Generate non-contrast enhanced MRT images of the liver
By receiving MRT images showing contrast enhancement of liver blood vessels and healthy liver cells and using prediction models to generate contrast enhancement images, the problem in the prior art is solved that it is difficult to generate contrast enhancement of liver MRT images during the same MRT image acquisition process, and efficient and accurate image analysis is achieved.
Patent Information
- Application Number
- CN202080070311.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2019-10-08
- Filing Date
- 2020-10-05
- Publication Date
- 2025-03-14
- Estimated Expiration
- 2040-10-05
AI Technical Summary
It is difficult for prior art to generate contrast-enhanced liver MRT images during the same MRT image acquisition process, especially after hepatobiliary and dynamic phase image acquisition using contrast agents.
By receiving the first and second MRT images of the examined subject, the contrast enhancement caused by blood vessels and healthy liver cells in the liver through contrast agents, respectively, are shown, using a prediction model (a self-learning algorithm trained by supervised learning, such as an artificial neural network) to predict contrast enhancement caused by contrast agents.
It is realized that the non-contrast-enhanced MRT images of the liver or liver part of the object are generated without changing the original MRT image acquisition process, which improves the accuracy and efficiency of image analysis.
Smart Images

Figure CN114502068B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the generation of artificial MRT images of the liver. The subject of the invention is a method, a system and a computer program product for generating MRT images of the liver without contrast enhancement. Background Art
[0002] Magnetic resonance imaging, also known as MRT or MR (MRI in English), is an imaging method that is particularly used in medical diagnosis to depict the structure and function of tissues and organs in the human or animal body.
[0003] In MR imaging, the magnetic moments of the protons in the examination object are aligned in the basic magnetic field so that there is a macroscopic magnetization in the longitudinal direction. This is then deflected from the rest position by incident radiation of a high-frequency (HF) pulse (excitation). The recovery (relaxation) or magnetization dynamics from the excited state to the rest position is then detected as a relaxation signal by one or more HF receiver coils.
[0004] For spatial encoding, rapidly switching magnetic gradient fields are superimposed on the basic magnetic field. The captured relaxation signals or the detected and spatially resolved MR data are initially presented as raw data in the spatial frequency space and can be transformed into the physical space (image space) by a subsequent Fourier transformation.
[0005] For native MRT, tissue contrast is generated by different relaxation times (T1 and T2) and proton density.
[0006] T1 relaxation describes the transition of the longitudinal magnetization to its equilibrium state, T1 is the time required to reach 63.21% of the equilibrium magnetization before resonant excitation. It is also called the longitudinal relaxation time or the spin-lattice relaxation time.
[0007] Similarly, T2 relaxation describes the transition of the transverse magnetization towards its equilibrium state.
[0008] MR contrast agents exert their effect by modifying the relaxation times of structures that take up the contrast agent. A distinction can be made between two groups of substances: paramagnetic substances and superparamagnetic substances. Both groups of substances have unpaired electrons that induce magnetic fields around individual atoms or molecules.
[0009] Superparamagnetic contrast agents cause a significant shortening of T2, while paramagnetic contrast agents cause mainly a shortening of T1. The shortening of T1 time leads to an increase in signal intensity in T1-weighted sequences, while the shortening of T2 time leads to a decrease in signal intensity in T2-weighted sequences.
[0010] The effect of the contrast agent is indirect, since the contrast agent itself does not emit a signal, but only influences the signal intensity of the hydrogen protons in its surroundings.
[0011] In T1-weighted images, paramagnetic contrast agents result in brighter (higher signal) delineation of areas containing contrast agent compared to areas without contrast agent.
[0012] In T2-weighted images, superparamagnetic contrast agents result in darker (lower signal) delineation of areas containing contrast agent compared to areas not containing contrast agent.
[0013] Both higher signal delineation and lower signal delineation result in contrast enhancement.
[0014] An example of a superparamagnetic contrast agent is iron oxide nanoparticles (SPIO, English: superparamagnetic iron oxide).
[0015] Examples of paramagnetic contrast agents are gadolinium chelates, such as gadopentetate dimeglumine (trade name: etc.), Gadobenate dimeglumine (trade name: ), Gadoteric Acid Gadolinium Gadoteridol and gadobutrol
[0016] Extracellular, intracellular, and intravascular contrast agents can be distinguished based on their diffusion pattern in tissue.
[0017] Contrast agents based on gadoxetic acid are characterized by specific uptake by liver cells, hepatocytes, and by enrichment in functional tissue (parenchyma), and by enhancement of the contrast agent in healthy liver tissue. The cells of cysts, metastases and most hepatocellular carcinomas no longer function like normal liver cells, do not take up contrast agents or take up little or no contrast agents, are not depicted by enhancement and are therefore identifiable and localizable.
[0018] Examples of contrast agents based on gadoxetic acid are described in US Pat. No. 6,039,931 A; they are available, for example, under the trade name or Purchased.
[0019] The contrast enhancement effect of is mediated by the stable gadolinium complex Gd-EOB-DTPA (gadolinium ethoxybenzyl diethylenetriaminepentaacetic acid). DTPA forms a complex with paramagnetic gadolinium ions that has extremely high thermodynamic stability. The ethoxybenzyl (EOB) free radical is a mediator of the hepatobiliary uptake of contrast agents.
[0020] It can be used to detect and characterize tumors in the liver. The blood supply of healthy liver tissue is mainly achieved via the portal vein (Vena portae), while the hepatic artery (Arteria hepatica) supplies most primary tumors. After an intravenous injection of a dose of contrast agent, a time delay between the signal rise of the healthy liver parenchyma and the signal rise of the tumor can be observed accordingly.
[0021] During the distribution period With the contrast enhancement achieved, a typical perfusion pattern is observed that provides information for characterizing the lesion. Delineating the wash-in behavior, wash-out behavior, and vascularization helps characterize the lesion type and determine the spatial relationship between the tumor and the blood vessels.
[0022] In the case of T1-weighted images, It results in a clear signal enhancement in the healthy liver parenchyma 10-20 minutes after injection (in the hepatobiliary phase), while lesions containing no or only a few hepatocytes, such as metastases or moderately to poorly differentiated hepatocellular carcinomas (HCC), appear as darker areas.
[0023] However, blood vessels also appear as darker areas in the hepatobiliary phase, which means that in the MRT images generated in the hepatobiliary phase, it is usually not possible to distinguish between liver lesions and blood vessels based solely on the contrast. The distinction between liver lesions and blood vessels can only be achieved in further MRT images, such as images of the dynamic phase (in which the blood vessels are highlighted), or with the aid of MRT images without contrast enhancement caused by contrast agent. However, if, for example, an MRT image acquisition method that is shortened for the examination object is used, for example if a contrast agent has been administered for a certain time span before the MRT image acquisition to directly acquire MRT images in the hepatobiliary phase and then - after a second administration of contrast agent - to create an MRT image of the dynamic phase, it is no longer possible to create an MRT image without contrast enhancement (original MRT image) in the same MRT image acquisition process. Summary of the invention
[0024] The invention solves this problem by the subject matter of the independent claims. Preferred embodiments of the invention are found in the dependent claims, in the description and in the drawings.
[0025] In a first aspect, the present invention provides a method comprising the following steps:
[0026] - receiving at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent,
[0027] - receiving at least one second MRT image of the same examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0028] - feeding the received MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject, in which blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, and based on an MRT image of the same liver or the same part of the liver of the same examination subject, in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0029] - receiving one or more predicted MRT images from the prediction model, the one or more predicted MRT images showing the liver or a portion of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0030] - displaying and / or outputting the one or more predicted MRT images and / or storing the one or more predicted MRT images in a data storage medium.
[0031] The present invention also provides a system, comprising:
[0032] Receiving unit,
[0033] control and computing units, and
[0034] Output unit,
[0035] the control and computation unit is configured to cause the receiving unit to receive at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent,
[0036] the control and computation unit is configured to cause the receiving unit to receive at least one second MRT image of the examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0037] the control and computation unit is configured to predict one or more MRT images based on the received MRT images, the one or more predicted MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0038] The control and calculation unit is configured to cause the output unit to display the one or more predicted MRT images, to output the one or more predicted MRT images or to store the one or more predicted MRT images in a data storage medium.
[0039] The invention also provides a computer program product comprising a computer program, the computer program being loadable into a memory of a computer, wherein the computer program causes the computer to perform the following steps:
[0040] - receiving at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent,
[0041] - receiving at least one second MRT image of the same examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0042] - feeding the received MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, and based on an MRT image of the same liver or the same part of the liver of the same examination subject, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0043] - receiving one or more predicted MRT images as output of the prediction model, the one or more predicted MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0044] - displaying and / or outputting the one or more predicted MRT images and / or storing the one or more predicted MRT images in a data storage medium.
[0045] The present invention also provides the use of the contrast agent in an MRT method, wherein the MRT method comprises the following steps:
[0046] - administering the contrast agent, which diffuses in the liver of the subject being examined,
[0047] - generating at least one first MRT image, which shows the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by the contrast agent,
[0048] - generating the at least one second MRT image, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by the contrast enhancement caused by the contrast agent,
[0049] - feeding the generated MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, and based on an MRT image of the same liver or the same part of the liver of the same examination subject, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0050] - receiving one or more predicted MRT images as output of the prediction model, the one or more predicted MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0051] - displaying and / or outputting the one or more predicted MRT images and / or storing the one or more predicted MRT images in a data storage medium.
[0052] The present invention also provides a contrast agent used in an MRT method, wherein the MRT method comprises the following steps:
[0053] - administering the contrast agent, which diffuses in the liver of the subject being examined,
[0054] - generating at least one first MRT image, which shows the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by the contrast agent,
[0055] - generating at least one second MRT image, which shows the same liver or the same part of the liver, wherein healthy liver cells are depicted by the contrast enhancement caused by the contrast agent,
[0056] - feeding the generated MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, and based on an MRT image of the same liver or the same part of the liver of the same examination subject, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0057] - receiving one or more predicted MRT images as output of the prediction model, the one or more predicted MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0058] - displaying and / or outputting the one or more predicted MRT images and / or storing the one or more predicted MRT images in a data storage medium.
[0059] Also provided is a kit comprising a contrast agent according to the invention and a computer program product.
[0060] The present invention is explained in more detail below without distinguishing the subject matter of the present invention (method, system, computer program product, use, contrast agent used, complete set of components). On the contrary, the following explanation should be applied similarly to all subjects of the present invention, regardless of the context in which they appear (method, system, computer program product, use, contrast agent used, complete set of components).
[0061] If steps are stated in one order in this description or in the claims, this does not necessarily mean that the invention is limited to the stated order. On the contrary, it is conceivable that the steps are also performed in a different order or in parallel with each other, unless one step builds on another step, which absolutely requires that the built-up step is performed subsequently (however, this will be clear in the individual case). Therefore, the stated order is a preferred embodiment of the present invention.
[0062] The present invention generates one or more artificial MRT images of the liver or a part of the liver of the examination object, wherein the one or more MRT images show the liver or a part of the liver without contrast enhancement caused by a contrast agent. The artificial MRT images are created based on MRT images that are all recorded with contrast enhancement caused by a contrast agent. The artificial MRT images can be created with the aid of a self-learning algorithm and simulate an MRT image of the liver or a part of the liver of the examination object without contrast enhancement by administering a contrast agent.
[0063] The "examination subject" is usually a living body, preferably a mammal, very particularly preferably a human.
[0064] A portion of the subject to be examined is subjected to a contrast-enhanced magnetic resonance imaging examination. An "examination region" is also referred to as an image volume (field of view, FOV) and refers in particular to a volume imaged in a magnetic resonance image. The examination region can usually be determined by a radiologist, for example on an overview image (localizer). It goes without saying that the examination region can also be determined automatically, for example on the basis of a selected protocol, as an alternative or in addition. The examination region includes at least a portion of the liver of the subject to be examined.
[0065] The examination region is introduced into a basic magnetic field.
[0066] The contrast agent diffused in the examination region is administered to the examination subject. The contrast agent is preferably administered intravenously (eg, into an arm vein) as a bolus using a weight-based dose.
[0067] A “contrast agent” is understood to mean a substance or a substance mixture, the presence of which in a magnetic resonance measurement leads to a changed signal. Preferably, the contrast agent leads to a shortening of the T1 relaxation time and / or a shortening of the T2 relaxation time.
[0068] Preferably, the contrast agent is a hepatobiliary contrast agent, such as, for example, Gd-EOB-DTPA or Gd-BOPTA.
[0069] In a particularly preferred embodiment, the contrast medium is a substance or a substance mixture with gadoxetic acid or a gadoxetic acid salt as the contrast-enhancing active substance. Very particular preference is given to the disodium salt of gadoxetic acid (Gd-EOB-DTPA disodium).
[0070] The examination region is subjected to an MRT method and in the process an MRT image is generated (measured) which shows the examination region during the examination phase.
[0071] The measured MRT image can be presented as a two-dimensional image, showing a section through the inspection object. The measured MRT image can be presented as a stack of two-dimensional images, each individual image of the stack shows a different section. The measured MRT image can be presented as a three-dimensional image (3D image). For simpler illustration, the present invention will be explained in some places in this specification based on the existence of two-dimensional MRT images, however, it is not desired to limit the present invention to two-dimensional MRT images. For those skilled in the art, it is clear how the described content can be applied to stacks of two-dimensional images and 3D images respectively (for this, see, for example, M.Reisler, W.Semmler:Magnetresonanztomographie (magnetic resonance imaging), Springer Verlag, 3.Auflage, 2002, ISBN:978-3-642-63076-7).
[0072] After intravenous administration of hepatobiliary contrast agents in the form of bolus injections, the contrast agents first reach the liver via the arteries. In the corresponding MRT images, these are depicted by contrast enhancement. In the MRT images, the period during which the liver arteries are depicted by contrast enhancement is called the "arterial phase". The period begins immediately after the administration of the contrast agent and usually lasts 15 to 25 seconds.
[0073] Subsequently, the contrast agent reaches the liver via the liver veins. Although the contrast in the liver artery is already decreasing, the contrast in the liver veins is just about to reach a maximum. The period of depicting the liver veins by contrast enhancement in the MRT image is called the "venous phase". The period may have already begun during the arterial phase and overlap with it. Typically, the period begins 20 to 30 seconds after intravenous administration and usually lasts 40 to 60 seconds.
[0074] After the venous phase comes the "late phase" in which the contrast in the hepatic arteries decreases further, the contrast in the hepatic veins also decreases, and the contrast in healthy liver cells gradually rises. The phase typically begins 70 to 90 seconds after contrast agent administration and typically lasts 100 to 120 seconds.
[0075] The arterial phase, venous phase and late phase are also collectively referred to as the "dynamic phase".
[0076] 10-20 minutes after injection, hepatobiliary contrast agents cause a significant signal enhancement in the healthy liver parenchyma. This period is called the "hepatobiliary phase". The contrast agent is only slowly eliminated from liver cells; therefore, the hepatobiliary phase can last two hours or longer.
[0077] The stated periods are described in more detail, for example, in the following publications: J. Magn. Reson. Imaging, 2012, 35(3): 492-511, doi: 10.1002 / jmri.22833; Clujul Medical, 2015, Vol. 88 no. 4: 438-448, DOI: 10.15386 / cjmed-414; Journal of Hepatology, 2019, Vol. 71: 534-542, http: / / dx.doi.org / 10.1016 / j.jhep.2019.05.005).
[0078] In the present description, a "first MRT image" refers to an MRT image identifying a vessel, wherein the vessel is depicted by contrast enhancement due to a contrast agent. Preferably, the at least one first MRT image is at least one MRT image measured in the dynamic phase. Particularly preferably, in each case at least one MRT image is measured in the arterial phase, in the venous phase and / or in the late phase. Very particularly preferably, in each case one MRT image is measured in the arterial, venous and late phase. Preferably, the at least one first MRT image is a T1-weighted depiction.
[0079] When using paramagnetic contrast agents, blood vessels are characterized by high signal intensities in the at least one first MRT image due to contrast enhancement (high signal description). Therefore, in the first MRT image, those (continuous) structures whose signal intensities are within an empirically determinable range can be assigned to blood vessels. This means that in the case of the at least one first MRT image, there is information about where in the MRT image the blood vessels are depicted or which structures in the MRT image can be attributed to blood vessels (arteries and / or veins).
[0080] In the present specification, the "second MRT image" refers to an MRT image showing the examination area in the hepatobiliary phase. In the hepatobiliary phase, healthy liver tissue (parenchyma) is depicted by contrast enhancement. Therefore, in the second MRT image, those (continuous) structures whose signal intensity is within an empirically determinable range can be assigned to healthy liver cells. Therefore, at least one second MRT image contains information about the location of healthy liver cells depicted in the MRT image or which structures in the MRT image can be attributed to healthy liver cells. Preferably, at least one second MRT image is a T1-weighted depiction.
[0081] The MRT image acquisition of the dynamic phase and the hepatobiliary phase of the liver extends over a relatively long time span. Within the time span, the movement of the patient should be avoided, thereby minimizing the movement artifacts in the MRT image. Long-term movement restrictions may be unpleasant for the patient. Therefore, what is now established is a shortened MRT image acquisition procedure, in which the contrast agent has been applied to the examination object for a certain time span (i.e. 10 to 20 minutes) before the MRT image acquisition, so that the MRT image in the hepatobiliary phase can be directly acquired. Then, after the second dose of contrast agent is applied, the MRT image of the dynamic phase is acquired with the same MRT image acquisition process. Compared with the conventional MRT image acquisition process, the MRT residence time of the patient or the examination object is thus significantly shortened. Therefore, the present invention preferably relates to recording at least one MRT image of the liver or a part of the liver in the hepatobiliary phase after the first contrast agent is applied to the examination object (for the first time), and recording at least one MRT image of the same liver or a part of the same liver in the dynamic phase after the second contrast agent is applied to the same examination object or the first contrast agent is applied for the second time. The first contrast agent is a hepatobiliary paramagnetic contrast agent in this regard. The second contrast agent may also be an extracellular paramagnetic contrast agent.
[0082] The "first MRT image" and the "second MRT image" are fed to a prediction model. The prediction model is a model configured to predict one or more MRT images showing the liver or a portion of the liver of the examination subject without contrast enhancement caused by contrast agent based on the received MRT images.
[0083] In this context, the term “prediction” means that an MRT image showing the same examination region with contrast enhancement due to a contrast agent is used to calculate an MRT image of the liver or a part of the liver of the examination subject showing no contrast enhancement due to a contrast agent.
[0084] Preferably, the prediction model is created by means of a self-learning algorithm in a supervised machine learning process. Learning is achieved by using training data, the training data comprising a plurality of MRT images of the liver or a portion of the liver of the subject in the dynamic phase and the hepatobiliary phase. In addition, preferably, training data created from MRT images of the same liver or a portion of the same liver of the same subject and without contrast enhancement (i.e., generated without the administration of a contrast agent) are also used.
[0085] Self-learning algorithms generate statistical models based on training data during machine learning. This means that instead of simply memorizing examples, the algorithm "recognizes" patterns and regularities in the training data. As a result, the algorithm can also evaluate unknown data. Validation data can be used to test the quality of the evaluation of unknown data.
[0086] The self-learning algorithm is trained by supervised learning, i.e., MRT images with contrast enhancement in the dynamic phase and the hepatobiliary phase are successively submitted to the algorithm, and it is told which MRT images without contrast enhancement are associated with these MRT images with contrast enhancement. Then, the algorithm learns the relationship between MRT images with contrast enhancement and MRT images without contrast enhancement, thereby predicting one or more MRT images without contrast enhancement for MRT images with contrast enhancement.
[0087] Self-learning algorithms trained by supervised learning are widely described in the prior art (see, for example: C. Perez: Machine Learning Techniques: Supervised Learning and Classification, Amazon Digital Services LLC - Kdp Print Us, 2019, ISBN 1096996545, 9781096996545).
[0088] Preferably, the prediction model is an artificial neural network.
[0089] Such an artificial neural network includes at least three layers of processing elements: a first layer with input neurons (nodes), an Nth layer with at least one output neuron (node), and N-2 inner layers, where N is a natural number greater than 2.
[0090] The input neurons are used to receive the digital MRT image as input values. Typically, there is one input neuron for each pixel or voxel of the digital MRT image. There may be additional input neurons for additional input values (e.g., information about the examination region, information about the examination object, and / or information about conditions that prevailed when the MRT image was generated).
[0091] In such a network, the output neurons are used to generate a third artificial MRT image for the first MRT image and the second MRT image.The processing elements of the layer between the input neurons and the output neurons are connected to each other in a predetermined pattern with predetermined connection weights.
[0092] Preferably, the artificial neural network is a so-called convolutional neural network (CNN for short).
[0093] Convolutional neural networks are able to process input data in the form of matrices. This makes it possible to use digital MRT images depicted as matrices (e.g., width × height × color channels) as input data. In contrast, ordinary neural networks (e.g., neural networks in the form of multilayer perceptrons (MLPs)) require vectors as input, i.e., using an MRT image as input, the pixels or voxels of the MRT image will have to be unfolded sequentially in a long chain. As a result, ordinary neural networks, for example, cannot recognize objects in an MRT image independently of the position of the object in the MRT image. The same object at different locations in an MRT image will have completely different input vectors.
[0094] CNNs basically consist of alternating and repeating filters (convolutional layers) and aggregation layers (pooling layers), and finally one or more layers of "ordinary" fully connected neurons (dense / fully connected layers).
[0095] When analyzing sequences (sequences of MRT images), space and time can be considered as equivalent dimensions and folded, for example, by 3D processing. This has been shown in papers by Baccouche et al. (Sequential Deep Learning for Human Action Recognition; International Workshop on Human Behavior Understanding, Springer 2011, pages 29-39) and Ji et al. (3D Convolutional Neural Networks for Human Action Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (1), 221-231). Furthermore, different networks responsible for time and space can be trained and features merged at the end, as described in the publications by Karpathy et al. (Large-scale Video Classification with Convolutional Neural Networks; Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, 2014, pp. 1725-1732) and Simonyan & Zisserman (Two-stream Convolutional Networks for Action Recognition in Videos; Advances in Neural Information Processing Systems, 2014, pp. 568-576).
[0096] A recurrent neural network (RNN) is a series of so-called feedforward neural networks that contain feedback connections between layers. RNNs allow modeling of sequence data by jointly utilizing parameter data through different parts of the neural network. The architecture of RNNs contains loops. A loop represents the influence of the current value of a variable on its own value at a future point in time, because at least part of the output data from the RNN is used as feedback for processing subsequent inputs in the sequence.
[0097] Detailed information can be gleaned from the prior art (see, e.g., S. Khan et al.: A Guide to Convolutional Neural Networks for Computer Vision, Morgan & Claypool Publishers 2018, ISBN 1681730227, 9781681730226).
[0098] The training of a neural network can be carried out, for example, by the back-propagation method. In this respect, the network seeks to map a given input vector to a given output vector as reliably as possible. The quality of the mapping is described by an error function. The goal is to minimize the error function. In the case of the back-propagation method, the artificial neural network is taught by changing the connection weights.
[0099] In the training state, the connection weights between the processing elements contain information about the relationship between contrast-enhanced MRT images and MRT images without contrast enhancement in the dynamic phase and the hepatobiliary phase, which information can be used to predict one or more MRT images, which show the examination area without contrast enhancement and are calculated only by contrast-enhanced MRT images of the examination area.
[0100] A cross-validation method can be used to divide the data into a training data set and a validation data set. The training data set is used for back-propagation training of network weights. The validation data set is used to check the prediction accuracy of the trained network that can be applied to unknown multiple MRT images.
[0101] As already mentioned, further information about the examination object, about the examination region and / or about the examination conditions can also be used for training, validation and prediction.
[0102] Examples of information about the subject being examined are: sex, age, weight, height, medical history, nature and duration and amount of medication already taken, blood pressure, central venous pressure, respiratory rate, serum, albumin, total bilirubin, blood sugar, iron content, respiratory capacity, etc. These can also be collected, for example, from a database or electronic patient file.
[0103] Examples of information about the area examined are: pre-existing conditions, surgery, partial resection, liver transplantation, iron liver, fatty liver, etc.
[0104] It is conceivable that the received MRT images are retrospectively motion corrected before being fed to the prediction model. Such motion correction ensures that the pixels or voxels of the first MRT image show the same examination area as the corresponding pixels or voxels of the second MRT image that is downstream in time. Motion correction methods are described in the prior art (see, for example: EP3118644, EP3322997, US20080317315, US20170269182, US20140062481, EP2626718).
[0105] The present invention provides a system, which can execute the method according to the present invention.
[0106] It is contemplated that the recited units are components of a single computer system; however, it is also contemplated that the recited units are components of multiple discrete computer systems that are connected to each other via a network to transmit data and / or control signals from one unit to another.
[0107] A "computer system" is an electronic data processing system that processes data through programmable computing rules. Such a system usually includes a "computer" and peripheral devices, and the "computer" unit includes a processor for performing logical operations.
[0108] In computer technology, "peripheral devices" refer to all devices that are connected to a computer and are used to control the computer and / or serve as input and output devices. Examples of peripheral devices are monitors (screens), printers, scanners, mice, keyboards, drives, cameras, microphones, speakers, etc. Internal ports and expansion cards are also considered peripheral devices in computer technology.
[0109] Computer systems today are generally divided into desktop PCs, portable PCs, laptops, notebooks, netbooks and tablet PCs as well as so-called handheld devices (eg smartphones); all of these systems can be used to carry out the present invention.
[0110] Input to the computer system is achieved via input devices such as, for example, a keyboard, mouse, microphone, touch-sensitive display, and / or the like.
[0111] The system according to the present invention is configured to receive at least one first MRT image with contrast enhancement in the hepatobiliary phase and at least one second MRT image with contrast enhancement in the dynamic phase, and based on these data and optionally other data to generate (predict, calculate) one or more MRT images showing the examination area (i.e. the liver or part of the liver) without contrast enhancement.
[0112] The control and calculation unit is used to control the receiving unit, coordinate the data and signal flow between multiple units, and process and generate MRT images. It is conceivable that there are multiple control and calculation units.
[0113] The receiving unit is used to receive the MRT image. The MRT image can be transmitted from the magnetic resonance system, or read from the data storage medium. The magnetic resonance system can be a component of the system according to the invention. However, it is also conceivable that the system according to the invention is a component of the magnetic resonance system.
[0114] The at least one first MRT image and the at least one second MRT image and optionally further data are transmitted from the receiving unit to the control and computing unit.
[0115] The control and computing unit is configured to predict one or more MRT images based on MRT images showing the examination region with contrast enhancement in the dynamic phase and the hepatobiliary phase, the predicted MRT images showing the examination region without contrast enhancement. Preferably, a prediction model for calculating the MRT images without contrast enhancement can be loaded into the memory of the control and computing unit. Preferably, the prediction model is generated (trained) by supervised learning with the aid of a self-learning algorithm.
[0116] Via the output unit, the at least one predicted MRT image can be displayed (eg on a monitor), output (eg via a printer) or stored in a data storage medium.
[0117] Another embodiment of the present invention relates to the use of a contrast agent in an MRT method or a contrast agent used in an MRT method, the MRT method comprising the following steps:
[0118] - administering the contrast agent, which diffuses in the liver of the subject being examined,
[0119] - generating at least one first MRT image, which shows the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by the contrast agent,
[0120] - generating the at least one second MRT image, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by the contrast enhancement caused by the contrast agent,
[0121] - feeding the generated MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by the contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject and wherein blood vessels in the liver are depicted by contrast enhancement caused by the contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by the contrast agent,
[0122] - receiving one or more predicted MRT images as output of a prediction model, said one or more predicted MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0123] - displaying and / or outputting the one or more predicted MRT images and / or storing the one or more predicted MRT images in a data storage medium.
[0124] In a preferred variant, the at least one "second MRT image" is generated after the (first) administration of the first contrast agent to the examination subject, and the at least one "first MRT image" is generated after the second administration of the first contrast agent or the administration of the second contrast agent to the same examination subject. This means that, in terms of time, the "second MRT image" defined above is generated before the "first MRT image" defined above. BRIEF DESCRIPTION OF THE DRAWINGS
[0125] The present invention will be explained in more detail below with reference to the accompanying drawings, but it is not intended to limit the present invention to the features or combinations of features shown in the accompanying drawings.
[0126] in:
[0127] Figure 1 The temporal distribution of the contrast agent concentration in the hepatic artery (A), the hepatic vein (P) and the hepatocytes (L) is schematically shown.
[0128] Figure 2 An exemplary embodiment of a shortened MRT image acquisition procedure is schematically shown.
[0129] Figure 3 A preferred embodiment of the system according to the invention is schematically shown.
[0130] Figure 4 An embodiment of the method according to the invention is shown schematically and exemplarily.
[0131] Figure 5 A further embodiment of the invention is shown exemplarily and schematically. DETAILED DESCRIPTION
[0132] Figure 1 The time distribution of the contrast agent concentration in the hepatic artery (A), the hepatic vein (P) and the hepatocytes (L) is schematically shown. The concentration is described in the form of the signal intensity I in the region stated during the magnetic resonance measurement (hepatic artery, hepatic vein, hepatocytes) as a function of time t. After the intravenous bolus injection, the concentration of the contrast agent first rises in the hepatic artery (A) (short dashed line). The concentration passes a maximum and then decreases. The concentration in the hepatic vein (P) rises slower than the concentration in the hepatic artery and reaches its maximum value later (dashed curve). The concentration of the contrast agent in the hepatocytes (L) rises slowly (continuous curve) and only reaches its maximum value at a very late time point ( Figure 1 ). Several characteristic time points can be defined: At time point TP0, the contrast agent is administered intravenously as a bolus. At time point TP1, the concentration (signal intensity) of the contrast agent in the hepatic artery reaches its maximum. At time point TP2, the curves of the signal intensity of the hepatic artery and the hepatic vein intersect. At time point TP3, the concentration (signal intensity) of the contrast agent in the hepatic vein passes its maximum. At time point TP4, the curves of the signal intensity of the hepatic vein and the hepatocytes intersect. At time point TP5, the concentrations in the hepatic artery and the hepatic vein have dropped to a level where they no longer cause a measurable contrast enhancement.
[0133] Figure 2 An embodiment of a shortened MRT image acquisition procedure is schematically shown. In the shortened MRT image acquisition procedure, a contrast agent is first administered (1). After a certain waiting period (e.g. 10 to 20 minutes), the subject is introduced to the MRT (2). Thereafter, the MRT process is started and first an MRT of the liver or a part of the liver in the hepatobiliary phase is performed (3). Thereafter, another intravenous bolus injection is administered to the subject (4) and then directly an MRT of the liver or a part of the liver in the dynamic phase is performed.
[0134] Figure 3 A preferred embodiment of the system according to the invention is schematically shown. The system (10) comprises a receiving unit (11), a control and calculation unit (12) and an output unit (13).
[0135] The control and computing unit (12) is configured to cause the receiving unit (11) to receive at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent.
[0136] The control and computation unit (12) is further configured to cause the receiving unit (12) to receive at least one second MRT image of the examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by the contrast agent.
[0137] The control and computation unit (12) is further configured to predict one or more MRT images based on the received MRT images, the one or more predicted MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by contrast agent.
[0138] The control and calculation unit (12) is further configured to cause the output unit (13) to display the at least one predicted MRT image, to output the at least one predicted MRT image or to store the at least one predicted MRT image in a data storage medium.
[0139] Figure 4 An embodiment of the method according to the present invention is schematically and exemplarily shown. The method (100) comprises the following steps:
[0140] -(110) receiving at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a portion of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent,
[0141] (120) receiving at least one second MRT image of the same examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent,
[0142] -(130) feeding the received MRT image to a prediction model, which has been trained by supervised learning, so as to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent based on an MRT image showing the liver or a part of the liver of the examination subject in which blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent.
[0143] (140) receiving one or more predicted MRT images from the prediction model, the one or more predicted MRT images showing the liver or a portion of the liver of the examination subject without contrast enhancement caused by a contrast agent,
[0144] -(150) displaying and / or outputting one or more predicted MRT images and / or storing one or more predicted MRT images in a data storage medium.
[0145] Figure 5 Another embodiment of the present invention is shown exemplarily and schematically. A first MRT image (1) is provided, which shows the liver or a part of the liver of an examination subject, wherein blood vessels in the liver are depicted by contrast enhancement (signal enhancement) caused by a contrast agent.
[0146] A second MRT image (2) is provided, which shows the same liver or the same part of the liver as the first MRT image, wherein healthy liver tissue (parenchyma) is depicted by contrast enhancement (signal enhancement) caused by the contrast agent.
[0147] The first MRT image (1) and the second MRT image (2) are fed to a prediction model (PM).
[0148] The prediction model (PM) is configured to generate a third MRT image (3) based on the first MRT image (1) and the second MRT image (2), wherein the third MRT image (3) shows an MRT image without contrast enhancement caused by a contrast agent.
[0149] Preferably, the prediction model is created by means of a self-learning algorithm in a supervised machine learning process with a training data set. The training data set comprises a plurality of first MRT images, second MRT images and associated third MRT images, which have actually been recorded, for example before the first intravenous bolus administration of contrast agent.
[0150] In the process of machine learning, a self-learning algorithm generates a statistical model based on the training data. This means that instead of simply memorizing examples, the algorithm "recognizes" patterns and regularities in the training data. As a result, the algorithm can also evaluate unknown data. Validation data can be used to test the quality of the evaluation of unknown data.
[0151] The self-learning algorithm is trained by supervised learning, i.e., the first MRT image and the second MRT image are submitted to the algorithm, and it is told which third MRT images are associated with specific first and second MRT images. The algorithm then learns the relationship between the MRT images, thereby predicting (calculating) the third MRT image for the unknown first and second MRT images.
[0152] Self-learning algorithms trained by supervised learning are widely described in the prior art (see, for example: C. Perez: Machine Learning Techniques: Supervised Learning and Classification, Amazon Digital Services LLC-Kdp Print Us, 2019, ISBN 1096996545, 9781096996545).
[0153] Preferably, the prediction model is an artificial neural network.
[0154] Such an artificial neural network includes at least three layers of processing elements: a first layer with input neurons (nodes), an Nth layer with at least one output neuron (node), and N-2 inner layers, where N is a natural number greater than 2.
[0155] The input neurons are used to receive the digital MRT image as input values. Typically, there is one input neuron for each pixel or voxel of the digital MRT image. Additional input neurons for additional input values (e.g., information about the examination region, information about the examination object, and / or information about the conditions when the MRT image was generated) may be present.
[0156] In such a network, the output neurons serve to generate a third artificial MRT image for the first MRT image and the second MRT image.
[0157] The processing elements of the layer between the input neurons and the output neurons are connected to each other in a predetermined pattern with predetermined connection weights.
[0158] Preferably, the artificial neural network is a so-called convolutional neural network (CNN for short).
[0159] Convolutional neural networks are able to process input data in the form of matrices. This makes it possible to use digital MRT images depicted as matrices (e.g., width × height × color channels) as input data. In contrast, ordinary neural networks (e.g., neural networks in the form of multilayer perceptrons (MLPs)) require vectors as input, i.e., using an MRT image as input, the pixels or voxels of the MRT image will have to be unfolded sequentially in a long chain. As a result, ordinary neural networks, for example, cannot recognize objects in an MRT image independently of the position of the object in the MRT image. The same object at different locations in an MRT image will have completely different input vectors.
[0160] CNNs basically consist of alternating and repeating filters (convolutional layers) and aggregation layers (pooling layers), and finally one or more layers of "ordinary" fully connected neurons (dense / fully connected layers).
[0161] Details can be gleaned from the prior art (see, e.g., S. Khan et al.: A Guide to Convolutional Neural Networks for Computer Vision, Morgan & Claypool Publishers 2018, ISBN 1681730227, 9781681730226).
[0162] The training of a neural network can be carried out, for example, by the back-propagation method. In this respect, the network seeks to map a given input vector to a given output vector as reliably as possible. The quality of the mapping is described by an error function. The goal is to minimize the error function. In the case of the back-propagation method, the artificial neural network is taught by changing the connection weights.
[0163] In the training state, the connection weights between the processing elements contain information about the relationship between contrast-enhanced MRT images and MRT images without contrast enhancement in the dynamic phase and the hepatobiliary phase, which information can be used to predict one or more MRT images, which show an examination area without contrast enhancement and are calculated only from contrast-enhanced MRT images of the same examination area.
[0164] A cross-validation method can be used to divide the data into a training data set and a validation data set. The training data set is used for back-propagation training of network weights. The validation data set is used to check the prediction accuracy of the trained network that can be applied to unknown multiple MRT images.
Claims
1. A method for generating a non-contrast enhanced MRT image of the liver, comprising the following steps: - receiving at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, - receiving at least one second MRT image of the same examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent, - feeding the received MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject and wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent, - displaying and / or outputting one or more predicted MRT images and / or storing one or more predicted MRT images in a data storage medium. 2 . The method according to claim 1 , wherein the at least one first MRT image is a T1-weighted depiction of the liver or a portion of the liver in a dynamic phase after administration of a hepatobiliary paramagnetic contrast agent.
3. The method according to claim 2, wherein the at least one first MRT image is such an MRT image: (i) showing the liver or a portion of the liver of the examination subject in the arterial phase, (ii) showing the same liver or the same part of the liver of the same examination subject in the venous phase, and (iii) The same liver or the same part of the liver of the same examination subject is shown at a later stage. 4 . The method according to claim 1 , wherein the at least one second MRT image is a T1-weighted depiction of the liver or a portion of the liver in the hepatobiliary phase after administration of a hepatobiliary paramagnetic contrast agent or an extracellular paramagnetic contrast agent.
5. A method according to claim 2 or 3, wherein at least one second MRT image is recorded, the at least one second MRT image having a T1-weighted depiction of the liver or a part of the liver in the hepatobiliary phase after the first administration of a hepatobiliary paramagnetic contrast agent to the examination subject, and at least one first MRT image is recorded, the at least one first MRT image having a T1-weighted depiction of the liver or a part of the liver in the dynamic phase after the second administration of the hepatobiliary paramagnetic contrast agent or the extracellular paramagnetic contrast agent to the same examination subject.
6. The method according to any one of claims 1 to 3, wherein the contrast agent is a substance or a substance mixture with gadoxetic acid or a gadoxetic acid salt as contrast-enhancing active substance.
7. The method according to any one of claims 1 to 3, wherein the examination subject is a mammal.
8. The method according to any one of claims 1 to 3, wherein the prediction model is an artificial neural network.
9. The method according to any one of claims 1 to 3, wherein the contrast agent is the disodium salt of gadoxetic acid.
10. The method according to any one of claims 1 to 3, wherein the inspection subject is a human.
11. A system for generating a non-contrast enhanced MRT image of a liver, comprising: Receiving unit, control and computing units, and Output unit, the control and computation unit is configured to cause the receiving unit to receive at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, the control and computation unit is configured to cause the receiving unit to receive at least one second MRT image of the examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent, the control and computation unit is configured to cause the prediction model to have been trained by supervised learning in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject and wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent, the one or more MRT images showing the liver or the part of the liver of the examination subject without contrast enhancement caused by a contrast agent, The control and calculation unit is configured to cause the output unit to display the one or more predicted MRT images, to output one or more predicted MRT images or to store one or more predicted MRT images in a data storage medium.
12. A computer program product comprising a computer program, the computer program being loadable into a memory of a computer, wherein the computer program causes the computer to perform the following steps: - receiving at least one first MRT image of the examination subject, the at least one first MRT image showing the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent, - receiving at least one second MRT image of the same examination subject, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by contrast enhancement caused by a contrast agent, - feeding the received MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject and wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent, - displaying and / or outputting one or more predicted MRT images and / or storing one or more predicted MRT images in a data storage medium.
13. The computer program product according to claim 12, wherein the computer program causes the computer to perform one or more of the steps listed in claims 2 to 10.
14. Use of a contrast agent in an MRT method, the MRT method comprising the following steps: - administering the contrast agent, which diffuses in the liver of the subject being examined, - generating at least one first MRT image, which shows the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by the contrast agent, - generating the at least one second MRT image, the at least one second MRT image showing the same liver or the same part of the liver, wherein healthy liver cells are depicted by the contrast enhancement caused by the contrast agent, - feeding the generated MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject and wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent, - displaying and / or outputting one or more predicted MRT images and / or storing one or more predicted MRT images in a data storage medium.
15. A contrast agent for use in an MRT method, the MRT method comprising the following steps: - administering the contrast agent, which diffuses in the liver of the subject being examined, - generating at least one first MRT image, which shows the liver or a part of the liver of the examination subject, wherein blood vessels in the liver are depicted by contrast enhancement caused by the contrast agent, - generating at least one second MRT image, which shows the same liver or the same part of the liver, wherein healthy liver cells are depicted by the contrast enhancement caused by the contrast agent, - feeding the generated MRT images to a prediction model, which has been trained by supervised learning, in order to predict one or more MRT images showing the liver or a part of the liver of the examination subject without contrast enhancement caused by a contrast agent, based on an MRT image showing the liver or a part of the liver of the examination subject and wherein blood vessels in the liver are depicted by contrast enhancement caused by a contrast agent and based on an MRT image of the same liver or the same part of the liver of the same examination subject in which healthy liver cells are depicted by contrast enhancement caused by a contrast agent, - displaying and / or outputting the one or more predicted MRT images and / or storing the one or more predicted MRT images in a data storage medium.
16. The contrast medium for use according to claim 15, wherein the contrast medium is a substance or a substance mixture with gadoxetic acid or a gadoxetic acid salt as contrast-enhancing active substance.
17. The contrast agent for use according to claim 15, wherein the contrast agent is the disodium salt of gadoxetic acid.
18. A kit comprising a contrast agent according to claim 15 and a computer program product according to claim 12 or 13.
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