A method of MRI calibration and a device for performing the calibration

Abstract

A method for quality assurance of an MRI system under test comprises: scanning a phantom including known materials to obtain scanner data; in dependence on reference data relating to the known materia

Description

The present invention relates to a method of MRI calibration and a device for performing the calibration. The invention also relates to a method of performing MRI quality assurance. Diffusion MRI is a unique medical imaging modality which is sensitive to the overall amount of water Brownian motion in each scan voxel. It has been demonstrated in the research literature to be sensitive to micro-scale changes in the tissue environment. It is therefore a probe of cellular-scale structure and potentially sensitive to changes caused by a variety of pathologies. A key application is prostate cancer, where there is evidence that diffusion measurements can provide information about the presence of tumours. The best current available way to detect and diagnose such matters is with the use of highly invasive biopsy. Diffusion MRI provides a non-invasive alternative. However, reproducibility is a significant challenge to clinical translation. Although the materials aspects are well understood, the use of phantoms to calibrate scanners for diffusion MRI is challenging because of position-dependent distortion and the high sensitivity of any tissue mimic to temperature. The present applicant has developed a phantom which can be placed alongside the patient during a scan, providing a per-patient reference. This system referred to herein as a “Within Image Calibration Device” (WICAD) functionswell. In our nationally copending applications derived from WO2019 / 180464 (PCT / GB2019 / 050837) which discloses the WICAD system, and the entire contents of which are hereby incorporated by reference, there is described a phantom, a method for manufacturing a phantom, a method for obtaining calibrated measurements from non calibrated images using a phantom, a system for obtaining calibrated measurements from non-calibrated images using a phantom, and a coil assembly for use in an MRI scanner. It is explained therein how magnetic resonance imaging (MRI) is one of the most commonly used imaging techniques for medical diagnosis. As a technique it is of huge value because it provides an imaging method which is non-intrusive, and which can provide information about physiological processes occurring in the body as well as detailed images of a patient’s anatomy. MRI works via the application of strong magnetic fields and radio frequency pulses which affect the behaviour of the intrinsic momentum of protons within hydrogen, and other atoms with odd numbers of protons, in the body. Radio frequency signals are emitted as atoms return to their equilibrium state following the application of a pulse of radiation. The speed at which various properties return to this state allows information to be gleaned about the surrounding material, and magnetic field gradients allow the signal to be spatially resolved. By varying the scanner settings, a range of different properties of the scanned tissue can be quantified. Particular examples are described below, some of which make use of two or more images taken in succession. Other imaging methods than those described, such as Arterial Spin Labelling and those using T2* weighting, can be used, depending on the tissue property of interest. T2* weighted dynamic contrast enhanced imaging, known as dynamic susceptibility contrast (DSC), can be used in place of or in addition to the T1 weighted imaging described below, for example. Other quantitative imaging techniques can be used for the quantification of water and fat, based on their difference in T1, T2 and / or resonance frequencies. The spin-lattice relaxation rate, also called T1 relaxation rate, is the most basic contrast in MRI. It represents the time for the induced magnetization to grow to equilibrium once an object is inserted into a magnet, or after an RF selection pulse has been used to produce an image. Importantly, it is also used as the basis of an important procedure to estimate the perfusion parameters into a tissue. In particular, in the case of tumours or tissue with abnormal vasculature, the injection of a T1 -shortening contrast agent, such as a contrast agent based on Gadolinium chelates will result in a sharp increase in a T1-weighted image, indicating the presence of abnormal vasculature and increase in blood volume, as well as more rapid extravasion of contrast agent into the tissue. All these aspects can be measured using a method called Dynamic Contrast Enhanced (DCE) MRI, in which a series of T1-weighted images are acquired continuously through the injection of a contrast agent such as a contrast agent based on Gadolinium chelates for example. These T1 -weighted images are then combined with a reference quantitative T1 measurement of the tissue to measure the increase in tissue perfusion locally. Quantification of the amount of signal changes can be used to infer the abnormal presence of non-well defined vasculature, characteristic of tumour or other lesions. Quantification of this signal change requires calibration of T1 values in the tissue of interest. Diffusion weighted imaging (DWI) is a type of magnetic resonance imaging used to produce a map of, among other parameters, an apparent diffusion coefficient (ADC) in different regions. The principle behind diffusion weighted imaging relies on the fact that a reduction in signal due to application of a pulse gradient in the magnetic field can be directly related to the amount of Brownian motion that is occurring in a particular imaged volume, therefore providing a direct measurement of the diffusion characteristics of water molecules. The main restriction on the diffusion of water molecules within a tissue is due to the presence of intracellular organelles and cell membranes, so that a denser tissue will result in more restricted diffusion than a less dense tissue. This results in a lower ADC in denser areas and is particularly useful in the detection and categorisation of tumours or cerebral infarction for example. The strength of the signal in a particular voxel of a DWI image allows a person operating the scanner to determine the rate of water diffusion in that region or the flux of water molecules across surfaces of the volume, since the strength of the image signal will be inversely proportional to the rate of diffusion. The ADC represents the mean diffusion within a voxel. In non-isotropic tissue, such as but not limited to the brain, the cardiac tissue, or most muscular or orientated tissues, the diffusion characteristics are anisotropic, as the water diffuses at different rates across the fibres and along the fibres. A simple model of diffusion is therefore represented by e.g. a mathematical object called a tensor. The ADC is in these cases sometimes calculated as the sum or average of the diffusion tensor’s diagonal elements (equal to the trace of the tensor) where the diffusion tensor components represent the diffusion rates fitted to a general three-dimensional Gaussian. Methods such as those described above generally quantify the differences between measured signal properties of the MRI images, such asT1, T2 orT2*, or ADC between two or more images taken in series. A measurement of the ADC, for example, requires two images between which the diffusion gradient is varied. Such parameters are a powerful tool for use in medical diagnosis. Methods for analysing MRI images are becoming increasingly more complex, and now involve the application of machine learning. Radiomics, for example, is a computer-based method for image analyses in which many different quantifiable parameters (such as but not limited to the ADC, T1 or T2 relaxation time, and parameters derived therefrom) are determined for each voxel within an image. Patterns of subtle tissue variations within the images can then be analysed algorithmically with the aim to improve the detection of abnormalities within a scanned region invisible to the naked eye. While these methods generally rely on different contrasts and not quantitative measurements, such methods could be vastly improved when used on reproducible or calibrated quantitative imaging methods. As the field of radiomics grows, accurate calibration of the measurements of physical properties derived using MRI will become increasingly more important. MRI, and in particular multi-parametric magnetic resonance imaging (mpMRI), is useful in the detection of abnormalities in a number of tissues and organs, including the prostrate as well as the brain and other soft tissues, tendons, and ligaments. Although mpMRI can be used to detect abnormalities in a variety of tissues, it has been found to be particularly useful in the diagnosis of prostate cancer, for which the term was coined, and which affects a sixth of all men and remains the most common cancer. In 2013 over 47,000 men were diagnosed with prostate cancer in the UK, with 90% of cancers which are detected early on having no associated symptoms. A high level of prostate specific antigen (PSA) in the blood can be an indicator of prostate cancer, however it can also be as a result of infection or inflammation and so is not a particularly reliable indicator. A recent study even revealed that neither is the case that a low level of PSA means a clean bill of health. If a raised level of PSA is detected, a biopsy will usually be recommended. This is an intrusive and uncomfortable procedure for the patient. A biopsy also requires the administration of an anaesthetic and can still result in a false negative since large regions of the prostate may be missed when not used in combination with MRI for planning and preparation. Only fairly recently has it been possible to diagnose prostate cancer using magnetic resonance imaging techniques. Multi-parametric MRI (which quantitative methods may include diffusion weighted imaging and dynamic contrast enhanced imaging based on the shortening of T1 through the passage of a T1 -shortening contrast agent, such as a contrast agent based on chelated Gadolinium) can both localise a tumour and estimate Gleason grade representing the aggressiveness of the cancer, making it a useful supplement to, or replacement for, tissue biopsy. The use of MRI in prostate cancer diagnosis has recently been implemented in revised NICE guidelines in the U.K’s National Health Service (NHS). This technique, however, is still not perfect (around 10 percent of patients with mpMRI negative are underdiagnosed and around 25 percent with mpMRI positive are over diagnosed). More recently, scientists have been working on the use of machine learning to improve the stratification of patients using mpMRI techniques. These methods require quantitative measurements of the signal within both quantitative T1 and Diffusion images to be able to effectively compare scans between patients. This may be possible in a single location using a single scanner, but it cannot at present be rolled-out across multiple centres due to the lack of consistency between measurements taken using different scanners. Although imaging methods, such as DWI, T1, T2, T2*, Proton Density Fat Fraction (PDFF), and arterial spin labelling (ASL) are constantly improving as the capability of the scanners used increases, there is still no consistent way to quantify the parameters measured using these methods. There is a need and desire to provide and enable the derivation of quantitative outputs from MRI machines. In addition, pretty much any measurable parameters including ADC orT1 in particular, and PDFF and T2 / T2* to a lesser extent, are highly dependent on temperature (since clearly motion of the water molecules will be affected by an increase or decrease in temperature, which will affect both diffusion values and potential for relaxation of the signal through the lattice or spin-spin interactions, while the difference in resonance frequencies between the water peak and the multiple fat peaks is also intrinsically dependent on the temperature of the tissue). Accounting for this can be complex and inaccurate. The current applicant’s WICAD system provides an effective way to calibrate MRI scanners for these imaging methods to achieve consistency across multiple centres, which in turn enables the widespread use of quantitative mpMRI to provide precise active surveillance metrics, reduce the percentage of equivocal diagnosis (which may lead to invasive interventions such as biopsy), and reduce the occurrence of under or overdiagnosis. The above benefits will help to reduce associated healthcare costs, conserving valuable funding. Phantoms for use in an MRI scanner are known. DE-A-10 2016 121 212 (HA Imaging GmbH) describes a phantom for deriving the spatial and ADC resolution in diffusion weighted images. The phantom comprises a cylindrical body including different compartments filled with PVP solution or another thickening agent at different concentrations. Since the ADC values of the liquids used are highly temperature sensitive, the phantom can include a thermometer to measure the temperature of the fluid. The ADC value can then be corrected to a reference temperature using calibration curves. CaliberMRI, Inc. advertises a phantom for quantitative MRI diffusion imaging which comprises a plastic sphere containing a number of vials each filled with an aqueous solution of PVP (polyvinyl pyrrolidone) at different concentrations. The vials are held at 0°C during a scan of the phantom using an ice-bath. US-A-2017 / 0184696 again describes a phantom for calibration of diffusion weighted images taken using an MRI scanner and used to calibrate images which track the brain’s fiber network. The phantom comprises a series of hollow tubular polymer fibers filled with a fluid. The phantom is maintained at a constant temperature by way of a temperature controlling fluid which is cycled through conduits next to an inner shell of the device. The National Institute of Child Health and Human Development (the NICHD) has developed a diffusion phantom, described in US patent number 9,603,546, which takes the form of a hollow sphere containing PVP. The PVP is chosen so that it has an ADC value similar to that of human tissue. The phantom includes a chamber containing an aqueous solution including polymers with different molecular weights. The relative proportion of the polymers in solution can be varied to adjust the diffusive properties of the phantom. In an embodiment, the phantom may include two separate chambers and a central reference compartment containing a saline solution which has an ADC very different from that of the solutions in the two surrounding compartments. It is not clear from the description whether the two compartments contain solutions having a different concentration relative to one another, or what substances make up these solutions. A thermometer is provided on the outside of the sphere. The article entitled “High-precision calibration of MRS thermometry using validated temperature standards: effects of ionic strength and protein content on the calibration” (Vescovo et al; NMR Biomed., 2013, 26, (2), 213-223) describes use of a material at a stable temperature to measure the effect of tissue material on temperature using magnetic resonance spectroscopic thermometry, due to the dependence in resonance frequencies on said temperature, as mentioned above. The National Institute of Standards and Technology (NIST) has developed a phantom for standardisation of T1 and T2 images taken of the head using an MRI machine. The phantom contains a number of spheres housed within a larger spherical housing. The same institute has produced a phantom for calibration of MRI imaging of ADC within breast tissue using ports filled with varying concentrations of PVP (this phantom is described in “Design of a Breast Phantom for Quantitative MRI”; Keenan et al; J. Magn. Reson. Imaging 2016). The WICAD phantom and methodology typically operates with a small number of discrete vials of material which provide individual data points that can be used for calibration. However, it has remained a challenge to obtain metrologically sound quantitative outputs from a scan even when using the WICAD phantom. In addition, there is a need for a system to enable determination of the parameters setup of a particular MRI machine based on the distribution of values derived from a particular vial of material used in a test scan. According to a first aspect of the present invention, there is provided a method for quality assurance of an MRI system under test, the method comprising: scanning a phantom including the known materials to obtain scanner data; in dependence on reference data relating to the known materials and the scanner data, identifying error in the scanner data; based on the identified error, determining a quality assurance level for the scanner under test. While such measurements can be made using independent phantoms scanned separately from patients as part of routine Quality Assurance (QA) procedure, the scanner may have deteriorated in the time since that measurement was done. In addition, these QA procedures are cumbersome and costly, taking time on the scanner, and therefore rarely really implemented in clinical practice. In an example, the phantom includes one or more containers with the known materials, and the scan determines a distribution of values of an MRI parameter of the known materials. In an example, the containers are vials and the distribution is of a specified MRI parameter in respect of the material in the vials. In an example, in dependence on the distribution, a signal to noise ratio is determined in respect of the scan. In an example, the method comprises measuring the temperature of the known materials in the phantom whilst a scan is taking place. In an example, the method comprises determining uncertainty in the temperature measurements. According to a second aspect of the present invention, there is provided a method for calibration of a scan in quantitative MRI, the method comprising, in response to the scanning of a patient in an MRI machine and the simultaneous scanning of a phantom in the MRI machine with the patient, in which the phantom includes materials with known MRI properties: determining uncertainty in scan results of the materials with known MRI properties in dependence on knowledge of MRI properties of the material; generating calibration data based on the scan of the material of known properties and the patient including an indication of uncertainty in the scan of the patient. Due to the interactions of the patients and phantoms with the MRI system (including, among others, power settings, RF coil loading, applied rotating magnetic field, receive coil sensitivity, interactions with gradient non-linearities, etc...) the measurement of a phantom separately from a human can provide an indication as to whether the scanner works properly, but cannot be directly used to calibrate it. The proposed method, by scanning both patient and phantom at the same time, enables precisely this. In an example, generation of the calibration data includes evaluation of the temperature of the materials with known properties and uncertainties in the evaluated temperatures. In an example, the temperature is measured using probes that are spatially distributed within the scanner. In an example, uncertainty is calculated in respect of the scan of the patient using numerical methods. In an example, the method comprises evaluating the actual values of an MRI parameter of the materials of known properties, based on the measured temperature. In an example, the method comprises determining an observed value for the MRI parameter as an output of the scan, including uncertainty in the observed value. In an example, the method comprises determining a polynomial function to enable calibration of a scan from an MRI machine. In an example, the calibration function is provided to relate a true parameter value to a corresponding observed parameter value. In an example, the calibration function relates true diffusion to observed ADC values in an MRI scan. In an example, the calibration function comprises polynomial parameters and covariances. In an example, the MRI parameter is selected from the group consisting of apparent diffusion coefficient (ADC), T1, T2, T2*, Tip, T2p, PDFF or any other MRI parameter. According to a third aspect of the present invention, there is provided a method for quantitative MRI, the method comprising: scanning a patient in an MRI machine at the same time, scanning a phantom in the MRI machine with the patient, the phantom including materials with known properties; determining uncertainty in scan results of the materials with known properties in dependence on knowledge of the material properties; generating calibration data based on the scan of the material of known properties and the patient; using the calibration data to determine a quantitative output for one or more MRI parameters of the patient including an indication of uncertainty in the quantitative output. Without proper assessment of the measurement precision, no traceability on any quantification is possible. As such, this method enables delivery of a complete set of measurements, including a value, a unit, traceable to national metrological institutions (such as NPL or NIST), and an indication of the precision of the measure, i.e. the error associated with the measured value(s). In an example, generation of the calibration data includes evaluation of the temperature of the materials with known properties and uncertainties in the evaluated temperatures. In an example, the temperature is measured using probes that are spatially distributed within the scanner. In an example, uncertainty is calculated in respect of the scan of the patient using numerical methods. In an example, the method comprises evaluating the actual values of an MRI parameter of the materials of known properties, based on the measured temperature. In an example, the method comprises determining a polynomial function to enable calibration of a scan from an MRI machine. In an example, the calibration function is provided to relate a true parameter value to a corresponding observed parameter value. In an example, the calibration function relates true diffusion to observed ADC values in an MRI scan. In an example, the calibration function comprises polynomial parameters and covariances. In an example, the MRI parameter is selected from the group consisting of apparent diffusion coefficient (ADC), T1, T2, T2*, T1 p, T2p, PDFF or any other MRI parameter. According to a fourth aspect of the present invention, there is provided a method of reconstructing a weighted MRI images, the method comprising, scanning a subject in an MRI machine; at the same time, scanning a phantom in the MRI machine with the patient, the phantom including materials with known properties; determining uncertainty in scan results of the materials with known properties in dependence on knowledge of the material properties and generating a correction factor based on the scan of the material of known properties; applying the correction factor to the entire image to generate a weighted MRI image corrected for any systematic bias in the data. While simple quantitative MRI data can be used to summarize the characteristics of a tissue, such as ADC in the context of Diffusion MRI, more advanced mathematical models enable derivation of a more complex and precise description of the microstructural characteristics of the tissue. In an example, for Diffusion MRI, methods such as the recently proposed VERDICT (Vascular, Extracellular, Restricted Diffusion for Cytometry in Tumours) scanning technique can be implemented robustly on any scanner based on the reconstructed bias-free diffusion-weighted images. In another example, multiparametric T2 measurements determining Luminal Water Content could also be implemented based on a bias-free reconstruction of the T2-weighted images in a similar manner. According to a fifth aspect of the present invention a computer system or program is provided to execute the steps of method of any of the first to fourth aspects of the invention. An MRI system is provided arranged to be controlled according to any of the aspects of the present invention. The system could comprise a known MRI system or machine including a controller or computer arranged to control it to be used so as to provide a metrologically sound measurement according to any of the earlier aspects of the present invention. In other words the MRI system when run according to the earlier aspect of the present invention functions fully as a measuring machine as opposed to simply as an imaging device. Accordingly, the phantom-based diffusion measurements and their uncertainties are interpolated to a continuous curve to allow determination of values measured in a patient, importantly together with defined errors or uncertainty. Thus, the three requirements of a metrologically sounds quantitative measurement are provided; a value, a unit and the value’s error. The present inventors have recognised that interpolation from a small number of discrete vials of material which provide individual data points to a continuous function that can be used for calibration is highly non-trivial. A calibration function has been created that is sufficiently robust so as to be in line with metrological standards. Accordingly, interpolation has been performed at a level that will satisfy standards authorities and medical regulators. It will be appreciated that a simple curve that expresses a one-to-one relationship between an input and an output variable does not in and of itself supply a measurement result since what is also required is the measurement uncertainty. Hence the present method and system that generates a calibration curve but also provides an indication of uncertainty does enable a true quantitative output from an MRI machine, in a manner not previously thought possible. Embodiments of the present invention will now be described in detail with reference to the accompanying drawings, in which: Figure 1 illustrates a possible location of the phantom housing relative to a patient; Figure 2A shows a perspective view of a diffusion phantom; Figure 2B shows a side view of the diffusion phantom shown in figure 2A with vials shaded to represent the concentration of PVP in the solution within each vial; Figure 3 is broad schematic view of a process for determining quantitative MRI values from an MRI scan; Figures 4 to 8 show, in more detail, stages of the process of Figure 3; and Figures 9A and 9B show schematic exemplary ADC calibration curves; and Figure 10 is a graph for explanation of an inverse image correction process. In Figure 1, a phantom is located above the body as part of a torso pad and might typically be strapped to the patient’s waist to prevent movement relative to the body during scanning. The phantom includes a housing that may be waterproof and designed to contain a phase change material which is used to keep vials within the phantom, at a constant temperature during the scan, as described in more detail below. The phantom is, in this example, also located underneath the patient’s torso. Figure 1 shows a side view of the patient with a phantom strapped around the patient’s middle. This may represent a single pad extending all of the way around the body or two separate pads, one strapped above the body and another positioned underneath the lower back of the patient, and possibly integrated into a table on which the patient can lie during a scan. Without loss of generality, phantoms can be placed within RF coils, patient padding, couch or directly within the main MRI scanner if relevant. The device shown in Figures 2A and 2B comprises 11 vials, however more or fewer vials may be provided to allow for a simpler structure, or for a more accurate calibration, for example two vials at different concentration of a contrast agent I contrast changing mechanism can be provided, or more than 11 vials can be provided. Generally, the number of vials present will be in the range 2 to 15, preferably 8 to 12 to cover a range that is large enough to cover healthy and abnormal tissue at high enough resolution to provide accurate calibration. It will be appreciated that the reference range given of 2 to 15 is merely exemplary and any suitable number can be used. The vial closest to one end of the phantom may contain a solution having the lowest concentration and the vial closest to the other end of the phantom may contain a solution having the highest concentration (as shown in Figure 2B). If this is the case, vial 4a in Figure 2B will contain the weakest solution and vial 4k will contain the strongest solution. Vials in between will contain solutions having intermediate concentrations. Concentrations may be increased between adjacent vials by equal increments in percentage by mass concentration in the solution. Non-linear increments in concentration may also be useful in some circumstances. Logarithmic or exponential increments could be used, for example. T1, T2, and ADC decay (among others) are generally represented by an exponential decay. This means that by using logarithmic-based increments in concentration of material within the vials, a linear change in signal strength between images of the various vials can be achieved. This is more straightforward to deal with in terms of processing. Further description of the phantom will not be included but can be found in coowned International patent application number WO2019 / 180464. It will be understood that with use of an exemplary system such as that shown in Figures 2A and 2B, discrete values for measured parameters can be determined based on MRI scans. In addition, the phantom may incorporate a thermometer (such as a fiber optic thermometer) to track the temperature of the phantom, and in particular of the solutions within the vials. This will help to ensure that the temperature has indeed remained constant throughout the scan. If this is found not to be the case, some correction may be applied to the value of the measured property to account for this change in temperature over the scan time. The system shown and described in WO2019 / 180464 works well. However, there is a desire to enable quantitative measurements to be derived from an MRI machine and to enable calibration of any MRI machine in accordance with metrological standards. The current applicants have recognised that with the introduction of metrologically sound and rigorous techniques it is possible to develop further the innovation of the WICAD technology to provide a mechanism and a system by which metrologically correct quantitative outputs from an MRI machine and scan can be obtained. The discussion herein relates predominantly to obtaining quantitative values for the parameter ADC (apparent diffusion coefficient), but it will be appreciated by the skilled person that the methods are not limited to use in determining values for ADC, but include, say, T1, T2, PDFF and other quantitative MRI (qMRI) data. The present method and system address this need. Figure 3 is schematic view of the system and method used for quantitative MRI measurements. In simple summary, the method 10 requires the measurement and determination 12 of uncertainties in the outputs of an MRI scan, the application 14 of these determined uncertainties to measurements from an MRI machine so as to enable the obtaining of quantitative measurements from a particular scan from a particular MRI machine under test, and subsequently validation 16 to ensure accuracy and correctness of the measurements taken. The method and system described herein is based on the applicant’s recognition of the fact that for a valid quantitative measurement from an MRI machine three things are necessary: a measured value; a knowledge of the uncertainty associated with the measured value and the units of measurement. Of these, determination and quantification of the uncertainties is a significant challenge, given how, in the complex and multi-variable field of MRI measurements, errors or uncertainty can come from numerous different sources. The present system and method provide a means by which error can be calculated and determined in such a way that a metrologically valid quantitative output can be obtain from an MRI scan. The method is not dependent on which particular MRI parameter is being measured. In an exemplary method, in a first step, one or more temperature probes are used together with scanner data to create calibration data. This is done by using temperature probes to estimate temperature of vials in a WICAD-type device and the uncertainty in the temperature. Values of a reference ADC are interpolated to the temperature of the vials in the scanner data. The observed values of ADC can be summarised by their mean and standard deviations. Next based on this data a calibration curve is created relating true ADC to observed ADC. This can be achieved using various numerical and mathematical methods, some examples of which are provided below. Preferably, a polynomial calibration function is determined. The calibration curve can then be used to estimate true ADC corresponding to observed ADC, and importantly provide a value that include data relating to uncertainty in the provided value of estimated true ADC. Each of these steps and processes will be described in greater detail below. A tangible result from the method described herein is the generation of calibration models for an MRI machine and the subsequent use of these models in correcting patient scan values for MRI parameters. These can be used in radiographic assessment of the probability of clinical significance for any identified cancer or abnormal tissue value (e.g. prostate lesion). Description herein will relate largely to ADC. However, it will be understood that the methods are applicable to use with other MRI parameters and are of course not limited to ADC values or indeed the identification of specifically prostate lesions. Importantly, the method incorporates measurement uncertainties, material characterisation and instrumentation error so as to provide a calibration function. An ADC map can be produced for a particular scan and scanner and, importantly, the uncertainty associated with a calibrated value will be calculated and propagated. Thus, ultimately calibrated prostate ADC maps are produced in combination with associated measurement uncertainties. Figure 3 shows the schematic plan of the steps of the method by which a quantitative MRI value can be derived from a scan on an MRI machine. As can be seen, in a broad sense the initial step of the process relies upon the determination and quantification 12 of measurement uncertainty sources. Once the measurement uncertainty sources have been understood and correctly built into any processing of image data, a solution can be derived by which a calibration curve is produced in relation to a particular scan. Importantly the outputs obtained include an indication of error or uncertainty and thus can be relied upon in medical diagnostic, therapeutic or experimental purposes. Validation 16, described below, is preferably performed to validate the model and the output data. Referring to Figure 4, the true diffusion measurements 20 are based on data provided by a recognised meteorological institute such as the NIST, NPL or any other National Measurement Institute. This will include SI traceable calibration, non-ideal pulse sequence, local environment data and data analysis. A problem associated with the determination of a quantitative value from an MRI machine is that for any MRI machine, when a scan is made of a phantom that includes a vial of material, the output provided by the machine will be a distribution of values. This is because each vial of material is made up of plural volume elements (voxels). The three-dimensional volume of the vial can be broken down into a three-dimensional grid and thus define a priority of voxels within the volume of the vial itself. Each voxel within the vial will produce its own individual measurement of a measured value when a scan is performed. When viewed as a complete set of values, the result will be a distribution of values. The distribution enables a user to infer from the reading, a value for the ADC of the vial together with an indication of uncertainty. The uncertainty will be dependent upon the distribution seen in the results and importantly represents an uncertainty or error in the measured value of the parameter in question for that vial. However, the present inventors have recognised that this error can be used to interpret simultaneously imaged volumes from within a patient’s body. Accordingly, it becomes possible to determine the quantitative value for a parameter together with the uncertainty which can be determined based on the determined uncertainty from the vial in question. Accordingly, the benefit of taking a scan and considering the result on a voxelbasis is that an indication of uncertainty can be achieved quickly since effectively what is being done is a large number of measurements are being taken in parallel and the distribution of those results will provide an indication of the measurement uncertainty. This is based on the assumption that the distribution of the material within the vial is uniform and of known composition, which is usually the case. Indeed, it is preferred that this is the case and indeed it usually follows in dependence on the quality of the manufacturing process. In addition to the uncertainty described above with reference to the vials which contain known concentrations of PVP, uncertainty can derive from the measurement 24 and values taken from the patients themselves. Accordingly, the patient who is being scanned, has tissue which also is made up of voxels in an analogous manner to that of the vials. The method and system to be described herein, enables a scan to be made of a patient and for the values to be processed according to the current method and thereby provide a numerical value for a measurement of the MRI parameter such as ADC within a patient together with an indication of the associated uncertainty. As a part of the process, and referring again to Figure 4, the possible uncertainty sources 12 are determined. There are broadly speaking 3 possible sources of uncertainty in an MRI measurement based on a WICAD system. These are the scanner vial measurements 22, the scanner patient measurements 24 and the phantom temperature measurements 26. The example shown relates to an example using 4 temperature probes, although it will be appreciated that any suitable number of probes can be used. To enable assessment and determination of the scanner vial 22 and scanner patient 24 uncertainties data is provided by a recognised metrological organisation (e.g. NIST) in relation to the vial materials also provided by the same organisation. This data, which may be referred to as the true diffusion (batch sample) measurements includes, importantly, the uncertainties associated with those values provided, which can be used in further processing, to be described below. In the schematic view shown in Figure 5, the true diffusion values 20 are provided taking into account a number of parameters and factors such as, SI traceable calibration, non-ideal pulse sequence, the local environment and data analysis. In other words, these four factors are, between them, able to ensure that true diffusion measurements are derived together with the associated uncertainties. Referring to Figure 6, the uncertainties associated with scanner (vial) measurements 22 are shown. They are shown in respect of ADC, but the method applies equally in respect of any MRI parameter. As shown, these are typically dependent on the temperatures of the vials in the scanner and the associated temperature uncertainty. Scanner patient measurements in respect of the same parameter (ADC in this case) are another source of potential uncertainty. Data for individual voxels is derived. Finally, phantom temperature measurements 26 are a source of uncertainty. Branch 12 (in Figure 4) shows all of the uncertainties which the present inventors have recognised are preferably understood and quantified so as to be able to determine calibration data for a scan in question, as will be described in greater detail below. A calibration curve is determined which is applicable to a particular scanner and a particular scan taken with the scanner. Thus, the calibration curve is specific to the scanner, the particular scan taken at a point in time, and the particular patient that is the subject of the scan. The reason that the calibration curve is specific to the scan and the patient in question is that the values for the scanner vial ADC measurements, the scanner patient ADC measurements and the phantom temperature measurement will change between scans. Although the true diffusion measurements (branch 20) will remain constant since it is data derived from NIST, the remaining data changes with each scan and therefore the output calibration curve is scan and patient specific. The calibration curve cannot be reused for a different scan or a different patient. It is simply a tool that is used to determine quantitative measurements for a particular patient for a particular scan at a particular point in time. The calibration curve enables a quantitative measurement to be taken from an MRI machine, and each time a new scan is taken, a corresponding new calibration curve is determined. Looking again at Figure 3, branch 14 is labelled “Solution” because it illustrates schematically the process by which actual numerical values can be achieved for a scan of a patient. This is achieved taking into account the measurement uncertainties 12 associated with a scan. Indeed, the determination and acknowledgment of the uncertainty sources is an important step in the determination of a calibration curve which can be used to provide a numerical observed value of ADC from step 2 (50) in the solution branch 28 (Figure 7). Referring now in greater detail to Figure 7, the solution 28 has three steps. First, a step “0” (46) in which reference data (true diffusion batch sample data (“20” in Figure 4)) and the scanner data (22, 24 and 26 from Figure 4) are used to create calibration data. This is achieved in that, as described above, a determination is made of the phantom’s vials’ temperatures and measurement uncertainties in the measured temperatures. This is typically achieved with the use of multiple temperature probes 34, and preferably also at multiple times 36. Thus, spatial variation and temporal variation in respect of the temperature measurements and uncertainties is derived. With the temperatures measured and having known uncertainties (branches 34 and 36), data from the true diffusion batch sample measurement can be used to determine, at step 38, the true diffusion values for each vial. Based on data from the diffusion (batch samples) measurements 20 and uncertainties described above, and with knowledge of the measured temperatures, true diffusion values can be evaluated for each of the vials. Typically the evaluation of the true diffusion values for each vial is achieved using a Monte Carlo approach 44. Other numerical or statistical methods can also be used. The method can be understood in general terms in the following way: At the point of scanning of a patient, the true temperature(s) of the vials are not known, but a temperature measurement (a value and uncertainty) is obtained, which represents a distribution of possible temperatures. From this distribution and, using this assumed temperature, polynomial model parameters that map the observed ADC (from the scanner) to the NIST-measured diffusion values is determined. This polynomial fitting takes into account the uncertainties from both, for example, by using an Errors-ln-Variables method. A set of model (polynomial parameters) and covariances is produced. This process thus includes two stochastic elements; the vials' temperatures and the polynomial model covariances. A Monte Carlo process is used in that for a given observed ADC value (e.g. a patient measurement) the true diffusion measurement can be obtained by sampling from the stochastic components until a distribution of values is produced that that has converged, i.e. there is no change in the resulting distribution from more sampling. In more detail an exemplary demonstration of the way in which the reference data and scanner data can be used to create calibration data is provided below: The reference data and the scanner data is provided as inputs to create calibration data: Di.c, u(Djc), Sj u(Si), I = 1,...,nv, where Di,c and Si are, respectively, the reference ADC and the observed ADC for the / th vial at the temperature Tc at which the measurements of the vials within the scanner are made. Temperature of the Vials within the Scanner As explained above an important aspect of the present method is that to ensure metrologically sound quantitative measurement can be made using an MRI machine, it is required that that uncertainty with measured parameters is accurately determined and used in any subsequent calculation. To demonstrate one non-limiting way in which this can be done it is assumed in an example that there are P temperature probes, located at different positions within the scanner, and that the pth probe acquires the temperature data: Tpj for p=1,...,P, and I = 1,..,,m. If it is assumed that there is no significant temporal drift in the temperatures measured by each probe, then is an estimate of the temperature measured by the pth probe. If it is assumed there is significant spatial variation in the temperatures measured by the probe compared to the uncertainty of the individual temperatures Tp, then 5 is an estimate of the average temperature within the phantom, and the associated standard uncertainty is If the spatial variation is not significant compared to the uncertainty of the individual temperatures Tp then which assumes the same standard uncertainty u2(Tp) for the temperatures measured by the probes and that those measurements are made independently. The evaluation of u(Tp) depends on the information that is available about the individual temperature measurements. If they are all subject to the same systematic error, perhaps expressed 15 as a “maximum permissible error” E, then in which E is considered as the half-width of a uniform (rectangular) distribution centred on zero. If they are all subject to different random errors with standard uncertainty u(Tpj) then These two expressions are the two extremes constituting overly-optimistic and overly-pessimistic evaluations. Statistical hypothesis testing, including Analysis of Variance (ANOVA), can be used to decide the significance of different effects. Thus the temperatures of the vials in the scanner can be determined in a metrologically valid manner, i.e. including an indication of error. True ADC The true diffusion values are now determined (38) based on the data provided by a recognized institution such as the NIST. For the / th vial, a generic model for Di,c is: Di,c=l(Ti,i„...T^t, Di,i,..., Di,NT,Tc). Two approaches can be implemented for the evaluation of the uncertainty u2 of Di|C. In a first approach, a framework such as that specified in BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Guide to the Expression of Uncertainty in Measurement, JCGM 100:2008, GUM 1995 with minor corrections is followed. This framework, being merely exemplary of course, is based on linearizing the above generic model about the values (estimates) of Dj.i,...,DiNt and Tc and then propagating (exactly) the standard uncertainties associated with these values through the linearised model, e.g. as defined in clause 5 of BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Guide to the Expression of Uncertainty in Measurement - Part 6: Developing and using measurement models, JCGM GUM-6:2020. Assuming that Di,i,...,DijNT and Tc are uncorrelated the following formula can be used to specify uncertainty in the True ADC: where all partial derivatives (also known as sensitivity coefficients) are evaluated at the values (estimates) of Di,i,..., Di^t and Tc. In the second approach, the framework is used as specified in BIPM. IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’ - Propagation of distributions using a Monte Carlo method, JCGM 101:2008. This, alternative, framework uses a numerical approach, and specifically a Monte Carlo approach. The advantages of the approach are that it does not require the explicit calculation of sensitivity coefficients, and it makes no assumptions about the nature of the model, i.e., it is linear or mildly non-linear, or about the nature of the probability distributions for the model output, i.e., that it is Gaussian or approximately Gaussian. The disadvantages of the approach, however, are that it can be computationally expensive, and it requires knowledge of the probability distributions for the model inputs (and not just the variances of those distributions). The Monte Carlo method involves repeating the following steps for r=1 ,...,M: I. Make independent random draws from the probability distributions for Di,i,...,Di,nt and Tc II. Evaluate the measurement model for these random draws to obtain a random draw dr.i.c for Di]C from its (unknown) probability distribution. The (sample) average and (sample) standard deviation of the samples dr,i,Cl provide, respectively, an estimate of Di,c and its standard uncertainty. The framework of “Supplement 1 to the ‘Guide to the Expression” referred to above, which makes fewer assumptions about the measurement problem, can be used to validate the appropriateness of applying the framework of the “Guide to the Expression of Uncertainty in Measurement - JCGM GUM-6:2020, also referred to above. A particular example of a model for Di,0 (corresponding to local linear interpolation) is: If the interval [Ti.k,Ti^i] contains Tc then The choice of a specific scheme depends on the nature and characteristics of the reference data, and so the skilled person will understand that alternatives can be chosen in dependence on the data being operated on. For this example of a model, the partial derivatives of Di,c with respect to Di,k, 10 Di k+i and Tc are given by the following expressions: Thus as result of the processing so far the user has an evaluation of phantom’s 15 vials’ temperatures with measurement uncertainties, i.e. true diffusion values for each vial based on data provided by NIST. To create the calibration data it is now necessary to obtain what are referred to as observed ADC values with corresponding uncertainties which can be correlated with the actual known values determined as described above to generate a calibration function. Observed ADC In one example, for the / th vial, the observed ADC is evaluated (45) as the arithmetic mean (47) of the observed values for the individual voxels, i.e., which has standard uncertainty (49) obtained from It is assumed that the errors in those values are independent and identically distributed, and the errors (and so the dispersion of values for each vial) capture all the influences to be considered and are propagated to the final measurement result On this basis and assuming mi is large enough, by applying the Central Limit Theorem the observed ADC can be characterized by a Gaussian distribution. Thus, a user now has two sets of data, which are the observed ADC values (45) of the vials and also the true ADC values, both with corresponding uncertainties providing the metrologically sound basis for use of the data and for its use in providing a calibration curve that can be used for obtaining quantitative data from the scan in question. It can be seen then that at step 46, observed ADC values for each vial are determined. Calibration data is thus created which associates the reference data and the scanner data. Calibration Curve Accordingly, at step 1 (48 in Figure 7), the calibration data derived at step 46, is used to create a calibration curve relating true diffusion to observe ADC values. The calibration curve referred to is, in essence, a polynomial calibration function that is used to relate true diffusion to observed ADC values. More generally it will be understood that the calibration function relates a true parameter value to a corresponding observed parameter value. A polynomial model is created which includes covariances and enables a determination of the true diffusion value based on an observed ADC value. In other words, as a result of the described process, a numerical output is achieved from the MRI machine which has meteorological basis and can thus be relied upon by practitioners and patients alike to give an indication of a real physiological condition. When traceable calibration values are provided by NIST they correspond to actual diffusion values for the materials in question. However, once these materials are put in vials and then provided within the phantom, the measurements taken by any machine of the vials produce ADC values rather than direct diffusion values. However, when a measurement is made of a patient, ADC values from the patient are taken and with knowledge of the original traceable calibration data in respect of the diffusivity, a modified ADC value can be determined. It is worth bearing in mind that in any biological tissue, it is not possible to get a true diffusion value because the three-dimensional distribution of the substance of the biological sample itself, will never be uniform in the way that a vial of a test material will be. Referring again to branch 48, the exemplary mathematical step that are executed to produce the calibration curve can be varied and any appropriate sequence of steps can be used so as to produce a calibration curve that relates true diffusion to observed ADC. One non-limiting exemplary method for generating a calibration curve will now be described. This step uses the calibration data from step 0 (46, Figure 7) to create a calibration curve defined by estimates a of the parameters of a calibration function with the covariance matrix Va for those estimates. It will be appreciated that what is important in this process is the creation of a polynomial function that can be used to relate the observed ADC values with the true ADC values. This function can in turn be used to determine quantitative outputs from an MRI scan taken at the same time as the data is derived for the true ADC values of the material in the WICAD vials. The description that follows is clearly exemplary and is provided so as to demonstrate at least one way in which this can be achieved. The skilled person will understand that such a method is not limiting. In the context of ISO / TS 28038, the reference ADC at the temperature Tc takes the role of the stimulus variable and the observed ADC at the temperature Tc takes the role of the response variable. They are also termed, respectively, the independent variable denoted by x and the dependent variable denoted by y. Furthermore, the concern here is with the cases where uncertainty information about the calibration data comprises response data uncertainties only, and stimulus and response data uncertainties only. The first of these cases is applied in its own right when the stimulus data uncertainties are zero or small compared to the response data uncertainties, but it is also applied to provide initial parameter values for the treatment of the second of these cases. A polynomial calibration function relating y and x is denoted by pn(x), where n is the degree of the polynomial. It is denoted by pn(x, a) when it is necessary to indicate that it depends on n+1 parameters a = (a0,...,an)T. It is assumed that as regards the calibration function, there is no misspecification of the calibration function, i.e., it can represent faithfully the calibration data accounting for the uncertainty information provided as part of that data. Polynomials are often suitable for representing a smooth curve or data generated from a smooth curve over a given interval. They are extremely flexible in that mathematically a polynomial of an appropriate degree can approximate any smooth (continuous) curve to a given numerical precision. On this basis, the / th point (xi.y) in the calibration data is considered to result from a measurement of the model value Oy?;) that satisfies y = y j v... a) for estimates u of a. Polynomials as calibration functions A general representation of a polynomial calibration function of degree n is p (x sd) =a.4> (X) + ... 4- a <|> ( / ) = h‘ (x) g, ' i 0 0 .7- where ft. — : ), $, (x), • ”, <|> (x)j is a row vector of length n+1. A natural choice for the basis functions r(x) are the monomial basis functions 4>0(4 = 1., 4>t(x) = x ..., 4yfx) = . / . Although this representation works appropriately, it can lead to difficulties with numerical computation and interpretation of the contribution of individual terms. However, these difficulties can be alleviated for polynomials of modest degree by using a representation in terms of monomial basis functions that are expressed in terms of a normalised variable X in the interval [-1 ,+1] where and Xmin and xmax are the smallest and largest values of x to be encountered, such as the smallest and largest values of the stimulus data. A preferred representation for polynomials of general degree is in terms of basis functions that are orthogonal with respect to some discretely or continuously defined inner product. An example of such basis functions are the Chebyshev polynomials. A practical issue with using the Chebyshev representation is that they are only defined for values of x strictly in the interval [Xmin, xm3x] and, when considering a problem with stimulus data uncertainties, it is necessary to set xmin to be strictly less than the smallest value of the stimulus data and xmax to be strictly greater than the largest value of the stimulus data. The limits xmin and xmax will often be set using some heuristic rule, e.g., extending the interval defined by the smallest and largest values of the stimulus values by an amount equal to a proportion of the difference between those values, but it is necessary to monitor that they are set appropriately during the computations in steps 1 and 2 below and possibly re-stat the computations as necessary. For the case here where the polynomial degree is likely to be modest, the use of monomial basis functions expressed in terms of a normalised variable is likely to be adequate. Response Data Uncertainties Two non-limiting examples of the processing of response data (observed patient ADC) will now be provided including determination of the uncertainties. In one, only response data is considered and in another, response and stimulus (NIST reference) data are considered. Response Data Only The input comprises the calibration data in which there are uncertainties associated only with the measured values of the observed ADC (response data). Estimates of the parameters a of the polynomial model pn are obtained by minimising with respect to the model parameters a the objective function where This is referred to as weighted least-squares (WLS) problem: it is a linear least-squares problem that can be solved using standard approaches for solving overdetermined linear equations. The weights w, are set equal to the reciprocals of the standard uncertainties associated with the observed ADC values S, and their inclusion ensures that the variances of we^ are all equal to one. In the case that observed ADC can be characterised by a Gaussian distribution then the solution corresponds to a maximum-likelihood estimator (MLE). Furthermore, in the case that a flat (non-informative) prior is assumed for the parameters then the solution corresponds to a maximum a posterion (MAP) estimator derived from a Bayesian regression analysis. Denoting by Hthe scaled Vandermonde (scaled by weights equal to the inverses of the standard uncertainties associated with the response data) matrix of dimension nv x (n+1) whose / th row is the row vector and by y the column vector of dimension nv 1 whose / th element is the solution is given formally by a = (ff if y with covariance matrix .-V =(H if) . For reasons of numerical stability, it is recommended that the above formulae are not implemented explicitly, but instead the overdetermined linear equations Hr? = y are solved using a matrix factorisation of H (such as a QR-factorisation) and the covariance matrix is also evaluated in terms of that matrix factorisation. Since the model parameters are related to the response data ' through a linear measurement function (given formally above) the evaluation of the covariance matrix Va is exact, and is consistent with the framework given in “Guide to the Expression of Uncertainty in Measurement”, JCGM 100:2008, GUM 1995 referred to above. Stimulus and Response Data Uncertainty In this example, both stimulus and response data uncertainties are considered. Again, the input comprises the calibration data in which there are uncertainties associated both with the measured values of the observed ADC at the temperature Tc (response data) and with the measured values of the true ADC at the temperature Tc (stimulus data). Estimates of the parameters a of the polynomial model pn are obtained by minimising with respect to the model parameters a and parameters representing values for the true ADC for the different vials, the objective function where s.= 5 — p fS i = , J. ’ 1.4’ ' >' And d = D. — .c i = , Reference here is again made to ISO / TS 28038:2018 referred to above already on the determination and use of polynomial calibration functions. This is referred to as an errors-in-variables (EIV) problem as well as a generalised regression problem or a total least-squares problem: it is a non-linear least-squares problem that can be solved using standard (optimisation) approaches, such as Gauss-Newton or Levenberg-Marquadt. These approaches generate an approximation to the solution through an iterative process that needs to be initialised. Initial values for the parameters S, c can be set equal to the stimulus data values Dj,c and initial values for the parameters a can be set equal to the solution to the weighted least-squares problem (above) in which only response data uncertainties are considered. In the case that both the true ADC and observed ADC can be characterised by a Gaussian distribution then the solution corresponds to a maximum-likelihood estimator (MLE). The covariance matrix * ~ associated with the solution parameters $ as u is given by where / is the Jacobian matrix of (e, ¢0 with respect to (3, a] evaluated at the solution (5, a) Here, 1., and the matrix J is of dimension 2nv(nv+n+1) and comprises the blocks It will be noted that the third of these blocks is a diagonal matrix and the last is the zero matrix. An exemplary model and method for the calculation of uncertainties in output is provided which thus enables a quantitative output, with metrological rigor, to be obtained from an MRI scan. The example above has been expressed with reference to ADC, but as mentioned, the method applies equally to other MRI parameters. Since the evaluation of the covariance matrix Va is based on a linearisation of the (implicit) measurement function relating the model parameter a to the stimulus and response data, it is approximate, albeit it is evaluated in a way that is consistent with the framework given in “Guide to the Expression of Uncertainty in Measurement, JCGM 100:2008, GUM 1995” referenced above. The evaluation of the covariance matrix can also be undertaken using a Monte Carlo method, as a means to validate the matrix. Uncertainties in the observed ADC values (response data) and the stimulus data (data from NIST) have thus been considered and incorporated into the calibration function. This is significant as it means that the calibration function can be used to obtain quantitative outputs from an MRI scan with metrological robustness. An example of this will now be described. The following is an exemplary process corresponding to step 2 50 shown schematically in Figure 7. Estimates of the parameters of the polynomial calibration curve and the covariance matrix associated with those estimates are used, together with the patient data to obtain the required measurement result, which comprises an estimate Do of the measurand (Dthat represents “the corrected ADC corresponding to a calibration undertaken at the temperature Tc") for a single voxel within the region of interest with standard uncertainty u(Do). The estimate Do is given as the solution to the single (generally) non-linear equation = = 0 ?? (D ,a)and p (D ,a), If So lies between " where Dm / n and Dmax are the minimum and maximum values of D used to define the normalisation of the stimulus (independent) variable, then Do will lie between Dmin and DmaX- Monotonicity of the calibration curve ensures that there is at most one solution, which can be found using recognised methods for finding the zero of a function, including, but not limited to, the bisection method. For the purposes of uncertainty evaluation, the equation for Do is regarded as an implicit univariate model of the form = = 0 having the model inputs So and a and single model output Do. By applying a treatment such as that described in described in clause 6.3 of Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’ - Extension to any number of output quantities, JCGM 102:2011, and assuming So and a are independent, the standard uncertainty u(Do) is obtained from The evaluation of the uncertainty can also be undertaken using a Monte Carlo method, as a means to validate the uncertainty, which depends on a linearisation of the model. The formula above giving the standard uncertainty u(Do) can be used both when u(So) is zero and u(So) is non-zero. In the latter case, a means is required to evaluate u(So) because, unlike the measurements made of the vials, there is no “repeated” measured values for So, which relates to a single voxel within a region of interest. Instead, we propose the following approach. For each vial, calculate the arithmetic mean of the observed values for the individual voxels, i.e., as above, and the sample variance s2(Si) from which gives the standard uncertainty for an observed value of So corresponding to an individual voxel within the vial. Then, u(S0), the observed ADC for a single voxel of patient data, is obtained by interpolating the data or 5 , -u (5 ). : = 1,™, n . at The choice of a specific interpolation scheme depends on the nature and characteristics of the data. Referring to Figure 7 again, in step 50, the calibration curve is used to estimate true diffusion values corresponding to an observed ADC. Estimates of the parameters of the polynomial calibration curve and the covariance matrix are provided as an input at step 52. Next, the patient voxel data is derived 54 as the output data from the physical scan process itself. At step 56, the required measurement result is obtained. In other words by the described process a quantitative output has been achieved from the MRI scan, in this case for a value of ADC. To determine the required uncertainty, a partial derivative or Monte Carlo approach can be used to evaluate the measurement uncertainty at step 58. In one optional process, patient measurement uncertainty can be evaluated from observed ADC uncertainty 60. Thus, by starting with the true diffusion batch sample measurement data produced it is possible to generate a calibration curve that relates true diffusion to observed ADC. This can then be used to produce a quantitative numerical output from an MRI machine in a way that previously it has not been possible with the required uncertainties and meteorological soundness. The described method enables automatic QA in such a way that determination can be made as to whether or not a particular scan made using a particular set of parameters on an MRI machine in its configuration is reliable and capable of producing results that can be trusted medically or scientifically. The method further provides, independently, a means of calibration of qMRI data including all quantities that can be measured or derived from measurements taken by an MRI machine. Non-limiting examples include ADC.T1, T2, PDFF, etc. Furthermore and independently again, the method provides a means by which estimation of error on the measurement of a qMRI marker can be made. As explained above in detail, a series of mathematical processing steps can be taken (the example above being merely exemplary) that enables an estimation of the error on the measurement of a qMRI marker. The present methods and system enable a number of independent improvements to be achieved and delivered to users of MRI machines and system. These will be explained and exemplified in detail below. In summary the four independent, but related, developments are as follows: Automatic Quality Assurance (QA) As discussed above, when an MRI system is used to capture data about a patient there are many factors that can affect the output or produced image in addition to the patient’s ability to lay still, and their physiological functions. These include aspects of the physical hardware and the way it has been set up and also aspects of the software and parameter settings that are used for the capture of the image. The use of the presently described methods enables a user to make a determination as to whether or not the MRI machine and readings are of sufficient quality to enable a quantitative reading to be taken. For example, they could provide an indication of whether or not the parameters being used by the machine have been set up in a way that enables the machine to produce a quantitative output that can be relied upon in, say, clinical therapeutic settings or trials. This can be important in the running of clinical trials as it enables an individual scan to be deemed not good, and therefore rescanned on the spot (if it is determined not to be of sufficient quality) without affecting the validity of any other of the data that has been collected. The method enables an indication of whether or not the signal to noise ratio in respect of the individual voxels is narrow or accurate enough to enable an overall scan to be relied upon. This is achieved by looking at the distribution of values for each of the independent vials which are as matter of design and empirical fact all the same. In dependence on how well or badly the parameters of the machine have been set, the width of the distribution of the values of the measured parameter from the voxels of a particular vial can vary. The narrower the distribution of the values of the measured parameter from the voxels of a particular vial, the more qualified that scan will become. As described above, the results can be processed and then a minimum standard set below which the results are marked as not reliable. This therefore enables a less skilled operator to reliably achieve quantitative outputs from an MRI machine. The level of qualification (or quality) of a scan is application specific. General measures of dispersion, such as standard deviation can be used here, or in some cases more advanced statistics, or even machine learning methods. Such methods typically rely on advanced statistical methodology. Further it is to be noted that outside centres of medical excellence it is not uncommon for MRI machines to have been set up or to be run with protocols which do not produce sufficiently precise or calibrated outputs. This can relate to qualitative as well as quantitative outputs in such a way that the output is often not reliable, even though an operator is unaware of this. The method described herein thus enables QA to be automatically achieved and users or operators notified of the reliability or safety of reliance on the derived outputs. If the users or operators are sophisticated users of MRI systems, outputs are provided which include suggestions for modification of some of the parameters of the system. Alternatively, a simple traffic light output can be provided, i.e. red light or green light to indicate that the results can be used or not. The option of an amber light is also possible, say, to indicate that a result can be used but with caution. The outputs can be based on any possible MRI parameters that might be being measured or types of MRI scan being performed. In one example, the measurements are preferably in respect of the ADC, but any qMRI data can be measured and qualified in this way. Calibration of qMRI data and Estimation of Error on qMRI Markers The present system has also provided a way in which qMRI data can be calibrated. This enables estimation of error on qMRI markers. As discussed above a calibration function can be derived and one mathematical means by which a polynomial output function can be produced has been shown by way of example. The calibration of qMRI data offers a technical solution to the problem of what to do when a value has deviated such that it can be brought back to its true value and provided with an indication of the likely error. A metrologically valid measuring function has in other words been added to the MRI machine. As explained in detail above, the theory of metrology requires a complete measurement to be made up of a measured value, an error or uncertainty in the measured value and a unit (preferably SI units). Typically the data can relate to any MRI parameter. Non-limiting examples include, ADC, T1, T2, T2*, T1rho, T2rho or any derived content, e.g. iron content. Other examples include PDFF (Proton Density Fat Fraction). Validation Referring once more to Figure 3, a stage of validation 62 is also preferably provided. Validation, as is well known, serves to confirm (or otherwise) the reliability of results obtained. In this case validation is preferably performed to confirm the reliability of results obtained. Referring to Figure 8, a schematic representation of validation 62 is shown. In this case the reliability of the results obtained are checked 64 using Monte Carlo methods. The Monte Caro calculations themselves are checked 66 to ensure that they have stabilised solution, e.g. to a certain number of significant digits. The produced calibration function is preferably checked 68 for monotonicity. Other tests can also be performed as desired to perform validation. For example, goodness-of-fit 70 measures can be conducted for the derived functions, chi-squared tests 72 can be used for distributions that are assumed to be Gaussian. It will be recognised that these steps of validation require the application of known mathematical and numerical methods to validate the technical result achieved. The validation thus itself serves a technical function in confirming the output of the qMRI as a valid output. In more detail, verification is a check that the correct solution has been implemented. Where the evaluation of measurement uncertainty in steps 0, 1 or 2 (46, 48, 50 in Fig 7) uses a framework of propagating variances through a linearisation of a measurement function, the reliability of the results obtained can be checked using the Monte Carlo method. This validation step does not have to be undertaken for every patient scan but can be undertaken for a selection that is representative of those to be encountered in practice. It involves selecting a number M of Monte Carlo trials to ensure that the results from a Monte Carlo calculation have “stabilised” to a specified number of significant digits, for example, three digits, i.e., the results are reproduced to the specified number of digits when the Monte Carlo calculations are repeated then. Then, the results obtained using the framework of [2] are validated by the results obtained from a Monte Carlo method if they agree to a smaller number of significant digits, for example, two digits. To be useful as a calibration function, a function generally has to be strictly monotonic, i.e., the function must be strictly increasing or decreasing throughout the interval over which it is defined and to be used. This condition ensures that a unique stimulus value will be given for any feasible response value when the function is used for inverse evaluation. A simple way to check monotonicity, which is not fool-proof, is to evaluate the calibration function for a fine discretisation of the interval in x (e.g., 1,000 uniformly spaced points, say, over the stimulus interval) to see whether these values form an increasing or decreasing set. The degree n of the polynomial calibration function is often unknown a priori. It can be chosen by fitting polynomial functions of increasing degree, forming a goodness-of-fit measure for each function, and using these measures to select a suitable polynomial degree. In “ISO / TS 28038:2018 Determination and use of polynomial calibration functions. ISO, International Organization for Standardization, Geneva, Switzerland, 2018”, use is made of generally accepted model-selection criteria. Specifically, these include Akaike's Information Criterion (AIC), corrected AIC (AICc) and the Bayesian Information Criterion (BIC), which apply when the calibration data errors can be regarded as drawn from Gaussian distributions, as assumed above. For nv data points and a polynomial model with n+1 parameters, these criteria are: BiWO = 4- {?■. + 1) irs . All three criteria are designed to balance goodness of fit and simplicity of model. Given a number of candidate models, namely, for polynomial degrees n=1,...,nmax, fora suitable choice of the maximum degree nmax, the model having the smallest value of AIC (or AICc or BIC) would usually be selected. Further discussion is given in ISO / TS 28038:2018 referred to above. Under the assumption that the calibration data can be regarded as realisations of random variables having Gaussian distributions, the distribution for the measure for which Ravia) is a realisation is chi-squared with nv-n-1 degrees of freedom. Consequently, the probability that the measure takes values that exceed RQ\ / (a) can be calculated and the resulting probability value used to test the null hypothesis that the computed calibration and the calibration data are consistent. In the case of inconsistency, it can be that the calibration data uncertainties are unreliable and / or the form of the calibration curve does not provide a reliable description of the data. Either way, in such a case it is preferred that the calibration curve is not be used for the purposes of inverse evaluation. Figures 9A and 9B show schematic views of calibration curves. In figure 9A a calibration curve is shown which provides a mapping between observed ADC values from a particular MRI scan and actual diffusion values based on a phantom alone. It takes into account sources of uncertainty that derive from the characterisation of the batch samples (in the vials in the phantom), the temperature measurements taken of the phantom including the vials within it, and additionally, the values that are measured by the scanner of the material in the vials. It does not take into account any error associated with the scanning of an actual patient. Figure 9B is a calibration curve that shows the output based on the measurement of an actual patient. In other words, it takes into account the measurement uncertainty associated with the patient ADC (voxel) measurements. This generates a calibration curve with larger error or uncertainties. For any numerical value of observed ADC an actual diffusion value can be determined together with the error in the measurement. In the non-limiting example shown the errors represent 95% confidence + / -1.96 standard deviations. Looking at the Figure 9B, for an observed value of ADC of, say 1.5 10-3mm2 / s it can be determined that this corresponds to an actual diffusion value of approximately 1.3 10‘3mm2 / s and within the error range of 1.22 (78) to 1.38 (79) 10‘3mm2 / s. These are metrologically determined errors and thus the graph enables a metrologically sound quantitative output to be determined based on the observed ADC value (of 1.5). In addition, the calibration curve including errors enables a determination of a range of observed ADC values that might merit further investigations. Specifically, in the example shown, the intercepts 80 and 82 of the upper error limit (80) for the lowest possible observed ADC and the lower error limit (82) for the highest possible determined observed ADC give values that could correspond to diffusion values within the known error range for the actual observed ADC. Accordingly once an initial observed ADC value 84 is determined, corresponding observed ADC values that might merit further medical investigations can be determined using the calibration curve. These determined boundaries may thus be considered boundaries of detection for, say, cancer. This is a significant result since it enables diagnostic determinations to be made with a clear understanding of the likelihood of any particular outcome. Figure 10 shows a graph for the explanation of a weighted image correction method according to the fourth aspect of the present invention. The applicants have recognised that it is possible to invert the equations used to calculate the quantitative MR biomarkers, and, following from the estimation of the calculated physical constant (e.g. ADC), reconstructing the weighted images originally used to calculate it, but 'calibrating' them based on the corrected constant. This will now be described with reference to figure 10. The process to be described may be considered reverse calibration. In the process described above, it has been shown how example demonstrates the possibility to recalibrate diffusion-weighted images following from the recalibration of the apparent diffusion coefficient. In short, using a WICAD phantom, it is possible to recalibrate each voxel (3D pixel) in a calculated ADC map coming from a gradient applied in a particular direction on a scanner so as to derive a quantitative and metrologically sound output. The recalibration enables a correction for any systematic bias present in the data. This correction comes with an associated error, calculated following strict metrological methods. Referring to figure 10, the additional method can be understood. The method is based on the principle that for each diffusion-weighted image, with a particular b value and gradient direction, the earlier described methods will have provided a corrected diffusion-weighted value for all the reference phantoms. This can then be used to rescale the whole image accordingly. Such a method can be used for any linear (e.g. water / fat) or exponential / non-linear image acquisitions (relaxation times T1, T2, T2*, non-standard diffusion models - e.g. NODDI, VERDICT, etc...). The importance of such a method would be to enable the use of the WICAD validation solution to be used as a first order correction method for more advanced models (i.e. multi-exponential decays for relaxation constants or advanced diffusion models). Embodiments of the present invention have been described with particular reference to the examples illustrated. However, it will be appreciated that variations and modifications may be made to the examples described within the scope of the present invention.

Claims

1. A method for quality assurance of an MRI system under test, the method comprising:scanning a phantom including known materials to obtain scanner data;in dependence on reference data relating to the known materials and the scanner data, identifying error in the scanner data;based on the identified error, determining a quality assurance level for the scanner under test.

2. A method according to claim 1, in which the phantom includes one or more containers with the known materials, and the scan determines a distribution of values of an MRI parameter of the known materials.

3. A method according to claim 1, in which the containers are vials and the distribution is of a specified MRI parameter in respect of the material in the vials.

4. A method according to claim 3, in which in dependence on the distribution, a signal to noise ratio is determined in respect of the scan.

5. A method according to any of claims 1 to 4, comprising measuring the temperature of the known materials in the phantom whilst a scan is taking place.

6. A method according to claim 5, comprising determining uncertainty in the temperature measurements.

7. A method for calibration of a scan in quantitative MRI, the method comprising, in response to the scanning of a patient in an MRI machine and the simultaneous scanning of a phantom in the MRI machine with the patient, in which the phantom includes materials with known MRI properties:determining uncertainty in scan results of the materials with known MRI properties in dependence on knowledge of MRI properties of the material;generating calibration data based on the scan of the material of knownproperties and the patient including an indication of uncertainty in the scan of the patient.

8. A method according to claim 7, in which generation of the calibration data includes evaluation of the temperature of the materials with known properties and uncertainties in the evaluated temperatures.

9. A method according to claim 8, in which the temperature is measured using probes that are spatially distributed within the scanner.

10. A method according to claim 7 or 8, in which uncertainty is calculated in respect of the scan of the patient using numerical methods.

11. A method according to claim 8, comprising evaluating the actual values of an MRI parameter of the materials of known properties, based on the measured temperature.

12. A method according to claim 9, comprising determining an observed value for the MRI parameter as an output of the scan, including uncertainty in the observed value.

13. A method according to any of claims 7 to 12, comprising determining a polynomial function to enable calibration of a scan from an MRI machine.

14. A method according to claim 13, in which the calibration function is provided to relate a true parameter value to a corresponding observed parameter value.

15. A method according to claim 14, in which the calibration function relates true diffusion to observed ADC values in an MRI scan.

16. A method according to claim 15, in which the calibration function comprises polynomial parameters and covariances.

17. A method according to any of claims 1 to 16, in which the MRI parameter is selected from the group consisting of apparent diffusion coefficient (ADC), T1, T2, T2*, Tip, T2p, PDFF or any other MRI parameter.

18. A method for quantitative MRI, the method comprising:scanning a patient in an MRI machineat the same time, scanning a phantom in the MRI machine with the patient, the phantom including materials with known properties;determining uncertainty in scan results of the materials with known properties in dependence on knowledge of the material properties;generating calibration data based on the scan of the material of known properties and the patient;using the calibration data to determine a quantitative output for one or more MRI parameters of the patient including an indication of uncertainty in the quantitative output.

19. A method according to claim 18, in which generation of the calibration data includes evaluation of the temperature of the materials with known properties and uncertainties in the evaluated temperatures.

20. A method according to claim 19, in which the temperature is measured using probes that are spatially distributed within the scanner.

21. A method according to claim 18 or 19, in which uncertainty is calculated in respect of the scan of the patient using numerical methods.

22. A method according to claim 18, comprising evaluating the actual values of an MRI parameter of the materials of known properties, based on the measured temperature.

23. A method according to any of claims 18 to 22, comprising determining a polynomial function to enable calibration of a scan from an MRI machine.

24. A method according to claim 23, in which the calibration function is provided to relate a true parameter value to a corresponding observed parameter value.

25. A method according to claim 24, in which the calibration function relates true diffusion to observed ADC values in an MRI scan.

26. A method according to claim 25, in which the calibration function comprises polynomial parameters and covariances.

27. A method according to claim 24, in which the MRI parameter is selected from the group consisting of apparent diffusion coefficient (ADC), T1, T2, T2*, Tip, T2p, PDFF or any other MRI parameter.

28. A method of reconstructing a weighted MRI images, the method comprising, scanning a subject in an MRI machine;at the same time, scanning a phantom in the MRI machine with the patient, the phantom including materials with known properties;determining uncertainty in scan results of the materials with known properties in dependence on knowledge of the material properties and generating a correction factor based on the scan of the material of known properties;applying the correction factor to the entire image to generate a weighted MRI image corrected for any systematic bias in the data.

29. A method according to claim 28, in which the weighted MRI image is corrected for systematic bias in the first MRI image.

30. A method according to claim 28 or 29, in which the weighted MRI image is an image indicating values of an MRI parameter selected from the group consisting of apparent diffusion coefficient (ADC), T1, T2, T2*, T1 p, T2p, PDFF or any other MRI parameter.

31. A method according to any of claims 28 to 30, in which producing the first image comprises simultaneously scanning a phantom including known materials and a patient to generate scanner data.

32. A method according to claim 31, in which the phantom includes one or more containers with the known materials, and the scan determines a distribution of values of an MRI parameter of the known materials.

33. A method according to claim 32, comprising generating calibration data based on the scan of the material of known properties and the patient including an indication of uncertainty in the scan of the patient to generate the correction factor.

34. A method according to claim 33, in which generation of the calibration data includes evaluation of the temperature of the materials with known properties and uncertainties in the evaluated temperatures.

35. A method according to claim 34, in which the temperature is measured using probes that are spatially distributed within the scanner.

36. A method of calibration of an MRI scan, the method comprising based on the simultaneous scan of a patient and a phantom including vials of material of known MRI properties:performing a temperature measurement to produce a value and uncertainty in temperature representing a distribution of possible temperatures.from the distribution and using an assumed temperature from the scan, using stochastic methods to determine polynomial model parameters to generate a calibration curve.

37. A method according to claim 36 in which the calibration curve relates observed apparent diffusion coefficients to actual diffusion values.

38. A method according to claim 36 or 37, in which the MRI parameter is selected from the group consisting of apparent diffusion coefficient (ADC), T1, T2, T2*, Tip, T2p, PDFF or any other MRI parameter.

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