Peripheral perfusion analysis

Abstract

The present invention relates to peripheral perfusion analysis. To provide improved information for perfusion analysis, a device 10 for peripheral perfusion analysis is provided. The device comprises a data input 12, a data processor 14 and an output interface 16. The data input is configured to provide a sequence of 2D angiograms 18 and to provide a measured perfusion signal 20 of perfused contrast agent in a region of interest. The data processor is configured to extract a region of interest, define a blood supply section including blood inflow and blood outflow to the region of interest, segment the blood supply section to extract an area occupied by detectable blood vessels, identify blood vessels involved in inflow to extract blood inlets to the region of interest and sum all blood inlets of the section to provide a perfusion sum. The output interface is configured to deconvolve the perfusion signal of the region of interest with the perfusion sum.

Description

[Technical field]

[0001] The present invention relates to a device for peripheral perfusion analysis, a medical imaging system and a method for peripheral perfusion analysis. [Background technology]

[0002] Analysis of pre- and post-intervention perfusion of the foot from angiographic sequences provides information on changes in downstream perfusion after treating an upstream lesion. This is achieved by comparing contrast agent concentration curves as a function of time, for example in the form of time concentration curves (TDCs), for regions of interest (ROIs) of the foot angiograms. The resulting TDCs change in shape characteristics influenced by several factors, among which are the amount and timing of blood supply, i.e., perfusion, to the area. The more oxygenated blood reaches the tissue area and the sooner it restores metabolism and reduces ischemia. Shape characteristics can be compared visually between the two curves or quantitatively via parameterized models after fitting the information parameter sets, but it has been shown that it is difficult to extract information in a reliable manner. WO2005 / 104936A1 concerns the acquisition of data perfusion measurements. Summary of the Invention [Problem to be solved by the invention]

[0003] Therefore, there is a need to provide improved information for perfusion analysis.

[0004] The object of the present invention is solved by the subject matter of the independent claims, further embodiments are incorporated in the dependent claims. It is noted that the aspects of the present invention described below also apply to a device for peripheral perfusion analysis, a medical imaging system and a method for peripheral perfusion analysis. [Means for solving the problem]

[0005] According to the invention, a device for peripheral perfusion analysis is provided. The device comprises a data input, a data processor and an output interface. The data input is configured to receive a sequence of 2D angiograms and to receive a measured perfusion signal of a perfused contrast agent in a region of interest. The input provides the data to the data processor. The data processor is configured to extract a region of interest from the received data. The data processor is also configured to define a blood supply section including a blood inflow to the region of interest and a blood outflow from the region of interest. The data processor is configured to segment the blood supply section in order to extract an area occupied by detectable blood vessels. The data processor is also configured to identify blood vessels involved in the inflow in order to extract the blood inlets to the region of interest and to sum all blood inlets of the section to provide a perfusion sum. The data processor is also configured to deconvolve the perfusion signal of the region of interest with the perfusion sum. The output interface is configured to provide the deconvolution result.

[0006] As a result, the perfusion signal associated with the region of interest is correlated with the actual blood supply and normalized for improved analysis.

[0007] According to one example, by deconvolution, the measured contrast agent concentration signal is normalized to a perfusion kernel.

[0008] The term "standardized" relates to the possibility of providing a relative value of perfusion. As an example, deconvolution leads to the elucidation of a general perfusion kernel, such as the basic perfusion characteristics in the region of interest. The term "standardize" refers to setting the measured perfusion values ​​in a more objective context in order to be able to better evaluate the results. Deconvolution is provided to qualify the measured contrast agent concentration signal and obtain results in terms of the perfusion kernel. By deconvolution, the measured contrast agent concentration signal is normalized to the perfusion kernel. Standardization provides a kind of calibration, since the measured perfusion value itself only provides information about the perfusion itself, whereas deconvolution provides enhanced information in that it establishes a relationship to the actual flow supply that resulted in the perfusion state with the perfusion characteristics for that actual flow supply.

[0009] According to one example, for identification, blood inflow and outflow are determined for the detected blood vessels.

[0010] According to one example, the subject's region of interest belongs to at least one of the group consisting of the subject's feet, hands, and head.

[0011] According to one example, identification of vessels with inflow is performed by extracting the Arterial Input Function (AIF) of each angiogram. The AIF extraction is provided covering a region of the image plane within the silhouette of the foot, the silhouette of the hand, or the silhouette of the head.

[0012] According to one example, the AIF covers all entrances to a perfusion region of interest (ROI).

[0013] As an alternative option, the AIF covers the exits. Optionally, the AIF covers at least some of the exits. Optionally, all of the exits are considered.

[0014] According to one example, the blood supply section is provided as a boundary layer surrounding the area as the region of interest.

[0015] The term "boundary layer" refers to a (virtual) layer in tissue next to the region of interest. The boundary layer separates the region of interest from other regions. Instead of a line-type enclosure, the enclosure is defined with a certain "thickness", i.e. a certain wall thickness of the enclosing structure. The boundary layer is also called an enclosing sheath, an enclosing shell, an enclosing liner, or an enclosing coating, where the sheath / shell / liner / coating has a certain (sheath / shell / liner / coating) thickness. In one example, the blood supply section is provided as a layer that encloses the area as the region of interest. The layer that encloses the region of interest thus defines the blood supply layer for the region of interest. The boundary layer thus provides a feed zone against which the amount of blood to be delivered is determined.

[0016] According to one example, the blood supply section is provided as an enveloping layer that surrounds the area as the region of interest.

[0017] According to one example, the blood supply section is provided as a convex form surrounding the region of interest.

[0018] According to one example, starting from a defined blood supply section, increasing subportions are determined and an approximation index is provided to reflect possible ambiguity due to increasing distance of the perfused portion from the blood supply section.

[0019] According to one example, a blood supply section is provided at the lower end of the tibia, perpendicular to the longitudinal direction of the tibia.

[0020] According to one example, a display is provided. The deconvolution includes generating a result in the form of at least one of the group consisting of parameters and a curve. The result is provided for clinical evaluation. Optionally, the result is displayed on the display.

[0021] According to the invention there is also provided a medical imaging system. The system comprises an X-ray imaging device configured to generate X-ray images of a region of interest. The X-ray images include images with and without injection of a contrast agent. The system further comprises a device for peripheral perfusion analysis according to one of the previous examples. The X-ray imaging device generates X-ray images of a sequence of 2D angiograms.

[0022] According to the present invention there is also provided a method for peripheral perfusion analysis, the method comprising: - receiving or acquiring a sequence of 2D angiograms; - extracting a region of interest; - defining a blood supply section including a blood inlet to the region of interest and a blood outlet from the region of interest; - segmenting the blood supply section in order to extract the area occupied by detectable blood vessels; - identifying the blood vessels involved in the inflow in order to extract the blood inlets to the region of interest; - summing all blood inlets of a section to provide a total perfusion; - providing a measured perfusion signal of perfused contrast agent in a region of interest; - deconvolving the perfusion signal of the region of interest with the total perfusion; - providing a deconvolution result.

[0023] In effect, a standardized perfusion kernel is provided for analyzing any region of a peripheral angiogram of the foot.

[0024] The field of use is minimally invasive perfusion monitoring.

[0025] The solution facilitates the analysis of situations, e.g., time concentration curves (TDCs), and in particular the comparison between pre- and post-intervention TDCs from the same patient or patient population. The solution eliminates factors unrelated to the body's ability to perfuse a particular foot region, i.e., the dependence of the contrast curve shape on changes in the injection protocol or the time-competitive effects of different components of the contrast flow, by taking into account the supply characteristics of the particular region.

[0026] In one example, existing deconvolution techniques are provided that can be leveraged to deconvolve acquired TDCs into a standardized perfusion kernel suitable for such comparison.

[0027] According to one aspect, the proposed solution is dedicated to automatically extracting the AIFs of peripheral angiograms and standardizing them to the perfusion kernel, i.e. the expected contrast agent concentration response to a short (Dirac) impulse at the input, as a prerequisite for deconvolving the measured contrast agent concentration signal of the foot. In one example, this is achieved by considering the following requirements: The region of the AIF extraction needs to cover only the region of the image plane within the silhouette of the foot. Furthermore, the deconvolution operation is associative and commutative, i.e. the AIF does not need to be concatenated to the perfusion ROI, but it needs to cover all inlets to the perfusion ROI, since the deconvolution cannot take into account the complete loss of signal components. Furthermore, the AIF ignores all outlets that may overlap with the inlets.

[0028] According to one embodiment, knowledge of the AIF specific to each ROI is provided, which can also provide deconvolution.

[0029] An option for automatic acquisition of the AIF provides for detection of inflow events at the edge of any ROI as a more generalized form of: An option for automatic acquisition of the AIF provides for detection of the tibial condyle and use of local anatomical knowledge to define the AIF for ROIs bordering the ankle: Both options rely on the extraction of large vessel activity on 2D angiograms and are used to assess the local effect on tissue perfusion by comparing kernels or parameterizations of selected kernels.

[0030] According to one aspect, as a result of AIF correction, the perfusion kernel of the present solution does not look similar to the one measured without AIF correction. This is due to the fact that the natural input to the foot vasculature is usually not a Dirac impulse. The difference becomes more noticeable at higher acquisition rates. Furthermore, one feature of the perfusion kernel is that if any perfusion ROI is in direct contact with the AIF extraction region, the arrival time, i.e., the time of the start of the rising edge of the TDC, will always be zero, since the deconvolution with the delayed AIF compensates for the arrival time. This is not the case for non-deconvolved signals.

[0031] The method is a computer-implemented method, whether embodied in a computer program or not, stored on a computer-readable medium or not. It is executed by a system having an input for receiving data, a processor for processing the data, and an output for providing result data. The data is received by the input. Alternatively, or additionally, the processor is configured to cause the input to receive the data. Similarly, the method comprises a step of causing reception of the data. This is referred to as obtaining the data under control of the processor or the method, although reception of the data also includes merely passively receiving the data without control by the processor or the method. The processor is communicatively coupled to the input and the output, and provides the data received by the input to the processor, enabling the processor to provide result data at the output, for example to another system, device, or user.

[0032] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.

[0033] Exemplary embodiments of the present invention will now be described with reference to the following drawings, in which: [Brief description of the drawings]

[0034] [Figure 1] 1 illustrates a schematic diagram of an example of a device for peripheral perfusion analysis. [Diagram 2] 1 illustrates an example of a medical imaging system. [Diagram 3] 1 illustrates steps of an example of a method for peripheral perfusion analysis. [Figure 4a] 1 shows a first example of the extraction of an arterial input function. [Figure 4b] 1 shows a first example of the extraction of an arterial input function. [Figure 5a] 13 shows a second example of the extraction of an arterial input function. [Figure 5b] 13 shows a second example of the extraction of an arterial input function. [Figure 6]5b shows an example of a graph of the determined perfusion in the selected region of interest of FIG. 5a. [Figure 7] 4 shows different curves for different kernels for a region of interest. [Figure 8] An example of increasing the effective perfusion region of interest is shown for the example of FIG. 5a. [Figure 9] 1 shows a first example of a perfusion image and a mask image. [Figure 10] FIG. 9B shows an example of a graph illustrating the large vessel response in the arterial input function of the first example of FIGS. 9a and 9b. [Figure 11] FIG. 9B shows an example of a graph illustrating the microvascular response within the remaining part of the foot of the first example of FIGS. 9a and 9b. [Figure 12] 13 shows a second example of a perfusion image and a mask image. [Figure 13] FIG. 13 shows an example of a graph illustrating the large vessel response in the arterial input function of the second example of FIGS. 12a and 12b. [Figure 14] FIG. 12 shows an example of a graph illustrating the microvascular response within the remaining part of the leg of the second example of FIGS. 12a and 12b. [Figure 15a] 9b shows an example of the inlet extraction module of the example of FIG. 9a as a binary mask having four components. [Figure 15b] 15a shows a digital subtraction angiography (DSA) maximum intensity projection (MIP) image associated with FIG. 15a. [Figure 15c] 1 shows the Hough transform being used to detect lines, i.e., vascular components, within a binary global mask. [Figure 15d] To detect a set of inlet components, an example is shown in which each of the final components is subjected to an individual comparison with the reference flow vector. [Figure 16] 13 shows an example of a graph illustrating the AIF in the deconvolution process. [Figure 17] 1 shows a graph illustrating a perfusion signal and a perfusion kernel. [Figure 18] 1 shows curves for the application of the Fast Fourier Transform (FFT) based Wiener deconvolution for different values ​​of the regularization parameter λ. [Figure 19] 13 shows the reconstructed signal after using FFT-based Wiener deconvolution for various values ​​of the regularization parameter λ. [Figure 20] An example of perfusion analysis results via a perfusion kernel that is comparable to angiograms of other patients and therefore can be exploited for outcome prediction or diagnosis is shown. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] Next, specific embodiments will be described in more detail with reference to the accompanying drawings. In the following description, similar drawing reference numbers are used for similar elements even in different drawings. Matters defined in this specification, such as detailed configurations and elements, are provided to assist in a comprehensive understanding of the exemplary embodiments. Also, well-known functions or configurations will not be described in detail to obscure the embodiments due to unnecessary details. Furthermore, expressions such as "at least one of," when preceding a list of elements, modify the entire list of elements and do not modify individual elements of the list.

[0036] FIG. 1 shows a schematic example of a device 10 for peripheral perfusion analysis. The device 10 comprises a data input 12, a data processor 14 and an output interface 16. The data input 12 is configured to provide a sequence of 2D angiograms, indicated by a first input arrow 18. The data input 12 is also configured to provide a measured perfusion signal of perfused contrast agent in a region of interest, indicated by a second input arrow 20. The data processor 14 is configured to extract the region of interest. The data processor 14 is also configured to define a blood supply section including blood inflows to the region of interest and blood outflows from the region of interest. The data processor 14 is configured to segment the blood supply section in order to extract an area occupied by detectable blood vessels. The data processor 14 is further configured to identify blood vessels involved in the inflow in order to extract the blood inlets to the region of interest. The data processor 14 is also configured to sum all blood inlets of the section to provide a perfusion sum. The data processor 14 is also configured to deconvolve the perfusion signal of the region of interest with the perfusion sum. The output interface 16 is configured to provide the deconvolution result.

[0037] As shown as an option in Figure 1, a display 24 is provided. Output arrow 26 indicates the provision of display data from output interface 16. Deconvolution includes generating outcomes in the form of at least one of the group consisting of parameters and curves. The outcomes are provided for clinical evaluation. Optionally, the outcomes are displayed on display 24.

[0038] The data input 12, data processor 14, and output interface 16 may be provided within a common structure, such as a housing, represented by frame 22, or as separately located components.

[0039] The data input section 12 is also referred to as a data input module. The data processor 14 is also referred to as a data processing module. The output interface 16 is also referred to as an output interface module. The data input section 12 is also referred to as a data supply section, an image supply section, an image data supply section, an input unit, or simply an input section.

[0040] In one example, the data input unit 12 is data connectable to an imaging source device such as an X-ray system, for example a C-arm, that provides 2D image data of the subject that is used for the information retrieval step.

[0041] In one example, the image data input unit 12 is data connectable to a data storage device that stores 2D image data.

[0042] The data processor 14 may also be referred to as a data processing device, a processor unit, or a processor. In one example, the data processor 14 is data connected to an image data input and output interface.

[0043] The output interface 16 may also be referred to as an output section or an output unit. In one example, the output interface 16 may be data-connected to a display device, such as a display 24. In another example, the output interface 16 is data-connected to the display 24.

[0044] In one example, not further shown in FIG. 1, the measured contrast agent concentration signal is normalized to a perfusion kernel by deconvolution.

[0045] In one example, also not further shown in FIG. 1, blood inflow and outflow are determined for the detected blood vessels for identification.

[0046] In one example, not further shown in Figure 1, the subject's region of interest includes at least one sub-region of at least one of the group consisting of the subject's feet, hands, and head, and thus the subject's region of interest is associated with or belongs to the feet, hands, or head.

[0047] In one example, also not shown in further detail, identification of vessels with inflow extracts the arterial input function of each angiogram. Further, AIF extraction is provided covering regions of the image plane within the foot silhouette, hand silhouette, or head silhouette.

[0048] In one example, not further shown in Figure 1, the AIF covers all entrances to the perfusion ROI. Optionally, additionally, or alternatively, the AIF ignores all exits.

[0049] As another alternative option, the AIF also covers at least some of the exits, with the option that all of the exits are considered.

[0050] In one example, also not shown in further detail, the blood supply section is provided as a boundary layer surrounding the area as the region of interest.

[0051] In one example, not further shown in FIG. 1, the blood supply section is provided as a convex feature surrounding the region of interest.

[0052] In one example, also not shown in further detail, starting from a defined blood supply section, increasing subportions are determined and approximation indices are provided to reflect possible ambiguities due to increasing distance of the perfused portion from the blood supply section.

[0053] In one example, not further shown in FIG. 1, a blood supply section is provided at the lower end of the tibia, perpendicular to the longitudinal direction of the tibia.

[0054] 2 shows an example of a medical imaging system 50. The medical imaging system 50 comprises an X-ray imaging device 52 configured to generate X-ray images of a region of interest. The X-ray images include images with and without injection of a contrast agent. Furthermore, the medical imaging system 50 comprises a device 10 for peripheral perfusion analysis according to one of the previous examples. The X-ray imaging device 52 generates X-ray images of a sequence of 2D angiograms.

[0055] As an example, the medical imaging system 50 is shown in the context of a hospital operating room, e.g. a catheterization lab. The X-ray imaging device 52 is shown as a C-arm device with an X-ray source 54 and an X-ray detector 56 mounted on either end of a movably supported C-arm 58. For example, a ceiling mounted rail system is provided for suspending the C-arm. Furthermore, a monitor device 60 and lighting equipment are shown. A subject support 62, e.g. a table, is provided for positioning a subject 64 for X-ray imaging. A console 66 is shown in the foreground providing control of the operation of the medical imaging system 50. In one example, the console 66 includes an example of a device 10 for peripheral perfusion analysis (not further shown in FIG. 2). A data connection 68 indicates the provision of 2D X-ray images from the X-ray imaging device 52 to the console 66, i.e. to the device 10 for peripheral perfusion analysis.

[0056] FIG. 3 shows the steps of an example of a method 100 for peripheral perfusion analysis. The method 100 comprises the following steps: In a first step 102, a sequence of 2D angiograms is provided. In a second step 104, a region of interest is extracted. In a third step 106, a blood supply section is defined, including blood inflows to and outflows from the region of interest. In a fourth step 108, the blood supply section is segmented to extract the area occupied by detectable blood vessels. In a fifth step 110, blood vessels involved in the inflow are identified to extract the blood inlets to the region of interest. In a sixth step 112, all blood inlets of the section are summed to provide a perfusion sum. In a seventh step 114, a measured perfusion signal of the perfused contrast agent in the region of interest is provided. In an eighth step 116, the perfusion signal of the region of interest is deconvolved with the perfusion sum. In a ninth step 118, the deconvolution result is provided.

[0057] Deconvolving is also referred to as deconvoluting.

[0058] In one example, extracting a region of interest is also referred to as defining a region of interest.

[0059] In one example, the blood supply section is defined as a border region having a predetermined thickness.

[0060] Optionally, the region of interest is first defined / extracted and the blood supply sections are defined as adjacent boundary sections.

[0061] In another option, the blood supply section is first defined / extracted, for example as a boundary section or boundary layer, and the region of interest is defined as an adjacent region, ie an area that contacts the blood supply section.

[0062] According to one exemplary method, the measured contrast agent concentration signal is normalized to a perfusion kernel by deconvolution.

[0063] According to another example of the method, not shown in detail, the deconvolution includes generating a result in the form of at least one of the group consisting of parameters and curves. Further, the result is provided for clinical evaluation, and preferably the result is displayed.

[0064] In one example, for a 2D angiogram, a sequence of 2D contrast-injected x-ray images of the region of interest is provided, and a non-contrast mask image of the region of interest is subtracted from each of the sequence of 2D contrast-injected x-ray images to generate the 2D angiogram.

[0065] The blood supply section may also be referred to as the blood supply area, the blood supply boundary, or a section of the blood supply.

[0066] In a further example of the method, for identification, i.e. for the purpose of identification, blood inflow and outflow are detected, i.e. determined, for the detected blood vessels.

[0067] The blood inlet is also called the blood inlet.

[0068] In one example of a method, not shown in detail, identification of vessels with inflow extracts the arterial input function for each angiogram. Further, AIF extraction is provided covering regions of the image plane within the foot silhouette, hand silhouette, or head silhouette.

[0069] In one example method, the AIF covers all entrances to the perfusion ROI. Optionally, the AIF ignores all exits.

[0070] In one example, "ignored" means that they are not taken into account when calculating the AIF, i.e. only vessels that drain into the ROI are considered. Outlets are not a subset of the blood supply section.

[0071] Another option is that outputs, e.g. arteries but not veins, are not ignored, i.e. taken into account. As an example, the outlets are subtracted since they bypass the perfusion region of interest (but are not relevant for the ankle scenario, since only veins return).

[0072] In a further example, the time delay between the inlets and outlets of large vessels in the region of interest is taken into account by utilizing the detected large vessel connections in the region of interest, and it is known which inlets and which outlets (in sum) pass through the region of interest without flowing into it. Optionally, a (temporal) correlation between the inlet and outlet curves is provided to identify the time shift and correct it before subtraction. This shift is small at clinical frame rates in large vessels and is only measurably impaired in severely diseased patients.

[0073] In one example, the region of the AIF extraction needs to cover only the region of the image plane that is within the silhouette of the foot.

[0074] In one example, the defined blood supply section is provided as an arterial input function for the perfusion region of the region of interest.

[0075] This definition is also referred to as selecting a blood supply section.

[0076] In one example method, the blood supply section is provided as a boundary layer surrounding an area as a region of interest.

[0077] In one example method, the blood supply section is provided as a convex form surrounding the region of interest.

[0078] By way of example, a blood supply section having one of the following shapes is provided: circular, elliptical or oval, square, rectangular, and polygonal.

[0079] According to one example method, starting from a defined blood supply section, increasing subportions are determined and an approximation index is provided to reflect possible ambiguity due to increasing distance of the perfused portion from the blood supply section.

[0080] A sub-portion may also be referred to as a sub-volume, a sub-quantity, or a sub-portion.

[0081] In one example method, a blood supply section is provided at the lower end of the tibia, perpendicular to the longitudinal axis of the tibia.

[0082] In one example, the sub-portions are provided to increase in the distal direction.

[0083] 4a and 4b show a first example of the extraction of the arterial input function.

[0084] Fig. 4a shows the option of arterial input function region extraction. Fig. 4a shows a 2D x-ray perfusion image 200 of an anatomical structure 202, e.g., a foot. The 2D x-ray perfusion image 200 shows vascular structures 204 within the silhouette of the foot. The arrows 206 indicate providing a mask for large vessel candidates.

[0085] FIG. 4b shows, as an example, that the AIF region 208 of any user-defined perfusion region of interest (ROI) is found by morphologically extending the user-defined ROI to obtain a thin border region 210 (patterned) for AIF extraction. Thus, no prior anatomical knowledge of the inlet flow direction is exploited. Rather, inlet extraction requires comparing the detected flow gradient of the vessel fragment within the border region 210 with a reference vector 212 perpendicular to the outer edge of the perfusion ROI 210 (e.g., determined by fitting a cubic spline to the edge pixels of the ROI).

[0086] 5a and 5b show a second example of the extraction of the arterial input function.

[0087] FIG. 5a shows a 2D x-ray perfusion image 212 of an anatomical structure 214, e.g., a foot. The 2D x-ray perfusion image 212 shows a vascular structure 216 within the foot silhouette. FIG. 5a shows the option of arterial input function region extraction. Using knowledge of the foot anatomy, the module first detects a fiducial point 218 at the condyle of the lower end of the tibia and the pose of the tibia (cross and arrow 222), then constructs the AIF region (patterned region) as a small stripe 224 perpendicular to the tibia and masked by the foot silhouette. Suitable perfusion regions 226, 228, 230 (further patterned, e.g., dotted or shaded regions) where the AIF meets all the required criteria are generated by morphologically enriching regions within the foot silhouette seeded in the AIF region. The resulting perfusion kernels after deconvolution are displayed for different enrichment conditions.

[0088] 5b shows an x-ray image 232 of a foot 234 to identify the lower end of the tibia, indicated by contour lines 236. Dotted lines 238 indicate the spatial shift in location from the x-ray image 232 to the perfusion image 212.

[0089] Stripes 224 are provided to identify vessel segments 242, 244 within this region or layer that supply the perfusion region, as indicated by small feeding arrows.

[0090] The twisted arrow 240 indicates the morphological increase in area within the silhouette of the foot.

[0091] Figure 6 shows an example of a graph with a curve 250 of the determined perfusion in the selected region of interest of Figure 5a. The vertical axis 252 represents the associated arterial input function and the horizontal axis 254 represents time.

[0092] Figure 7 shows a graph with different curves for different kernels for a region of interest. A first curve 260 shows the kernel for the first region of interest 226 of Figure 5a. A second curve 262 shows the kernel for the second region of interest 228 of Figure 5a, and a third curve 264 shows the kernel for the third region of interest 226 of Figure 5a.

[0093] Figure 8 shows an example of increasing the effective perfusion region of interest for the example of Figure 5a, i.e. the second option of AIF region extraction. A first region of interest 270 is shown with light grey values. A second region of interest 272 is shown with medium grey values ​​and a third region of interest 274 is shown with darker grey values.

[0094] 8, a first region of interest 270 is provided as a strip. A second region of interest 272 is provided as a much smaller strip. The remaining region, i.e., a third region of interest 274, is much larger.

[0095] 8, the first region of interest 270 is again provided as a band. However, the second region of interest 272 is also provided as a small band. The remaining region, i.e. the third region of interest 274, is still quite large.

[0096] In the third portion from the top of Figure 8, a first region of interest 270 is again provided as a band. However, a second region of interest 272 is provided that extends from the band of the first region of interest 270 and is larger. A third region of interest 274 is still larger.

[0097] 8, a first region of interest 270 is still provided as a swath, however a second region of interest 272 is provided as a larger area and a third region of interest 274 is slightly smaller.

[0098] In this way, augmented regions are provided that are treated as distinct, as an example, because the interpretation of the perfusion signal associated with a fed region becomes more ambiguous the further away from the fed region.

[0099] Fig. 9a shows a first example of a mask image for the perfusion image shown in Fig. 9b. Fig. 9a shows an exemplary segmentation of the vasculature. As an example, a single DSA frame 280 is provided at a time marked by vertical bar 282 in Figs. 10 and 11. The AIF region 284 is marked with a first pattern and includes a large vessel portion indicated by reference number 286. A large vessel segmentation 288 is provided for the entire frame time, as marked by vertical bar 282. The large vessel response 290 in the AIF (see Fig. 10) and the microvascular response 292 of the remaining part of the foot (see Fig. 11) are shown.

[0100] Fig. 12a shows an exemplary segmentation of the vasculature. As an example, a single DSA frame 300 is provided at a time marked by vertical bar 302 in Figs. 13 and 14. The AIF region 304 is marked with a first pattern and includes a large vessel portion indicated by reference number 306. A large vessel segmentation 308 is provided for the entire frame time, as marked by vertical bar 302. The large vessel response 310 in the AIF (see Fig. 13) and the microvascular response 312 of the remaining part of the leg (see Fig. 14) are shown.

[0101] FIG. 15a shows an example of the entrance extraction module of the example of FIG. 9a as a binary mask 320 with components.

[0102] FIG. 15b shows a digital subtraction angiography (DSA) maximum intensity projection (MIP) image related to FIG. 15a.

[0103] FIG. 15c shows the Hough transform being used to detect lines, i.e., vascular components, within the binary global mask.

[0104] FIG. 15d shows an example where each of the final components is subjected to an individual comparison with the reference flow vector to detect the set of inlet components.

[0105] Using time as the third dimension, connected components 322 of the macrovasculature are detected within the AIF region (e.g., as shown in Figure 15a, Figures 9a, 9, 12a, and 12b as a binary mask with four components).

[0106] Figure 15b shows a DSA MIP image 324 masked by the binary mask of Figure 15a. Due to the nature of 2D angiographic projections, vessels of different flow components still overlap, i.e. form a single connected component, due to the loss of depth information.

[0107] Figure 15c shows that the Hough transform is used to detect lines 326, i.e., vascular components, in the binary global mask. Each line represents a peak in Hough space, and by filtering this set of lines to those that are most dissimilar and assigning mask pixels to the closest lines, even seemingly connected flow components can be separated.

[0108] Figure 15d shows an example where, to detect a set of inlet components, each of the final components is subject to an individual comparison 328 with a reference flow vector 330. The flow vector for each component is approximated by the average optical flow response in the corresponding region (right).

[0109] 16 shows an example of a graph showing the AIF during the deconvolution process. The horizontal axis 350 shows time in frames. The vertical axis 352 shows the AIF. The first curve 354 relates to the original AIF signal during preprocessing. The second curve 356 relates to the smoothed and resampled AIF signal during preprocessing.

[0110] 17 shows a graph illustrating the perfusion signal and the perfusion kernel. The horizontal axis 360 shows time in frames. The vertical axis 352 shows the AIF. The first curve 364 relates to the original AIF signal during pre-processing. The second curve 366 relates to the smoothed and resampled AIF signal during pre-processing.

[0111] 18 shows curves for application of a Fast Fourier Transform (FFT) based Wiener deconvolution for various values ​​of the regularization parameter λ. The horizontal axis 370 shows time in frames. The vertical axis 372 shows the estimation kernel versus the maximum estimation kernel. A number of curves 374 are shown for parameter λ values ​​of, for example, 0.01, 0.025, 0.05, 0.075, 0.1, 0.2, or 1.0.

[0112] 19 shows the reconstructed signal after using FFT-based Wiener deconvolution for various values ​​of the regularization parameter λ. The horizontal axis 380 shows time in frames, and the vertical axis 382 shows the signal scaled to 0, 1. Again, a number of curves 384 are shown for parameter λ values ​​of, for example, 0.01, 0.025, 0.05, 0.075, 0.1, 0.2, or 1.0. Additionally, an input signal curve 386 is also shown.

[0113] 16-19 show an example of the deconvolution process. The plots show the AIF and perfusion signal after using (as an example) an FFT-based Wiener deconvolution, as well as the perfusion kernel and reconstructed signal, for various values ​​of the regularization parameter λ (lambda).

[0114] 20 shows that the visualization of the perfusion analysis results via the perfusion kernel is comparable to other patient angiograms and can therefore be exploited for outcome prediction or diagnosis. The curve 390 is provided with indicators 392 for the individual measurements. The scale 394 (healthy vs. diseased) is provided with marks 396.

[0115] In one example, the deconvolution technique assumes a linear relationship between the AIF and the perfusion signal in the ROI. If this assumption were true for the entire vasculature, the perfusion kernel for a region would be determined even for AIFs that are missing an inlet component (at the expense of the perfusion kernel being defined for this incomplete AIF). However, due to the high probability of nonlinear effects occurring in the entire vasculature, we assume that the AIF is not missing any relevant components and focus only on ROIs in the foot that are not too far from the AIF region, allowing for the assumption of linearity.

[0116] This serves to analyze areas supplied with blood by multiple vessels over a particular section, thus making it possible to rely on 2D image data rather than 3D projection data.

[0117] Although large vessel perfusion can be detected by visual angiography, there is also information related to large vessel perfusion that is beyond the resolution limit of digital subtraction angiography, such as microvascular perfusion, e.g., capillaries, arterioles, and venules.

[0118] In one example, angiograms are provided as a sequence of 2D X-ray images (frames) for AIF extraction. Additionally, user-defined regions of interest (ROIs) are provided for perfusion analysis. First, the proposed algorithm determines a suitable AIF region (e.g., in an AIF region extraction module). Second, a segmentation module extracts the region occupied by major vessels (as opposed to microvessels, whose vascular network cannot be resolved at the angiogram resolution) in each frame. Third, an inlet extraction module distinguishes between vessels involved in inflow and outflow. Finally, a deconvolution and analysis module calculates a standardized perfusion kernel according to one of many established methods and, in some cases, extracts parameters from this curve. The curves and parameters are then presented to the user for clinical evaluation. To be comparable between patients (region by region), the parameters are illustrated in a population context, for example, by using individual markers in the population distribution, a color bar that maps the closeness of the parameters to those of the diseased subpopulation to colors.

[0119] In one example, during a perfusion-related intervention, an upstream vascular occlusion or stenosis is identified and treated to improve blood supply to the foot, where symptoms of perfusion dysfunction appear first, followed by ischemia and hypoxia. The vascular system of the foot does not usually change morphology due to treatment, but the behavior of the system does. After the intervention, different input pathways to perfuse the foot are balanced and used in a different way than in the pre-intervention environment. As a result, the proportion and timing of blood reaching different sub-regions of the foot changes, which changes the measured dynamics. In addition, these dynamics also depend on the contrast injection protocol. Therefore, the measured contrast concentration signal is normalized with respect to the arterial input signal to the foot, which is usually formed by the superposition of the supply from multiple arteries, e.g., ATA (anterior tibial artery), PTA (posterior tibial artery), PEA (peroneal artery). Especially in the case of critical limb ischemia (CLI) patients, even these inlet features become highly complicated with morphologically altered vascular trees, total occlusions, neovascularization, and side branches, which the proposed solution addresses.

[0120] In one example, the automated extraction of AIF regions specific to each selected perfusion ROI can be easily tested by deconvolving the raw perfusion ROI signal, since it is readily available in the perfusion kernel provided by the algorithm: when using a global AIF, the signal does not change with the selection of different ROIs.

[0121] The proposed solution can be generalized, at least in part, to 3D perfusion analysis and is therefore applicable to any type of perfusion analysis, such as MRA, CTA, or X-ray angiograms. In particular, the solution is specialized for 2D peripheral angiograms and further specialized for perfusion analysis based on interventional data.

[0122] The proposed solution is an enabler for comparing extracted perfusion features within or between patients and is therefore essential if we aim to predict clinical endpoints such as long-term treatment outcomes. The standardization of perfusion measurements achieved by this solution is also a key enabler for correlating angiography-based perfusion measurements with other measurement approaches of hemodynamic properties that do not depend on contrast agents, such as iPPG (imaging photoplethysmography).

[0123] By considering the delivery to the region of interest, i.e. the input region, confounding factors of the TDC shape can also be taken into account. Examples of influences taken into account by considering the delivery region are the contrast injection protocol, i.e. the bolus volume and injection rate, or the variations during the passage of the injected bolus wave through the lower leg, which includes ATK / BTK (above knee / below knee) lesions (the bolus is split into several components at the bifurcation depending on the lesion / intervention, resulting in different delays before reaching the leg, resulting in the so-called contrast race). These confounding factors prevent a valid comparison between cases of pre- and post-intervention recordings, and also with other patients when setting the current measurements in the context of a patient population, but the proposed solution overcomes this, at least in part.

[0124] By known deconvolution techniques, it is possible to "normalize" the measured signal with respect to the input signal. More formally, the measured input signal, the AIF associated with a particular region, and the measured signal S within the ROI Ω are Ω A linear relationship between is assumed in the form of a convolution,

number

[0125] In one example, first, the user ROI boundary is defined not to intersect with any entrance / exit. The user is notified or provided with a user ROI to find a suitable supply area and to grow the ROI until the entrance is included. Optionally, the TDC can be calculated from the small ROI, but the supply area is extracted as the boundary of the expanded ROI.

[0126] In one example, not shown in detail, the steps of region extraction, segmentation and inlet extraction are provided by modules. As an example, an inlet extraction module is provided. Independent of the approach used to extract the AIF region, the large vascular components found within this region include arteries and veins that conduct blood in different directions. The inlet extraction module separates the inflow and outflow of perfusion into the region of interest, thus ensuring a valid AIF.

[0127] In one example, venous and arterial outlets (i.e. bypasses) are differentiated and also detected via macrovascular connectivity within the region of interest. This segmentation described above is suitable when only the microvascular portion of the ROI curve is deconvoluted.

[0128] As a further example, an AIF region extraction module is provided. Given a leg angiogram, this module identifies suitable AIF regions for a given perfusion ROI that meet the above criteria. The present invention proposes two different options, as further explained above. See also Figures 4a and 4b, and 5a and 5b.

[0129] As another example, a segmentation module is needed to segment the macrovascular system for each frame of the DSA sequence. Using this micro / macro partitioning, the microvascular and macrovascular TDCs can be calculated as input of the AIF (partial macrovascular response in the constructed AIF region). Depending on the clinical application, the total TDCs in the selected perfusion ROI can be obtained as the deconvolved signal or its micro / macrovascular components. In the latter case, this segmentation module is also used to separate the two components of the perfusion ROI. Figures 10 and 11 as well as Figures 13 and 14 show examples of macrovascular responses in the AIF region (Figures 11 and 13) and microvascular responses in the rest of the foot (Figures 12 and 14). The vertical bars mark the time at which the left frame is plotted. The macrovascular segmentation is indicated by a straight line. The segmentation module is realized by a data-driven segmentation algorithm that is trained, for example, on the DSA MIP and the ground truth of its vessel segmentation. Since it is impractical to manually obtain ground truth for each frame, the model is transferred single frame during deployment.

[0130] In the first option, for any user-defined perfusion ROI as illustrated in Fig. 4a, the valid AIF region is constructed by morphologically extending the perfusion ROI to obtain a small marginal ROI for extracting the AIF. Since there is no single reference vector for the comparison of inflow vectors, a reference vector needs to be calculated locally taking into account the outer contour of the perfusion ROI. In one example, the outer edge of the ROI is detected, for example using a Canny edge filter, and a cubic spline contour is fitted through the edge points. For each point on this spline, a vector orthogonal to the contour is calculated and used as a local reference vector for determining the inlet component.

[0131] In the second option, a different approach is provided. A possible choice for the AIF region in a peripheral angiogram is the ankle region where all major blood vessels enter the foot. As illustrated in Fig. 5a, such an ROI can be constructed by first detecting the condyles at the lower end of the tibia and a direction vector resembling the longitudinal extent of the tibia. This can be achieved by using standard template matching algorithms or data-driven learning algorithms trained for landmark or contour detection. Given this reference point and the direction vector, the ROI can be constructed by generating a small stripe of pixels as a thick line orthogonal to the direction vector. The striped region is constrained by a binary mask of the foot silhouette, which can be extracted by one of many established 2D segmentation algorithms.

[0132] A benefit of this option is that it allows exploiting prior anatomical knowledge since the direction vector can be directly used as a single reference vector for the arterial inflow at the ankle against which the flow gradients of the detected candidates can be compared.

[0133] A valid perfusion ROI can be constructed by augmenting the region using morphological dilation (see Figure 8) within the silhouette of the seeded paw in the AIF stripe. This limits the range of perfusion regions in which this approach can be used if comparability with other patients needs to be maintained. It also assumes the absence of retrograde reflux from the forefoot, so it is only an approximation for some severely diseased patients.

[0134] It should be noted that if the analysis is limited to a single patient (e.g., pre-intervention vs. post-intervention comparison), this technique can also be used for any perfusion ROI. In this case, the real impulse response of the system is not calculated, but the impulse response of a virtually non-existent system is calculated (because no components of the AIF inflow reach the selected perfusion ROI). However, the comparison within a single patient is still valid if the interventional therapy does not directly affect the foot region and the assumption of linearity holds for the inflow, i.e., the magnitude of the outflow of the AIF subcomponents (e.g., ATA, PTA, peroneus) changes linearly with the overall input (e.g., if the overall input doubles, all subvascular components will also double).

[0135] The first step uses the binary macrovasculature map over time to extract connected components that lie within the AIF region. Figure 15a illustrates the components plotted as MIPs over time. This results in a set of binary submasks (Figure 15b), one for each component being investigated. Due to the nature of 2D angiographic projections, vessels with different flow directions still overlap in the 2D imaging plane due to the loss of depth information. They form a single connected component even though they are separate in the 3D world coordinate space and / or even show different directions of flow.

[0136] The Hough transform can be used to detect lines (see Figure 15c), i.e. vascular subcomponents within the binary overall mask. Each line represents one peak in Hough space. Filtering the set of lines in Hough space to the most dissimilar candidates results in a set of abstract vascular prototypes. Each mask pixel can be assigned to the closest line prototype to form as many submask components as there are lines in the set. Thus, even seemingly connected flow components can be separated.

[0137] Each of the final components is then subject to individual comparison with the reference flow vector to detect the set of entrance components. The flow vector for each component can be approximated by the average optical flow response of the corresponding region after spatially smoothing the DSA sequence (see Fig. 15d). When the fluoroscopy frame rate is too low compared to the flow velocity of the contrast medium to accurately determine the local flow direction, video frame interpolation techniques are utilized as a pre-processing step.

[0138] The component-by-component flow vector is compared to a local reference flow vector using a dot product and testing a specific angle range that excludes outward or tangential flows.

[0139] After constructing the AIF signal by superimposing the relevant single vascular components, the measured perfusion signal can be deconvolved based on any of the established regularized deconvolution methods (SVD-based, FFT-based, iterative, etc.). The resulting perfusion kernel can be used to either qualitatively judge perfusion or to extract parameters after fitting a perfusion model such as a gamma-variate curve.

[0140] The latter fitting becomes more appropriate after deconvolution, because the signal to be fitted is no longer composed of a set of delayed components, and their superposition leads to a curve shape that is far from the model, and the fitting error of the model strongly depends on the disease state. Figure 16 shows an example of an AIF, a perfusion signal (Figure 17), and the reconstructed signal after using a perfusion kernel (Figure 18) and FFT-based deconvolution (Figure 19).

[0141] From this example, it can be inferred that several parameters characteristic of the perfusion of a selected ROI can be derived from the estimated perfusion kernel. In particular, the peak time can be used as a standardized measure of the time delay in the AIF region and the perfusion of the perfusion ROI. Similarly, the time for the perfusion kernel to decay to half its maximum value serves as a measure of the washout time scale. The average of the (absolute value of) the perfusion kernel over time serves as a standardized measure of the perfusion intensity of a given ROI. Using the first option of AIF region extraction, such parameters can be evaluated for the whole leg by a sliding window approach with respect to the perfusion ROI. The results are visualized as a colored overlay on the angiogram.

[0142] Because parameters are comparable between patients (perfusion region), they are illustrated in a population context, e.g., by using individual markers within the population distribution and a color bar that maps the closeness of the parameter to that of the diseased subpopulation (see Figure 20).

[0143] The first option is referred to as the general approach, the first option is referred to as the primary option, and the second option is referred to as the secondary option.

[0144] The term "subject" may also be referred to as an individual. A "subject" may also be referred to as a patient, although it should be noted that this term does not imply the actual presence or absence of any disease or disorder in the subject.

[0145] In one example, a computer program or program element for controlling an apparatus according to the above examples is provided, which program or program element is adapted to perform the method steps of one of the methods of the above examples when executed by a processing unit.

[0146] Thus, the computer program elements may be stored in one computing unit or distributed among several computing units, which are also part of the embodiments of the present invention. This computing unit is adapted to execute or cause the execution of the steps of the above-mentioned method. It is further adapted to operate the above-mentioned device components. The computing unit is adapted to operate automatically and / or to execute user instructions. The computer program is loaded into the working memory of a data processor. The data processor is thus equipped to execute the method of the present invention.

[0147] Aspects of the invention may be embodied in a computer program product, which is a collection of computer program instructions stored on a computer readable storage device for execution by a computer. Instructions of the invention may be any interpretable or executable code mechanism, including, but not limited to, a script, an interpretable program, a dynamic link library (DLL), or a Java class. Instructions may be provided as a complete executable program, a partial executable program, a modification (e.g., an update) of an existing program, or an extension (e.g., a plug-in) of an existing program. Additionally, parts of the processing of the invention may be distributed across multiple computers or processors.

[0148] As mentioned above, a processing unit, e.g., a controller, performs the control method. The controller may be implemented in numerous ways, with software and / or hardware, to perform the various functions required. The processor is an example of a controller using one or more microprocessors that are programmed with software (e.g., microcode) to perform the required functions. However, the controller may be implemented with or without a processor, as well as a combination of dedicated hardware to perform some functions and a processor (e.g., one or more programmed microprocessors and associated circuitry) to perform other functions.

[0149] Examples of controller components used in various embodiments of the present disclosure include, but are not limited to, conventional microprocessors, application specific integrated circuits (ASICs), and field programmable gate arrays (FPGAs).

[0150] This exemplary embodiment of the invention encompasses computer programs that use the invention from the beginning, as well as computer programs that, through updates, turn existing programs into programs that use the invention.

[0151] Furthermore, the computer program element may provide all the necessary steps for implementing the procedures of the exemplary embodiments of the method as described above.

[0152] According to a further exemplary embodiment of the present invention, a computer readable medium, such as a CD-ROM, is provided having stored therein a computer program element, which is as described by the previous paragraph. The computer program is stored and / or distributed on a suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0153] However, the computer program may also be provided via a network, such as the World Wide Web, and downloaded from such a network into the working memory of a data processor. According to a further exemplary embodiment of the invention, a medium is provided for making it possible to download a computer program element, which computer program element is arranged to carry out a method according to one of the preceding embodiments of the invention.

[0154] It should be noted that the embodiments of the present invention are described with reference to different subject matters. In particular, some embodiments are described with reference to method type claims, and other embodiments are described with reference to device type claims. However, those skilled in the art will understand from the above and following description that, unless otherwise indicated, any combination of features belonging to one type of subject matter, as well as any combination of features related to different subject matters, are disclosed in the present application. However, all features can be combined to provide synergistic effects that go beyond the simple sum of the features.

[0155] While the invention has been illustrated and described in detail in the drawings and the foregoing description, such illustration and description are to be considered as illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the dependent claims.

[0156] In the claims, the word "comprising" does not exclude other elements or steps, and the singular elements do not exclude a plurality. A single processor or other unit fulfills the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be interpreted as limiting the scope.

Claims

1. A data input section; A data processor; and an output interface, said data input receiving a sequence of 2D angiograms and receiving a measured perfusion signal of perfused contrast agent within a region of interest; the data processor extracts the region of interest, defines a blood supply section including a blood inlet to the region of interest and a blood outlet from the region of interest, segments the blood supply section to extract an area occupied by detectable blood vessels, identifies blood vessels involved in inflow to extract blood inlets to the region of interest, sums all blood inlets of the section to provide a perfusion sum, and deconvolves the perfusion signal of the region of interest with the perfusion sum; The device, wherein the output interface provides a result of the deconvolution.

2. The device of claim 1 , wherein the deconvolution normalizes the measured contrast agent concentration signal to a perfusion kernel.

3. The device according to claim 1 or 2, wherein for said identification, the blood inflow and outflow are determined for the detected blood vessels.

4. The device of claim 1 , 2 or 3 , wherein the region of interest of the subject includes at least a sub-region of at least one of the group consisting of the subject's feet, hands and head.

5. The identification of the blood vessels with inflow extracts an Arterial Input Function (AIF) for each of the angiograms; The device according to claim 1 , wherein the extraction of the AIF is provided covering a region of the image plane within a foot silhouette, a hand silhouette or a head silhouette.

6. The device according to claim 1 , wherein the AIF covers all entrances of the perfusion to the region of interest.

7. The device of claim 1 , wherein the blood supply section is provided as a boundary layer surrounding an area as the region of interest.

8. The device of claim 7 , wherein the blood supply section is provided as a convex form surrounding the region of interest.

9. 9. A device according to claim 1, wherein starting from a defined blood supply section, increasing subportions are determined and an approximation index is provided to reflect possible ambiguity due to increasing distance of the perfusion portion from the blood supply section.

10. The device according to claim 1 , wherein the blood supply section is provided at the lower end of the tibia, perpendicular to the longitudinal direction of the tibia.

11. A display is provided, the deconvolution generating a result in the form of at least one of the group consisting of parameters and curves; The device of claim 1 , wherein the outcome is provided for clinical evaluation and displayed on the display.

12. an x-ray imaging device for generating x-ray images of a region of interest, the x-ray images including images with and without a contrast agent injected; A medical imaging system comprising a device according to any one of claims 1 to 11 for peripheral perfusion analysis, A medical imaging system, wherein the X-ray imaging device generates the X-ray images of the sequence of 2D angiograms.

13. receiving a sequence of 2D angiograms; Extracting a region of interest; defining a blood supply section including a blood inlet to the region of interest and a blood outlet from the region of interest; - segmenting said blood supply section to extract areas occupied by detectable blood vessels; - identifying blood vessels involved in the inflow to extract blood inlets into said region of interest; summing all blood inlets of said sections to provide a total perfusion; providing a measured perfusion signal of perfused contrast agent within the region of interest; deconvolving the perfusion signal of the region of interest with the perfusion sum; and providing said deconvolution result.

14. A computer program enabling a processor to carry out the method according to claim 13.

15. A computer-readable medium having stored thereon a computer program according to claim 14.

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