System for standardisation of a physical measurement

Abstract

A method and system for standardising a physical MRI measurement is disclosed whereby the physical measurement is independent of measurement conditions and systems. Standardisation enables accurate comparison of medical images across different systems: different vendor machines and different field strengths. An aspect of standardization is a virtual machine, VM, which is an ideal model for several various physical MRI machines.

Description

[0001]METHOD AND SYSTEM FOR STANDARDISATION OF A PHYSICALMEASURMENT Field of the InventionThe present invention relates to a method and system for magnetic resonance imagingwhich is also referred to as MRI. The method and system are devised to standardisea physical MRI measurement whereby the physical measurement is independent of measurement conditions and systems.It is an advantage of the present invention that standardisation enables accuratecomparison of medical images across different systems: different vendor machines and different field strengths. An aspect of standardization is a virtual machine, VM, which is an ideal model for several various physical MRI machines. It is a further advantage that the present invention enables evaluation of key outcomes across treatment interventions and patient groups by ensuring the comparability of data from multiple sites, deploying diverse systems. Background Magnetic resonance imaging (‘MRI’) is used to measure physical and biological quantities and processes in the human body non-invasively, for diagnosis, monitoring disease status and the response of tissue to treatment. MRI requires a strong magnetic field that is uniform across a scan volume. Mostcommercial MRI scanners operate at 1.5 Tesla (‘T’) or 3T. Machines are beingdeveloped that have a significantly lower magnetic field strength, e.g. 0.55T, while others have been developed at higher field strengths such as 4.7T, 7T and above, although these are used for research applications and not currently in clinical practice. During an MRI scan, energy from an oscillating magnetic field is temporarily applied to the patient at an appropriate resonant frequency (RF). Scanning with X and Y gradient coils causes a selected region to experience the same magnetic field required for the energy to be absorbed. The photons are excited by the RF pulse and the resultantsignal is measured by a receiving coil. The contrast between tissues is determined bythe rate at which excited atoms of each tissue return to an equilibrium state. The return to an equilibrium state is by relaxation processes (the measurement of which is referred to here as relaxometry) of T1 (magnetization in the same direction as the static magnetic field) and T2 (transverse to the static magnetic field). For a T1 weighted image, magnetization is allowed to recover before measuring the MR signal by changing the repetition time (TR). For T2 weighted images, magnetization is allowed to decay before measuring the MR signal by changing the echo time (TE). T1 and T2 are used to highlight different tissues and structures; for example, T1 to map fatty tissue, and T2 to map fatty and water-based tissue. That relaxometry measurements using MRI vary under different measurement conditions (e.g. MRI scanner model and / or field strength) is a well-known challenge in the field. Various studies have acknowledged such dependencies: for example, single- site studies (carried out using the same MRI scanner and the same acquisition protocol for all subjects) describe how the physical measurement may be dependent on the measurement conditions (for example, Tirkes, Temel, et al. "T1 mapping for diagnosisof mild chronic pancreatitis." Journal of Magnetic Resonance Imaging 45.4 (2017):1171-1176 and Evrimler, S., Swensson, J.K., Are, V.S. et al. Quantitative assessmentof disease severity of primary sclerosing cholangitis with T1 mapping and extracellularvolume imaging. Abdom Radiol 46, 2433–2443 (2021)); while multi-site studies thatuse MRI scanners with different field strengths (e.g.1.5T and 3T scanners) generally report results for 1.5T and 3T scanners separately (for example Tirkes, T., Mitchell, J.R., Li, L. et al. Normal T1 relaxometry and extracellular volume of the pancreas in subjects with no pancreas disease: correlation with age and gender. Abdom Radiol 44, 3133–3138 (2019) and, M.H., Auger, D., Smith, G.C. et al. T1 at 1.5T and 3T compared with conventional T2* at 1.5T for cardiac siderosis. J Cardiovasc Magn Reson 17, 102 (2015)S] ). However, such studies do not resolve the variation in relaxometry measurements by standardisation. Other studies, that work under the same field strength but different scanner manufacturer, have attempted standardization by optimizing MRI acquisition protocoldesign (for example, Tirkes, T., Yadav, D., Conwell, D.L. et al. Magnetic resonanceimaging as a non-invasive method for the assessment of pancreatic fibrosis (MINIMAP): a comprehensive study design from the consortium for the study of chronicpancreatitis, diabetes, and pancreatic cancer. Abdom Radiol 44, 2809–2821 (2019)and Tirkes, T., Yadav, D., Conwell, D.L. et al. Quantitative MRI of chronic pancreatitis: results from a multi-institutional prospective study, magnetic resonance imaging as anon-invasive method for assessment of pancreatic fibrosis (MINIMAP). AbdomRadiol 47, 3792–3805 (2022)). However, such standardization is attempted across alimited range of scanner variation, for example, a subset of MRI scanner models. Furthermore, MRI acquisition protocol optimization can be particularly challengingunder certain clinical MRI systems and residual differences might remain (Hernando,D., van der Heijden, R.A. & Reeder, S.B. A better understanding of liver T1. EurRadiol (2023)). For example, as described by Lee et al ((Lee, Yoojin, et al."Establishing intra-and inter-vendor reproducibility of T1 relaxation time measurementswith 3T MRI." Magnetic resonance in medicine 81.1 (2019): 454-465)) the samesequences / methods may not be available across scanners from differentmanufacturers: e.g. the native parallel imaging method had sensitivity encoding(‘SENSE’) on the Philips platform whereas Generalised Autocalibrating PartiallyParallel Acquisitions (‘GRAPPA’) was used on the SiemensTM platform. Limitedinformation on shimming procedure, which is the process by which the magnetic fieldis made more homogeneous, is made available by scanner manufacturers and otherdifferences in calibration settings are determined by the system at the outset of scanning. A potential solution to achieve complete standardization entails additional post- processing steps. Bachtiar et al, (‘Repeatability and reproducibility of multiparametric magneticresonance of the liver’ (2019) PloS one 14.4 (2019): e0214921) discloses a methodwhereby physical measurements are modified to be similar to those obtained using an existing ‘reference’ system, that is, a particular manufacturer and model of a physical MRI scanner (e.g. SiemensTM3T). While the method achieves ‘referencing’, it does not produce complete standardization, but rather values that will exhibit the same dependencies and biases (errors) to those of the reference system: i.e. an output measurement is only as unbiased as the output measurement produced by the least biased reference physical system. Various publications have also disclosed use of Bachtiar’s method, using a set of paired data and linear mappings; for example Dennis et al. (‘Multiorgan impairment in low-risk individuals with post-COVID 19 syndrome: a prospective, community based study’ (2021) BMJ Open 2021;11:e048391) for analysis of pancreas images, without iron correction, and an output T1 standardized to 3T. Tirkes et al. (‘Magnetic resonance imaging as a non-invasive method for the assessment of pancreatic fibrosis (MINIMAP): a comprehensive study design from the consortium for the study of chronic pancreatitis, diabetes, and pancreatic cancer’(2019), Abdominal Radiology, volume 44, pages 2809–2821) noted that T1 relaxationtimes of tissues measured on varying magnetic field strengths are expected to be different and that it is necessary to standardize the quantitative imaging across different institutions and MR manufacturers using a T1 phantom in order to obtainuniform and accurate T1 maps. Optimization of the dual flip-angle Spoiled Gradient-Recalled (‘SPGR’) image acquisition parameters is performed according to thephantom test results in each institution but no modification of the T1 value after measurement is proposed. Noting the known dependence of T1 on magnetic field strength of the MRI scanner, Virostko et al (‘Development of a standardized MRI protocol for pancreas assessment in humans’ (2021)) describe how different techniques used to generate T1 maps display discrepancies when scanning the pancreas of the same individual. Standardization of T1 across institutions (scanners) was undertaken using a phantom. Using 3T SiemensTMand PhilipsTMMRI scanners only, they found that several quantitative MRI parameters can be influenced by field strength, and translation of the standardisation protocol to 1.5T field strength would likely require adjustment of imaging parameters. They concluded that further work was needed to standardize T1 mapping techniques for application to the pancreas. Field strength standardization is mentioned in the context of myocardial iron mapping by Alam et al J ‘T’ (Alam, Mohammed H., Dominique Auger, Gillian C. Smith, Taigang He, Vassilis Vassiliou, A. John Baksi, Rick Wage et al. "T1 at 1.5 T and 3T compared with conventional T2* at 1.5 T for cardiac siderosis." Journal of Cardiovascular Magnetic Resonance 17, 102 (2015)) using the power regression equation: y= 0.324x^.^^^ (R^ = 0.715)concluding however, that considerable further work was required in standardisation and transferability between scanners and centres. Deoni et al. (‘Standardised structural magnetic resonance imaging in multicentre studies using quantitative T1 and T2 imaging at 1.5T’ (2008) Neuroimage 40.2: 662- 671) demonstrate the ability to standardize across multiple time-points and imaging centres by acquiring T1 and T2 brain maps of seven healthy volunteers using the rapid DESPOT1 and DESPOT2 (driven equilibrium single pulse observation of T1 and T2) mapping techniques using 1.5 T SiemensTMand GETMscanners from different manufacturers and / or with varying gradient performance. They found that relaxometry (via DESPOT1 and DESPOT2, i.e. Variable Flip Angle (VFA)) holds a number ofpotential advantages over qualitative T1- or T2-weighted imaging. However, the studyomits mention of T1 correction.Nacif et al (‘Myocardial T1 mapping with MRI: Comparison of look-locker and MOLLIsequences’ (2011), Journal of Magnetic Resonance Imaging 34.6: 1367-1373) evaluated the relationship between “Look-Locker” (LL) and modified Look-LockerInversion recovery (MOLLI) approaches for T1 mapping of the myocardium. Theyfound differences between the T1 acquisition protocols shown. In particular, the T1 values derived from the LL measurement were approximately 60 ms longer than those of MOLLI. However, only 1 MRI scanner manufacturer was included and they note that, in order to determine the applicability of T1 mapping, it will be necessary to evaluate T1 values on different MRI scanners. Morita et al, (‘Myocardial T1 mapping with a Saturation Recovery method usingcomposite RF pulse - preliminary study’ (2022) ISMRM abstract) concluded that T1mapping has garnered increasing attention as a basic tool for MR in the research and clinical settings, holds the promise of a method for scanner independent T1 contrast, and provides useful quantitative tissue information. Cicolari et al (‘Phantom study on magnetic resonance imaging(MRI) T1and T2 relaxation times measurements standardization (2020) Proc. Intl. Soc.Mag. Reson. Med.28 (2020)) disclose the design of sequences that produce scanner- independent T1 and T2, but do not seek to modify a T1 measurement to obtainscanner-independent or field strength-independent T1 measurement i.e. the solutiondoes not involve modification of T1 value after measurement. Commercial means are known to correct for scanner make and field strength bias to T1 which is referred to here as ‘srT1’. They comprise mapping system-dependent T1images to system-independent srT1 images to compare srT1 values over a variety ofMRI systems. Scan subjects are human volunteers, chemical phantoms, pre-clinicalanimals, pieces of meat and other matter of comparable materials. Each instance of amapping (e.g. GSTM T^.^which means to map a GE1.5T to a Siemens M 1.5T) may beestimated as follows: i) a number (e.g. ~20) of scan subjects are considered for whom there are two (or more) images wherein each image is from a respective MRI machine,for example for each scan subject there is a pair including a first image from aGETM 1.5T MRI machine and a second image from a SiemensTM 1.5T machine,and both first and second images are taken at approximately the same slice oranatomical location; ii) for each of these (40) images, a region-of-interest (ROI) in the organ of interest (e.g. liver, pancreas) is placed interactively by an expert; iii) the median value of the intensities within that ROI is calculated. This gives rise to a set of pairs of T1 values for each of the scan subjects, onemedian T1 from the first image of the pair from the first MRI machine, the othermedian T1 from the second image of the pair from the second MRI machine,{(a^, b^): i = 1, … , 20} ;iv) a mapping between the two MRI machines is then estimated by fittingan approximating function (for example, a linear function) to this set of 20 pairsof data points; v) the fitted approximating function is extrapolated across the range of values of clinical interest. However, among other shortcomings, the slices in each pairwise case may not beidentical. The result is an estimate and thus inevitably entails error. For example,there may be error due to the choice of ROI, use of the median as a “typical” value,and the choice of approximating function. Approximation for mapping introduceserror. For example, to map a PhilipsTM 1.5T to SiemensTM 3T, in composing theapproximated maps PS^.^ ∘ S^.^,^ , the approximation errors are compounded. (Thesymbol PS1.5 means map a PhilipsTM1.5T to a SiemensTM1.5T. The symbol S1.5,3means map from SiemensTM 1.5T to SiemensTM 3T.) There is an assumption that someparticular SiemensTM3T model is and will remain the best available. The present invention resolves the limitations and shortcomings of the prior art. It provides a generalised scheme for post-processing a physical MRI measurement by standardization, where the physical measurement is independent of (and thuscomparable across) different measurement conditions and systems.Summary of the InventionAccording to an aspect of the invention there is a system comprising all features ofclaim 1. The system implements a method of standardization of a physical measurement. Preferably the physical measurement is from a magnetic resonance imaging machine. Further features of the invention are disclosed in dependent claims. According to an aspect of the invention there is a system comprising a Virtual Machine VM implemented on a computer standardising a physical measurement of scannedtissue by assorted MRI machines, wherein first functional mapping parameters in afirst function map the physical measurement of each one of the assorted MRI machinesto a different one of the assorted MRI machines; and second functional mappingparameters in a second function map the physical measurements of each of the assorted MRI machines to an ideal measurement from the VM.In essence of the technical concepts that support the these aspects of the invention,the following concepts a, b, c, and d are noted.a. Every MRI machine, real or hypothetical whose design is sufficientlyarticulated, may be associated with a mathematical structure. Preferably themathematical structure is formally a manifold that relates functional mappingparameters in a function with a measurement.b. In the case of physical MRI machines only, one of them designated M* that isof excellence may be selected as a reference for all the physical machines. Then the manifold representations of all other physical machines may be transformed to that ofthe reference MRI machine M*. In that way measurements made on any othermachine may be transformed to closely approximate that which would have beenrecorded had the measurement been on the reference MRI machine M*.c. The reference MRI machine M* need not be physical. It may be a virtualmachine that is computer-implemented whose design enables construction of themanifold. Some or all measurements of T1 on any physical MRI machine may betransformed to what it would have been on the reference MRI machine M*.d. By changing the evolving “hypothetical” or “idealized” or “virtual” machine,measurements are standardized against a precisely defined entity, even if it does not yet physically exist.The physical MRI machines may each provide their own physical measurementestimate.A first set of parameters that are functional mapping parameters in a first function thatmaps the physical measurement estimate from each of the physical MRI machines to another one of the physical MRI machines.A virtual machine VM may provide an ideal measurement. A second set ofparameters that are functional mapping parameters in a second function may map thephysical measurement from each of the MRI machines to the ideal measurement ofthe VM.The functional mapping parameters in the second function may be determined for theVM to minimize a total dispersion of the first set and the second set of parameters.Advantageously the ideal measurement takes into account the physical measurementsfrom real physical MRI machines while being relatively independent of themeasurement conditions and systems of the real physical MRI machines. It facilitatesaccurate comparison of medical images across different systems: different vendormachines and different field strengths. Comparability of data from MRI scans byvarious and diverse physical MRI machines at multiple sites is improved.The first or the second function mapping parameters or both may comprise one ormore of: T1 measured, proton density fat fraction PDFF, T2*, T2* measured, tissue iron content by T2*, liver iron content, and iron content of the scanned tissue.T1 may be corrected for iron content. T1 may be corrected for T2* in order to correctfor iron content. The physical measurement may comprise one or more of: T1, T1corrected for iron content, T1 water, and T1 VM. T1 may be corrected for fat content. T1 may be corrected for PDFF. The physical measurement may comprise one or more of: T1, T1 corrected for fat content, T1 water, and T1 VM. Preferably T1 is corrected for both T2* and for PDFF. A manifold may, for example, map measurements of proton density fat fraction (PDFF), T2*, and an estimate of T1 to a “corrected” version of T1 that takes account of those non-T1 measurements.All the MRI machines may be actual devices that make the physical measurement.Certain ones of the MRI machines may be actual devices that make the physicalmeasurement. Other ones of the MRI machines may comprise a computer in whichthere is a computer simulation that executes the first function, the second function, or both functions. An inverse of the first function may map the physical measurement from the different one of the assorted MRI machines back to each one of the assorted MRI machines respectively such that the first function is reflexive. Preferably the inverse of the first function uses an inverse of the first functional mapping parameters. An inverse of the second functional mapping parameters in an inverse of the second function may map the ideal measurement from the VM back to each one of the assorted MRI machines respectively such that the second function is reflexive.Preferably the inverse of the second function uses an inverse of the second functionalmapping parameters.For any three of the assorted MRI machines: first, second, and third; the first functionmay map the physical measurement of the first one of the assorted MRI machines tothe second one, and the first function may map the physical measurement of thesecond one of the assorted MRI machines to the third one, and the first function may map the physical measurement of the first one of the assorted MRI machines to thethird one, such that composition with the first function is consistent and transitive forall of the assorted MRI machines.For the VM and any two of the assorted MRI machines there may be equivalencebetween an indirect mapping composition and a direct mapping. There may be the indirect mapping composition in which the second function may map the physical measurement of one of the assorted MRI machines to the ideal measurement of the VM and an inverse of the second functional mapping parameters in an inverse of the second function may map the ideal measurement from the VM back to the physical measurement of the different one of the assorted MRI machines. There may be the direct mapping in which the first function which may map the physical measurement of the one of the assorted MRI machines to the different one. The indirect mappingcomposition may be equivalent to the direct mapping. Consequently, the indirectmapping composition with the second function may be consistent and transitive for allthe assorted MRI machines via the VM. The first function mapping between any two of the assorted MRI machines may be equivalent to an indirect mapping composition of the second function mapping from one of the two assorted MRI machines to the VM with the inverse of the second function mapping from the other one of the two assorted MRI machines to the VM. The system may account for discrepancy in fidelity between: the first functional mapping parameters of a pair of the assorted MRI machines; or the second functional mapping parameters for the VM and a, or the, pair of the assorted MRI machines; or the physical measurements of a, or the, pair of the assorted MRI machines and the respective ideal measurements of the VM; the ideal measurement from the VM for each one of the assorted MRI machines in a, or the, pair. The system may account for the discrepancy in fidelity due to a combination of these, or all of them. The system may account for the discrepancy for every pair that is combination of two of all the assorted MRI machines.An inconsistency between the mapping of two of the MRI machines and itscorresponding mapping composition via the VM may be minimal.The system may be configured to compensate for an inconsistency between a direct mapping of two of the assorted MRI machines and an indirect mapping composition between the two of the assorted MRI machines via the VM, wherein the direct mapping uses the first functional mapping parameters in the first function and the indirect mapping composition uses the second functional mapping parameters in the secondfunction. The system may compensate by minimizing an aggregate of theinconsistency for every combination of two of all the assorted MRI machines and theVM. The aggregate may comprise a sum of the square of the inconsistency for everycombination. The system may determine an inconsistency as describe above as follows. The system may determine the indirect mapping composition in which the second function maps the physical measurement of one of the assorted MRI machines to the ideal measurement of the VM and an inverse of the second functional mapping parameters in an inverse of the second function maps the ideal measurement from the VM back to the physical measurement of the different one of the assorted MRI machines. The system may determine the direct mapping in which the first function which maps the physical measurement of the one of the assorted MRI machines to the different one. The system may determines the inconsistency as a difference between the indirect mapping composition and the direct mapping.Preferably the system or the VM comprises a computer program directly loadable intothe memory of a computer for operating the system. Preferably the system or the VM comprises the computer with the computer program loaded into the memory. The system may comprise the physical measurements provided by the MRI machine loaded into the memory. Preferably the first and second sets of parameters or the first and second functions are loaded into the memory.The system may comprise an electronic display screen operable by the computeraccording to the computer program to view images recorded by the MRI machine whencorresponding to the physical measurements or to display an image derived from adjusted by the ideal measurement provided by the VM.The invention will now be described, by way of example only, with reference to theaccompanying figures in which: Brief Description of the Figures Figure 1 shows an example of average representations of manifolds for measurementsystems defined by manufacturer and field strength (SiemensTM 3T, PhilipsTM 3T andGETM3T).Figure 2 shows background information where mappings are generated to achievescanner-referencing to a “reference system” that is for illustrative purposes, a canonical SiemensTM3T.Figure 3 shows the process of learning the mappings to the “virtual machine” system.Figure 4 illustrates the mathematical notation of the mapping functions betweendevices and the mathematical properties of such functions, which include, for examplereflexivity and composition.Figure 5 shows relationships between devices, for example physical MRI machines,da, db, dc, dD, dD-1, di versus the virtual machine VM, and mapping functions, ^^^ , Figure 6 shows the mapping function from each physical MRI machine to the VM andmapping between the physical MRI machines;Figure 7 shows a process overview of srT1 generation for scanner make and fieldstrength; andFigure 8 shows standardization of the T1 measurement under different scanningconditions where Scan A is from a GE 1.5T machine and Scan B is from a SiemensTM3T machine; andFigure 9 shows that measurements of T1 before the application of the proposedmethod show two distinct distributions, while the standardized T1 values after the application of the proposed method show comparable distributions. Detailed Description of the Invention In an embodiment of a method and system for standardisation of MRI measurement,a measurement system referred to here as a scanner or an MRI machine is associatedwith a manifold in the space of metrics. A manifold may, for example, map measurements of proton density fat fraction (PDFF), T2*, and an estimate of T1 to a “corrected” version of T1 that takes account of those non-T1 measurements. In this specific case, the manifold is a 2-dimensional surface embedded in the 3-dimensional parameter space. It is understood that this is just an illustrative example.More generally, an embodiment of the method for standardisation of MRImeasurement may comprise for example the steps:1. Simulation data: physical properties of a scanner of interest, as well as(optionally) biological properties of the tissue sample of interest, create a multi- dimensional manifold on which the ‘standardised’ values can be obtained. 2. Recordings of measurements: recorded measurements on the scannerof interest from step 1 are used to update the manifold created in step 1. Scansof phantoms containing a number of vials where a reference value is known may be used in this step. 3. Between-scanner corrections: Distances between manifolds createdfrom different measurement systems are calculated, and the manifolds are co- aligned to a common surface, which becomes the basis for standardisation. The common surface may or may not be embodied by the transfer function of any measurement system. We refer to the common surface as a ‘virtual machine’ (VM). Examples of average representations of manifolds for scanner families defined by manufacturer and field strength are shown in Figure 1. There is a manifold is for a SiemensTM3T MRI machine 101 shown at the top. There is a manifold for a PhilipsTM3T MRI machine 102 shown in the middle. There is a manifold for a GETM3T MRImachine 103 shown at the bottom. All three manifolds 101, 102, 103 have the samethree axes. On the vertical axis 111 is molliT1. On the second axis 112 is corrected water T1 input. On the third axis 113 is PDFF. In an embodiment, only physical properties of the scanners are available, not biological properties of the tissue sample being measured. Since the obtained raw T1 measurements are also fundamentally confounded by the biological properties of the tissue, the optimisation system is applied under higher level of uncertainty. In a separate embodiment, the biological properties of the tissue have been measured and are available. These biological properties may have been measured using a separate MR scan. Examples of biological properties can be tissue fat content by proton density fat fraction (PDFF) or tissue iron content by ^^∗(those skilled in the art may note that, in the context of specific organs of interest, ^^∗in ms can be mapped toiron content in mg / g, e.g. liver iron content or LIC in the liver). In such embodiment,the manifold may be a surface (a 2-manifold), for example dimension of the manifold to 1, a curve in the 2-parameter space. Equally, additional parameters may be added, increasing the dimensionality of the manifold. More generally, for any given MRI scanner, the parameters of interest, whether they are measured directly or are unobserved, vary together in a specific way. For example, if we consider the parameter set the space of all possible parameter values is the 4D space ℝ^. The set of allowable value combinations for these parameters can be viewed as a manifold or ‘surface’ embedded in ℝ^which can be expressed by the equation Where the functional form of ^ is determined by properties of the scanner and thesequence being applied. The manifold represented by equation is a 3-manifold embedded in ^^. By observation of some of the variables, inferences are made about the others. For example, a scanner of interest is used to estimate values ^^^and for the parameters ^^^^^^^^^^and ^^∗^^^^^^^^. Thus values of these variables in the above function are instantiated so that it reduces to ^′(^^^^^^^ , PDFF) = 0where the function ^′ represents the function ^ with the values of ^^^^^^^^^^and The manifold represented by the second equation is now a 1-manifold (curve) embedded in ℝ^(the plane). A value for ^^^^^^^, is then inferred by incorporating knowledge of a prior distribution for the values of PDFF. Figure 2 shows a mappings schematic 200. At nodes of the mapping schematic are assorted MRI machines including a SiemensTM3T 201, a PhilipsTM3T 202, a GETM3T 203, a GETM1.5T 204, a SiemensTM1.5T 205, and a PhilipsTM1.5T 206. A first function indicated by an arrow maps a physical measurement of each one of theassorted MRI machines to a different one of the MRI machines. The mappings aregenerated to achieve scanner-referencing to a “reference system”. In the case shownin Figure 2, the “reference system” is, for illustrative purposes, a canonical SiemensTM3T 201.Other MRI machines may be used for the reference system, and it is not intended toimply that any particular manufacturer or model of machine should be chosenpreferentially as the reference system. Users may chose a reference system to usea standard as they wish.In a further embodiment, the ‘between-scanner corrections’ are performed so that the manifold from one (reference) measurement system is fixed, and the manifolds from other measurement systems are automatically placed in correspondence to the reference. Depending on the manifold chosen in any embodiment, a range of methods may be used to map between corresponding values on one system’s manifold to that on the manifold of another system. For example, such correspondences may be obtained by algorithms such as the Iterative Closest Point, although mapping need not be linear.In an embodiment, an MRI machine and the VM are denoted by, ^^ and ^^^respectively. Preferably ^1^is recorded on a measurement system ^^for some data, ^^^^^. To determine what would have been recorded had it been ^1^^, we learn the mappings ∀^ ^1^^^^^^^^ → ^1^^(^^^^^^)^1^is measured on ^^but we want to report ^1^^as if it had been measured on^^^. Figure 3 shows a process of learning mappings to the VM system as a triad 300. There is a top left node T1i(data) 301, a bottom node T1VM302, and top right node T1j(data) 303.Certain factors affect a measured ^1 value, including, for example,^1^ , PDFF, ^^∗^^^^^^^^, which we refer to here collectively as “data”. To learn themapping between the top left node 301 and top right node 303:^1^^^^^^^^ → ^1^^where ^^^^^signifies that the data was measured on ^^may involve a mixture of actual data and simulated data (for example, where actual data is insufficient or yet to exist). Machine learning algorithms of such transforms are generally trained using a mix of real and simulated data, which can overcome the limitations of a simulator. Using actual data, pairs ^^to ^^are mapped. In essence, this process uses a setof actual experimental values to estimate a transform: ^1^ → ^1^ as shown from thetop left node 301 to the top right node 303 as shown in Figure 3. It partially correctsfor scanner make and field strength bias to T1 which is referred to here as ‘srT1’. Theprocess maps system dependent T1 images to system independent srT1 images inorder to compare srT1 values over a variety of MRI systems. Figure 7 is an illustration.In the mappings schematic 400 shown in Figure 4, there are devices da 410, db 411,dc 412, dD 414, dD-1413, di 415 representative of physical MRI machines disposed atnodes around a perimeter. Interconnection of the devices along the perimeter edgeis illustrative of each mapping function between the devices, for example the mappingfunction ^^^ 417 from device da 410 to db 411. A composition of an approximated map421 is shown.In the mappings schematic 500 shown in Figure 5 a virtual machine VM 516 is showndisposed within the perimeter of the graph. Interconnection of the virtual machine VM516 and each device da 510, db 511, dc 512, dD 514, dD-1513, di 515 at each node isillustrative of each mapping function between each device and the VM, for example,the mapping function 518 from device da 510 to the VM 516 and themapping function ^(⋅ ; ^^) 519 from device db 511 to the VM 516.In the mappings schematic 600 shown in Figure 6, the devices are shown as physicalMRI machines including a SiemensTM1.5T 620 as device da, a PhilipsTM1.5T 621 as device db, a GETM3T 622 as device dc, a PhilipsTM3T 623 as device dD-1, a GETM1.5T 624 as device dD, and a SiemensTM3T 625 as device di. There are interconnections between each physical machine to illustrate the mapping functions between them, for example a mapping function 627 from the Siemens®1.5T 620 to the PhilipsTM1.5T 621. There is also an interconnection shown between each physical machine and the VM 616 to illustrate the respective mapping function, for example the mapping function 628 from the SiemensTM1.5T 620 to the VM 626 and the mapping function from the PhilipsTM1.5T 621 to the VM 626.A device ^ , for example a physical MRI machine, provides an estimate of ameasurement ^ . Figures 5 and 6 show devices, for example MRI machines^^, ^^, … , ^^, and each provides its own measurement ^^, ^^, … , ^^ respectively.The estimates are mapped from one device to the other. An ‘ideal’ device which isthe VM shown in Figure 5 provides the ideal measurement.The measurements ^^, ^^, … , ^^ are all estimates of T1. Functions are sought thatmap the estimates, i.e. the measurements, from one device to another. Figure 4 andFigure 5 shows such a function ^^^ 517 from device ^^ to device ^^.For devices ^^ and ^^, function ^^^ is a function to map measurements from the firstdevice ^^ to the second device ^^. The function could take a single form ^ which canbe parameterized by a set of parameters ^^^such that: ^^^: = ^(^^; ^^^) ≈ ^^where (^^ , ^^) represent a pair of corresponding measurements corresponding toeach device. The measurements may each be of T1 from a respective MRI machine.Parameter(s) ^^^ are estimated given a set of paired data measurements for each ofthe devices. The data include, but is not limited to, PDFF, water T2*, fat content, andothers. The VM (an ideal device) ^ provides an ideal measurement ^. The virtualmachine (VM) has certain desirable properties that are iteratively approximated to an optimum from a plurality of existing machines and sets of pairwise data. Examples of the existing machines are shown by the perimeter nodes in Figure 6, and there may also be other existing machines. Desirable properties may include estimating T1precisely and accurately or estimating T1 with more accuracy or confidence thanobtainable from a measurement with an existing machine. For example, water T1 andphysical machines will more or less closely approximate the VM.In an embodiment the VM is a combination of a physical MRI machine or computerprogrammed model of the physical MRI machine, a set of scanning conditions and object properties. For example: a dedicated VM would produce a T1 value of 50 ms when scanning a vial of a NiCl2-agarose gel phantom at 23 degrees. In an embodiment the VM incorporates biophysical models. In an embodiment the VM incorporates a priori information of what is being scanned (anatomy, physiologicalprocesses, MRI-based measurements: water T2*, fat content, and others).It is an advantage that physical measurements of humans made by MRI systems are modified, and the modified measurements standardized to a virtual MRI machine, i.e. the modified physical measurements of humans are independent of the particular MRI system employed. Thus, the modified physical measurements depend only on the underlying physical properties of the human. Furthermore, T1 measurements of humans may be modified so that they are scanner-referenced to a virtual MRI machine, and therefore comparable across systems. A function maps measurements from each of the physical devices to the VM. Figure 5shows two of the functions ^(^^; ^^) 518 and ^(^^; ^^)519. For a specific actualdevice ^^ the function mapping its measurements to ^ is denoted by which isparameterized by parameter ^^ . i.e., ≔ ^(^^; ^^) ≈ ^.It is an advantage that the system and method provide a generalised scheme for post-processing a physical MRI measurement by standardization, where the physical measurement is independent (and thus comparable) across different measurement conditions or devices such as different MRI machines.The set of all mapping parameters Θ ≔ {^^, ^^ , … , ^^} from each of the observeddevices ^^, ^^, … , to the VM are unknown and need to be estimated.As shown by reflexivity 422 in Figure 4, ^^^ refers to the functional mappingparameters from a physical device ^^ to another physical device ^^. While as shownin Figure 5 by a mapping function f 518, ^^refers to the functional mappingparameters from the physical device ^^ 510 to the VM 516. Given some paired datasets for some set of pairs of devices, the actual devices canbe viewed as nodes in a graph ^ ≔ (^, ^) where ^ represents the nodes of the graphand ^ represents the edges. Figure 6 shows a mappings schematic 600 in which theactual devices as MRI machines, for example Siemens™ 1.5T 620, Philips™ 1.5 T621, GE™ 1.5T 624, Siemens™ 3T 625, Philips™ 3 T 623, GE™ 3T 625.In Figure 7 the symbol PS3 means a map 736 of a PhilipsTM 3T 731 to a SiemensTM 3T739. The symbol S1.5,3 means a map 738 from a SiemensTM 1.5T 733 to a SiemensTM3T 739. The symbol GS3 means a map 737 from a GETM 3T 732 to a SiemensTM 1,5T733. The symbol GS1.5 means a map 739 from a GETM1.5T 735 to a SiemensTM1,5T 733. It is an advantage that standardising physical measurements across MRI systems enables: cross-comparison of measurements over multiple MRI systems and establishing unique reference ranges for evaluation; clarifies clinical recommendationsand mitigates the risk of comparing physical properties without accounting for MRIsystem differences; provides a benchmark for support of new MRI systems; and simplifies statistical analysis downstream of multi-centre projects comprising multiple different MRI scanners.Explicitly: all pairs (^, ^), 1 ≤ ^ < ^ ≤ ^ , wherethere is data that can be used in the mapping function parameters ^^^.For any given pair of functional mapping parameter sets, for example the pair {^^^ , ^^^}or the pair {^^, ^^} a mapping function ^ can be defined that represents the ‘distance’or ‘discrepancy’ between the two parameter sets in the pair. The pairwise data maycomprise data for patients or objects that are acquired on MRI machines with differingproperties where the properties include manufacturer, model, and field strength. Forexample, a set of patients may undergo scans on both GE Signa 1.5T MRI machineand a Philips Ingenia 3T MRI machine. At any particular time, data may exist for acertain set of pairs of MRI machines and the VM may be approximated. At a later time,scans for a previously unseen pair of MRI machines may be obtained and the approximation process may be repeated to incorporate the new data. In an embodiment the VM integrates features via ‘scanner families’, that is, one or more subset(s) of existing MRI machines that have similar properties and diversemagnetic field strengths (e.g. 0.55T – 11T).For the VM, the total dispersion S of the parameters to each of the actual devices isminimized, i.e., the value of ^ where: An optimization scheme can initialize the VM parameter sets based on existing physical devices and sets of paired measurements and update iteratively to minimize the total dispersion ^. This is a direct data fidelity term or constraint. Optimization of the VM can be iterative and nonlinear, in contrast to linear. In an embodiment, the system iteratively ‘learns’ and maps to the VM optimum reference functions from each physical MRI machine. As a nonlinear computation, the iterative process by which VM is estimated starts from an initial point: that is, each initialization of a VM Is set to an optimal ‘global minimum’. In some cases the VM should be very close to a physical scanner, for example, a SiemensTM3T physical scanner in case of srT1. An objective is for the VM to becomepractically indistinguishable from a physical MRI machine to correlate with a medicaldevice.Properties of the method and system comprise:Reflexivity: Estimating a set of the mapping function parameters between a pair of devices, whether they are both actual, or one of them is virtual, should be reflexive, i.e., estimating in one direction should be consistent with estimating in the other. For actual devices ^^and ^^, the parameter ^^^set from a to b should lead to afunction that is the inverse of the parameter set ^^^ from b to a, or close to it.^(⋅ ; ^^^) ≈ ^^^(⋅; ^^^)For actual device ^^and the virtual machine VM, the parameter set ^^from a to the VM should lead to a function that is the inverse of the parameter set from VM to a. Composition: For the number of actual devices, for example, for three devices, a measurement mapping from the first to the second can be composed with a mapping from the secondto the third. This facilitates consistency.Consistency / transitivity:For a number of actual devices, for example, for three actual devices, ^^ , ^^ , ^^, thereis: ^(⋅ ; ^^^) ∘ ^(⋅ ; ^^^) ≈ ^(⋅ ; ^^^)The above can be verified for any data: for example, where data exist in the form of acquisitions of the same objects / patients on all three MRI machines. According to the definition of the VM, and according to the functional mappings from each of the physical devices to the VM, we can express the function mapping between two example physical devices ^^and ^^via the VM, as the composition of the mapping from ^^to VM with the mapping from VM to ^^, in the following way: We next assume we have a specification of a “virtual machine” ^^^, from which, for any data, we can generate an estimate of T1. Of course, we may not have a physical machine in this case, and so we have to rely on the Simulator, and assume we have no real data. We make this explicit with a tilde sign. With reference to Figure 3, wewould expect that ^^,^^(^^^^) ≈ ∘ ^^^)(^^^^), that is that This constraint would hold for all pairs (^, ^) and by propagation ^ → ^ → ^ … → ^^ andmay be used as part of a loss function in the optimization of the system. This constraint can be additional to a direct data fidelity term.The above can also be used to generate an additional loss function to optimize, or tominimize, the dispersion that represents inconsistency between the direct mappingsbetween any two physical devices ^^and and its corresponding mappingcomposition via the VM. The inconsistency is the direct mappings between any twophysical devices ^^ and ^^ differ from indirect mapping between the respective twophysical devices via the VM. For example, the total dispersion that is minimized mayby the sum of the squares of the absolute difference between the direct mapping andindirect mapping between any two physical devices ^^ and ^^ for all of the physicaldevices and the VM: When estimating the ideal device, by updating the set Θ, consistency is preserved.In an embodiment, a simulator for each machine ^^ gives ^1 as a function of^1^ , PDFF, ^∗ ^^1^ = ^^(^1^ , PDFF, ^^∗|^^) This represents prior knowledge about ^^. The ‘hat’ indicates that this approximates T1 because the mathematical model is an approximation to reality. Such a simulator embodies knowledge of the physics of MRI, for example the Bloch equations, which would be familiar to those skilled in the art. Furthermore, ^^does not need to exist as a physical entity. A sufficient set of parameters defines a real or virtual machine ^^^^^^^^to generate a function ^1^^^^^^^. That is, from time to time, based on advances in MRI technology, the design and specification of the current best MRI machine is determined, referred to as ^^^. An approximation can thus be derived. ^1^^ = ^^^(^1^ , PDFF, ^^∗|^^^)We have ^^1^ → ^1^ : ^^^^ ^^^ ^, ^^. But, in each case the number of “training” casesis small. Note that for each of the “training” cases for each pair of machines, the assumption of linearity amounts to: Where ^^^is (for example) the slope of the linear mapping and there may be a second term for an intercept. However, we do not restrict ourselves to linear relationships.Let’s consider any pair ^^ , ^^ of MRI machines. From an arbitrarily large set of data We can compute from the Simulator : In essence, this finds the differences at each data point (as noted above, a manifold) between the T1 valuesreported on each of the machines. Subject to whatever loss function we define, thislearns the transform ^ ^^^ : ^1 → ^1^.The reference measurement of T1 and srT1 may iteratively evolve, relative to the VM. This is an advance over a straightforward correction for scanner make and field strength bias to T1. Evidence may be seen in Figure 8. Four MRI images 841, 842m846m 847 are shown. There are two upper images 841, 842 that show T1 prior tostandardisation. The upper left image 841 Scan A is acquired from a GETM 1.5T MRImachine and the median T1 is 565 ms. The upper right image 842 Scan B is acquiredfrom a SiemensTM3T MRI machine and the median T1 is 750 ms. Beforestandardisation, the median T1 in the image acquired by the GETM 1.5T MRI machineis 32 percent less than the median T1 of the image acquired from the SiemensTM3TMRI machine as shown by the scale 844. There are two lower images 846, 847 thatshow T1 after standardisation. The lower left image 846 shows scan A afterstandardisation and the median T1 is 707 ms which is six percent less than the medianT1 of the image acquired from the SiemensTM 3T MRI machine as shown by the scale849.These differences are also shown in Figure 9. A graph on the left 901 plots imagedensity 903 versus T1 904 before standardisation of images from populations ofsubjects acquired by a SiemensTM1.5T MRI machine 921 and SiemensTM3.0 T MRImachine 922. The graph on the left 901 shows a distinct difference between peaks907, 908 in the density at 600 ms and 780 ms. There is also a significant differencein the height of the density peaks at .005 and .0068. A graph on the right 902 plotsimage density 905 versus T1 906 after standardisation of images from the samepopulations of subjects acquired by a SiemensTM1.5T MRI machine 923 andSiemensTM 3.0 T MRI machine 924.In the graph 901 before standardization, the plot from the SiemensTM1.5T machine921 is distinctly offset along the raw scanner T1 axis 904 from the form of theSiemensTM3.0T machine 922 plot. The graph on the right 902 shows peaks in thedensity at about 760 ms and 780 ms is about the same for the SiemensTM 1.5T machine923 and the SiemensTM 3T machine 924 . The heights of the peaks are also aboutthe same at .005 and .0051. The plots also have nearly the same form and are in register with each other.Therefore, for those pairs of machines for which we have both real and simulated datawe can learn the transform ^ ^^^: ^1 → ^1^ .ImputationIt is possible to impute data for ‘missing’ edges, ∉ ^. i.e., pairs of deviceswhere matched data are unavailable, for example, using composition etc. as described above. Consequently, the VM is able to anticipate new MRI machines and new system capabilities, as well as additional sets of pairwise data.Where a VM has been determined, a new MRI machine may be introduced via a newfunction that maps the new MRI machine to one of the existing MRI machines. Themethod could then be used to update the estimated VM. Alternatively, pre-existing mappings and the VM may be fixed and function parametersrelating to the new MRI machine may be estimated. Alternatively, some arbitrarilydefined subset of the parameters in the system may be re-estimated (e.g., thoserelating to an MRI machine family), keeping the remainder fixed.The invention has been described by way of examples only. Therefore, the foregoing is considered as illustrative only of the principles of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation shown and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the claims. .

Claims

1. Claims:

1. A system comprising a Virtual Machine VM implemented on a computer standardisinga physical measurement of scanned tissue by assorted MRI machines, whereinfirst functional mapping parameters in a first function map the physical measurement of each one of the assorted MRI machines to a different one of the assorted MRImachines; and second functional mapping parameters in a second function map the physicalmeasurements of each of the assorted MRI machines to an ideal measurement fromthe VM.

2. A system according to claim 1 wherein the first and the second function mappingparameters comprise one or more of: T1 measured, proton density fat fraction PDFF, T2*, T2* measured, tissue iron content by T2*, liver iron content, and iron content of the scanned tissue.

3. A system according to claim 1 or 2 wherein the physical measurement comprises one or more of: T1, T1 corrected for iron content, T1 water, and T1 VM.

4. A system according to claim 1 or 2 wherein the physical measurement comprisesone or more of: T1, T1 corrected for fat content, T1 water, and T1 VM.

5. A system according to claim 1 or 2 wherein the physical measurement comprisesone or more of: T1, T1 corrected for iron content using T2* and T1 corrected for fatcontent using PDFF, fat content, T1 water, and T1 VM.

6. A system according to any preceding claim wherein all the MRI machines are actualdevices that make the physical measurement.

7. A system according to any of claims 1 to 5 wherein certain ones of the MRI machinesare actual devices that make the physical measurement and other ones comprise acomputer in which there is a computer simulation that executes the first function, thesecond function, or both functions.

8. A system according to any preceding claim in which an inverse of the first functionmaps the physical measurement from the different one of the assorted MRI machinesback to each one of the assorted MRI machines respectively such that the firstfunction is reflexive.

9. A system according to any preceding claim in which an inverse of the secondfunction maps the ideal measurement from the VM back to each one of the assortedMRI machines respectively such that the second function is reflexive.

10. A system according to any preceding claim in which for any three of the assortedMRI machines: first, second, and third; the first function maps the physicalmeasurement of the first one of the assorted MRI machines to the second one, andmaps the physical measurement of the second one of the assorted MRI machines tothe third one, and maps the physical measurement of the first one of the assorted MRI machines to the third one, such that composition with the first function is consistent and transitive for all of the assorted MRI machines.

11. A system according to any preceding claim in which for the VM and any two of the assorted MRI machines: an indirect mapping composition in which the second function maps the physical measurement of one of the assorted MRI machines to the ideal measurement of the VM and an inverse of the second functional mapping parameters in an inverse of the second function maps the ideal measurement from the VM back to the physical measurement of the different one of the assorted MRI machines is equivalent to a direct mapping in which the first function which maps the physical measurement of the one of the assorted MRI machines to the different one such that the indirect mapping composition with the second function is consistent andtransitive for all the assorted MRI machines via the VM.

12. A system according to any of claims 1 to 10 wherein the first function mappingbetween any two of the assorted MRI machines is equivalent to an indirect mappingcomposition of the second function mapping from one of the two assorted MRImachines to the VM with the inverse of the second function mapping from the otherone of the two assorted MRI machines to the VM.

13. A system according to any preceding claim accounts for discrepancy in fidelity between the first functional mapping parameters of a pair of the assorted MRI machines.

14. A system according to any preceding claim accounts for discrepancy in fidelity between the second functional mapping parameters for the VM and a, or the, pair of the assorted MRI machines.

15. A system according to any preceding claim accounts for discrepancy in fidelity between the physical measurements of a, or the, pair of the assorted MRI machines and the respective ideal measurements of the VM.

16. A system according to any preceding claim accounts for discrepancy in fidelity between the ideal measurement from the VM for each one of the assorted MRI machines in a, or the, pair.

17. A system according to any of claims 13 to 16 accounts for the discrepancy for everypair that is a combination of two of all the assorted MRI machines.

18. A system according to any of claims 1 to 17 wherein an inconsistency between themapping of two of the MRI machines and its corresponding mapping composition via the VM is minimal.

19. A system according to any of claims 1 to 17 compensates for an inconsistencybetween a direct mapping of two of the assorted MRI machines and an indirectmapping composition between the two of the assorted MRI machines via the VM, wherein the direct mapping uses the first functional mapping parameters in the first function and the indirect mapping composition uses the second functional mapping parameters in the second function.

20. A system according to claim 19 which compensates by minimizing an aggregate ofthe inconsistency for every combination of two of all the assorted MRI machines andthe VM.

21. A system according to claim 20 wherein the aggregate comprises a sum of thesquare of the inconsistency for every combination.

22. A system according to any of claims 18 to 21 determinesthe indirect mapping composition in which the second function maps the physicalmeasurement of one of the assorted MRI machines to the ideal measurement of the VM and an inverse of the second functional mapping parameters in an inverse of thesecond function maps the ideal measurement from the VM back to the physicalmeasurement of the different one of the assorted MRI machines, the direct mapping in which the first function which maps the physical measurementof the one of the assorted MRI machines to the different one,and determines the inconsistency as a difference between the composition and the direct mapping.

23. The system according to any preceding claim comprising a computer program directly loadable into the memory of a computer for operating the system.

24. The system according to claim 22 comprising the computer with the computerprogram loaded into the memory.

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