of the adapted mathematical

representation of the spiral-shaped curve to each of the points in the complex plane corresponding to the determined complex summation values, the parameter of the adapted mathematical representation of the spiral-shaped curve for each specific point in time over a cardiac cycle may be determined according to the following equation, Eq. 7:

a = Ξ≥_ (Eq. 7)

2 · v enc

Since it is assumed that the body vessel is a body vessel with a laminar flow having an elliptical or circular cross-section, the mean value of the velocity, v_mean , of the flowing medium for each specific point in time over a cardiac cycle is substantially equal to half of

v

the maximum velocity in the flowing medium, that is, v_mean = - ^^L . Thus, an objective determination of the velocity of the fluid in the body vessel represented in the ROI in the PC-MRI images of the PC-MRI image sequence for each specific point in time over a cardiac cycle may be achieved. According to another exemplary embodiment of the invention, by determining the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve and the point in the complex plane where the spiral-shaped curve of the adapted mathematical representation intersect with the real axis, values relating to the parameters I _A ^■ A_A and I_B ^■ A_B may be derived. From Fig. 4B, it is seen that the distance between origo in the complex plane to the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve corresponds directly to the parameter/_^, · A_A , and that the distance between the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve and the point in the complex plane where the spiral shaped curve of the adapted mathematical representation intersects with the real axis corresponds directly to the parameter I_B ^■ A_B . However, in order to determine the actual area A_B of the body vessel represented in the ROI, the signal magnitude I_B that denotes the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represents the body vessel have to be determined. The signal magnitude I_B may, for example, be approximated by determining the signal magnitude I_B for the pixel in the ROI which has the highest probability of comprising a strictly flowing medium, that is, for example, a pixel in the centre of the body vessel. Thus, an objective determination of the actual area A_B of the body vessel comprised in the ROI in the PC-MRI images of a PC-MRI image sequence may be achieved. This determination of the actual area A_B of the body vessel is not limited to the number of pixels in the PC-MRI image (i.e. the pixel resolution of the PC-MRI image) as conventional methods. Such conventional methods may be arranged to only determine an area of the body vessel in the form of a multiple number of pixels. This may cause poor results when estimating an area of a body vessel using PC-MRI images with low resolution. According to a further exemplary embodiment of the invention, by determining the velocity of the fluid in the body vessel, e.g. v_mean as described above, for each specific point in time over a cardiac cycle and by determining the actual area A_B of the body vessel, the flow of the fluid Q in the body vessel may also be determined for each specific point in time over the cardiac cycle. The flow of the fluid Q may be calculated according to the following equation, Eq. 8:

Q = v_mean ^■ A_B (Eq. 8)

However, it should also be noted that according to yet a further exemplary embodiment of the invention, determining the velocity of the fluid in the body vessel for each specific point in time over a cardiac cycle as described above and then determining the actual area A_B of the body vessel according to another method than the method described above, may also be performed in order to determine the flow of the fluid in the body vessel for each specific point in time over the cardiac cycle.

Fig. 5A shows a graph illustrating the adaptation of a spiral-shaped curve in the complex plane of a mathematical representation or model by an operation according to an exemplary embodiment of the invention. In Fig. 5A, a spiral-shaped curve in the complex plane of a mathematical representation or model for a region of interest (I_R0I ) in 32 PC-MRI images of an PC-MRI image sequence has been adapted to the 32 data points corresponding to a plurality of complex summation values associated with specific points in time over a cardiac cycle obtained by complex summation over the regions of interest in the 32 PC-MRI images of the PC-MRI image sequence. Fig. 5B shows a graph illustrating the flow over a cardiac cycle as determined by the adaptation of the spiral-shaped curve in the complex plane of the mathematical representation or model according to the exemplary embodiment of the invention described in Fig. 5A. Fig. 5B also shows a flow determined according to a conventional method. The flow determined according to the exemplary embodiment of the invention is shown as the fully drawn line, and the flow determined according to a conventional method is shown as the dashed line. Here, the conventional method comprises a calculation of the flow using a signal phase mean value based on the signal phase information in a region of interest (ROI) and a manual delineation of the body vessel in the PC-MRI images of the PC-MRI image sequence to determine the region of interest (ROI).

Fig. 6A shows one PC-MRI image in a PC-MRI image sequence over a cardiac cycle comprising 32 PC-MRI images, in which four different regions of interests (ROIs) have been indicated. Fig. 6B shows the flow determined by an operation according to an exemplary embodiment of the invention for the four different regions of interest indicated in Fig. 6A over the 32 PC-MRI images in the PC-MRI image sequence representing one cardiac cycle. Fig. 6C shows the flow determined by a conventional method for the four different regions of interest indicated in Fig. 6A over the 32 PC-MRI images in the PC-MRI image sequence representing one cardiac cycle. Also here, the conventional method comprises a calculation of the flow using a signal phase mean value based on the signal phase information in a region of interest (ROI) and a manual delineation of the body vessel in the PC-MRI images of the PC-MRI image sequence to determine the region of interest (ROI). In Figs. 6A-6C, an example is seen where it is shown that the flow determined by an operation according to the exemplary embodiment of the invention is more robust than the flow determined by a conventional method, when the region of interest (ROI) is larger than the body vessel in the PC-MRI images in the PC-MRI image sequence.

Fig. 7 shows a flowchart illustrating a method according to an embodiment of the invention. In step S71, complex summation values are determined based on the signal magnitude and signal phase of voxels associated with pixels in a region of interest (ROI) comprising the body vessel in PC-MRI images of the PC-MRI image sequence. In step S72, at least one body vessel characteristic is determined based on the determined complex summation values. The characteristics may, for example, be the velocity of a fluid in the body vessel, the actual area of the body vessel and/or the flow of a fluid in the body vessel.

Fig. 8 shows a flowchart illustrating a method according to another embodiment of the invention. In step S81, complex summation values are determined in the same manner as described in step S71 of the previously described method in reference to Fig. 7. In step S82, a mathematical representation of a spiral-shaped curve in the complex plane is adapted based on the determined complex summation values. This may be performed by fitting the spiral-shaped curve to points in the complex plane corresponding to the determined complex summation values. In step S83, at least one body vessel characteristic is determined based on the characteristics of the adapted mathematical representation. This may be performed by determining the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve, the point in the complex plane where the spiral-shaped curve of the adapted mathematical representation intersect with the real axis, and/or the vector angles of vectors going from the centre point to each of the points in the complex plane corresponding to the determined complex summation values. These characteristics may then be used to determine the velocity of a fluid in the body vessel, the actual area of the body vessel and/or the flow of a fluid in the body vessel as described in the above.

Fig. 9 shows a flowchart illustrating a method according to a further embodiment of the invention. In step 91, information indicating a region of interest (ROI) in the PC-MRI images of a PC-MRI image sequence is received. In step 92, complex summation values are determined based on the pixels in the region of interest (ROI) indicated by the information received in step S91. In step S93, a mathematical representation of a spiral- shaped curve in the complex plane is adapted in the same manner as described in step S82 of the previously described method in reference to Fig. 8. In step S94, at least one body vessel characteristic is determined in the same manner as described in step S83 of the previously described method in reference to Fig. 8.

Fig. 10 shows an apparatus 1 for determining body vessel characteristics in PC-MRI imaging and a computer program product 7 according to an embodiment of the invention. The apparatus 1 may be an MRI scanner, an apparatus arranged to be incorporated into an MRI scanner or an apparatus arranged to be connected to and/or arranged to communicate with an MRI scanner. Thus, the apparatus 1 may be arranged to receive PC-MRI imaging data of a PC-MRI image sequence comprising PC-MRI images registered or detected by an MRI scanner. The apparatus 1 may be arranged to receive the PC-MRI imaging data of a PC-MRI image sequence comprising PC-MRI images in a processing unit 4 via an input means 3, such as, for example, an input port or input connecting unit. The processing unit 4 may also connected to a memory unit 5 and an output means 6, such as, for example, an output port or output connecting unit. The processing unit 4 may be arranged to receive information via the input means 3, store information in the memory unit 5 and output information via the output means 4. The processing unit 4 may be arranged to information to a display unit (not shown) to be displayed to a user of the apparatus 1.

The CPU 4 may also comprise processing means or logic for performing the functionality of the apparatus 1. This functionality may be implemented partly by means of a software or computer program, such as, the computer program product 7. The CPU 7 may also comprise storage means or a memory unit for storing such a computer program and processing means or a processing unit, such as a microprocessor, for executing the computer program (e.g. the programmed instructions of the computer readable code means comprised in the computer program product 7). The storage means or memory means may be a readable storage medium located internally in the CPU 4 or in a memory storage unit, such as, for example memory unit 5, separated from but connected to the CPU 7. As the CPU 4 in the apparatus 1 performs a certain function or operation it is to be understood that the CPU 7 may use its processing means or logic to execute a certain part of the computer program (e.g. the programmed instructions of the computer readable code means comprised in the computer program product 7) which is stored in the storage means or memory unit. The apparatus 1 may further comprise a computer program product 7 which comprises computer readable code means. The computer readable code means may comprise at set of programmed instructions 71, 72, 73, 7M. The programmed instructions 71 may be arranged to, when run in a processing unit, such as, the CPU 4, cause the apparatus 1 to perform the step S71 of the previously described method in reference to Fig. 7, the step S81 of the previously described method in reference to Fig. 8, or the step S91 of the previously described method in reference to Fig. 9. The programmed instructions 72 may be arranged to, when run in a processing unit, such as, the CPU 4, cause the apparatus 1 to perform the step S72 of the previously described method in reference to Fig. 7, the step S82 of the previously described method in reference to Fig. 8, or the step S92 of the previously described method in reference to Fig. 9. The programmed instructions 73 may be arranged to, when run in a processing unit, such as, the CPU 4, cause the apparatus 1 to perform the step S83 of the previously described method in reference to Fig. 8 or the step S93 of the previously described method in reference to Fig. 9. The programmed instructions 74 may then be arranged to, when run in a processing unit, such as, the CPU 4, cause the apparatus 1 to perform the step S94 of the previously described method in reference to Fig. 9.

The apparatus 1 may also be connected to and/or arranged to communicate with at least one input control units 2 via the input means 3. The at least one input control unit 2 may be arranged to receive manual inputs from a user of the apparatus 1 and output the manual inputs to a processing unit 4 in the apparatus 1. The at least one input control unit 2 may, for example, be a computer mouse, a joystick, or be incorporated in a display as a touch screen functionality.

The description above is of the best mode presently contemplated for practising the invention. The description is not intended to be taken in a limiting sense, but is made merely for the purpose of describing the general principles of the invention. The scope of the invention should only be ascertained with reference to the issued claims.

Claims

1. A method for determining body vessel characteristics from PC-MRI imaging data of a PC-MRI image sequence comprising said body vessel, wherein the PC-MRI imaging data is arranged to digitally represent a volume of space as a plurality of voxels, each voxel being assigned a complex value comprising a signal magnitude registered for a portion of the volume of space corresponding to said voxel and a signal phase registered for said portion of the volume of space corresponding to said voxel, and wherein each voxel is associated with a pixel in PC-MRI images of the PC-MRI image sequence, wherein the method is characterized in comprising the steps of:

determining complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in a region of interest comprising the body vessel in the PC-MRI images of the PC-MRI image sequence; and

determining at least one body vessel characteristic based on the determined complex summation values.

2. A method according to claim 1, wherein the at least one body vessel characteristic comprise the velocity of a fluid in the body vessel, the actual area of the body vessel and/or the flow of a fluid in the body vessel.

3. A method according to claim 1 or 2, further comprising the steps of:

adapting a mathematical representation of a spiral-shaped curve in the complex plane based on the determined complex summation values; and determining the at least one body vessel characteristic based on the characteristics of the adapted mathematical representation of the spiral- shaped curve in the complex plane.

4. A method according to claim 3, wherein the characteristics of the adapted mathematical representation of the spiral-shaped curve comprise the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve, the point in the complex plane where the spiral-shaped curve of the adapted mathematical representation intersect with the real axis, and/or the vector angles (a ) of vectors going from the centre point in the complex plane of the adapted mathematical representation of the spiral-shaped curve to each of the points in the complex plane corresponding to the determined complex summation values.

5. A method according to any one of the claims 1-4, wherein the PC-MRI images of the PC-MPJ image sequence is a sequence of PC-MPJ images each representing a specific point in time over at least one cardiac cycle.

6. A method according to any one of the claims 1-5, wherein the region of interest in the PC-MPJ images of the PC-MPJ image sequence is the complete PC-MPJ images or at least a part of the complete PC-MPJ images.

7. A method according to any one of the claims 1-6, further comprising the steps of:

receiving information indicating the region of interest in each of the PC-MRI images of the PC-MRI image sequence; and

determining the complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in the region of interest indicated by the received information.

8. A method according to any one of the claims 1-7, wherein the mathematical

representation of the spiral-shaped curve in the complex plane which is adapted to the complex summation values is described by the equation,

wherein

/ is the complex summation value in the region of interest in the PC-MRI images of the PC-MRI image sequence; I _A is the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represent stationary tissue;

I_B is the signal magnitude per unit area of the actual area shown in the ROI of the PC-MRI images of the PC-MRI image sequence that represents the body vessel;

A_A is the actual area of the stationary medium shown in the ROI in the PC- MRI image;

A_B is the actual area of the body vessel shown in the ROI in the PC-MRI image;

v_max is the maximum momentary velocity of a fluid in the body vessel; and v_enc is a PC-MRI scanner setting that controls the sensitivity of the PC-MRI scanner measurements.

9. A method according to any one of the claims 1-8, wherein the flow of a fluid in the body vessel is approximated as a laminar flow.

10. A method according to any one of the claims 1-9, wherein the body vessel is

approximated as a circular or elliptically shaped body vessel.

11. An apparatus (1) for determining body vessel characteristics from PC-MRI imaging data of a PC-MRI image sequence comprising the body vessel, comprising:

a processing unit (4) arranged to receive PC-MRI imaging data of a PC-MRI image sequence and digitally represent a volume of space as a plurality of voxels, each voxel being assigned a complex value comprising a signal magnitude registered for a portion of the volume of space corresponding to said voxel and a signal phase registered for said portion of the volume of space corresponding to said voxel, and wherein each voxel is associated with a pixel in the PC-MRI images of the PC-MRI image sequence, characterized in that the processing unit (4) is further arranged to

determine complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in a region of interest comprising the body vessel in the PC-MRI images of the PC-MRI image sequence, and

determine at least one body vessel characteristics based on the determined complex summation values.

12. An apparatus (1) according to claim 11, wherein the processing unit (4) is further arranged to

adapt a mathematical representation of a spiral-shaped curve in the complex plane based on the determined complex summation values, and

determine the at least one body vessel characteristics based on the characteristics of the adapted mathematical representation of the spiral-shaped curve in the complex plane.

13. An apparatus (1) according to claim 11 or 12, further comprising at least one input control unit (2) arranged to

receive manual inputs indicating a region of interest in the PC-MRI images of the PC-MPJ image sequence, and

send information to the processing unit (4) indicating said region of interest in the PC-MPJ images of the PC-MPJ image sequence, wherein

the processing unit (4) is further arranged to

receive information from the at least one input control unit (2) indicating the region of interest in the PC-MPJ images of the PC-MPJ image sequence, and determine the complex summation values based on the signal magnitude and signal phase of the voxels associated with the pixels in the region of interest indicated by the information received from the at least one input control unit (2).

14. An apparatus (1) according to any one of the claims 11-13, wherein the apparatus is a MRI scanner or an apparatus arranged to be connected to a MRI scanner.

15. A computer program product (7) for use in an apparatus (1) according to any one of the claims 11-14, which comprises computer readable code means (71, 72, 73, ..., 7M), which when run in a processing unit (4) in the apparatus (1) causes the apparatus (1) to perform the steps of: determining complex summation values based on the signal magnitude and the signal phase of voxels associated with the pixels in a region of interest comprising a body vessel in PC-MRI images of a PC-MRI image sequence; and

determining at least one body vessel characteristic based on the complex summation values.

16. A computer program product (7) according claim 15, comprising computer readable code means (71, 72, 73, ..., 7M), which when run in the processing unit (4) of the apparatus (1) causes the apparatus (1) to further perform the steps according to any one of the claims 2 to 10.

17. A computer program product according claim 15 or 16, wherein said code means (71, 72, 73, ..., 7M) is stored on a readable storage medium.