Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/60—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using electron paramagnetic resonance
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N24/00—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
  • G01N24/10—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects by using electron paramagnetic resonance
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
  • G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
  • G01R33/385—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using gradient magnetic field coils

Definitions

• the invention relates to the field of electron paramagnetic resonance. More specifically the present invention relates to methods and systems for reconstructing particle distribution data in an object based on electron paramagnetic resonance measurement data and computer related aspects based thereon, as well as to an electron paramagnetic resonance system comprising such a reconstruction system.
• Magnetic nanoparticles are increasingly applied for diagnostic and therapeutic purposes. They show a set of interesting physical properties including controllable sizes ranging from ten to several hundred nanometers, a high saturation magnetization and superparamagnetic behaviour. Their small size enables them to penetrate the endothelial walls that form the interface between circulating blood or lymph and the rest of the vessel wall and even to cross cell membranes. By custom functionalisation of the particles' surfaces, they can selectively bind to a defined biological entity (like cells or degraded extracellular matrix molecules) and deliver drugs or therapeutic DNA for targeted therapy.
• a defined biological entity like cells or degraded extracellular matrix molecules
• magnetic nanoparticle imaging By applying a controlled external magnetic field it is possible to perform different actions on the magnetic particles such as applying a mechanic force on the nanoparticles to guide them to a specific location and retaining them there for drug release (magnetic drug targeting, magnetic gene transfection); specifically heating the magnetic nanoparticles (magnetic hyperthermia); changing the local magnetic field in the particle's environment (MRI contrast agents, magnetic cell labelling); generating a specific magnetic signal that can be read from the outside (magnetic nanoparticle imaging); etc. All applications will benefit from a quantitative knowledge of the magnetic nanoparticle distribution to increase suitability, patient safety and efficacy. A non-invasive quantitative technique for magnetic nanoparticle imaging is at present not established, although several proposals have been made in literature.
• MPI Magnetic Particle Imaging
• Magnetic nanoparticles can be activated using an external magnetic field where the single domains of the superparamagnetic nanoparticles are aligned with the local magnetic field.
• magnetic relaxation occurs following two different relaxationprocesses (Brown and Neel).
• the magnetic field originating from the particles in the different positions can be measured using sensitive magnetic field sensors such as superconducting quantum interference devices (SQUIDS).
• SQUIDS superconducting quantum interference devices
• Electron paramagnetic resonance (EPR) and pulsed EPR detection as described by Teughels and Vaes in International patent application WO2010/037800 developed by Teughels and Vaes is able to sense the concentration of particles. Quantification of the concentration in a single voxel has been reported by Gamarra in International journal of Nanomedicine 5 (2010) pp 203-211. There is still room for an accurate spatial reconstruction of magnetic nanoparticles starting from EPR measurements.
• EPR Electron Paramagnetic Resonance
• the object is obtained by systems and methods according to embodiments of the present invention.
• the present invention relates to a system for determining a reconstruction of a particle distribution in an object based on electron paramagnetic resonance (EPR) measurement data of the object comprising the distribution of particles, the system comprising a data obtaining means for obtaining electron paramagnetic resonance measurement data of the object under study, a processor for processing the obtained data by applying a numerical model for solving a numerical inverse problem of deriving from the electron paramagnetic resonance measurement data a reconstruction of the particle distribution, an output means for outputting data based on the derived reconstruction of the particle distribution.
• EPR electron paramagnetic resonance
• the processing means may be adapted for deriving a reconstruction of the particle concentration profile. It is an advantage of embodiments according to the present invention that not only the distribution but also a concentration profile of particles in an object, expressing the amount of particles at a given position, can be accurately obtained.
• the processing means may comprise a quality determining means for determining a measure of the quality of the reconstructed particle distribution. It is an advantage of embodiments according to the present invention that the quality of the
• the system furthermore may comprise a controlling means for controlling the processing of the obtained data, as function of a determined measure of quality of the reconstructed particle distribution. It is an advantage of embodiments according to the present invention that the quality of the reconstructed particle distribution can be fine-tuned to obtain a predetermined quality so that a minimum quality requirement can be obtained.
• the controlling means may comprise a parameter selection means for selecting a parameter of the numerical model. It is an advantage of embodiments according to the present invention that fine-tuning can include adjusting the numerical modeling, thus allowing an internal optimization loop for determining the best reconstruction.
• the parameter selection means may be adapted for altering a set of eigenvalues of the numerical problem solved using the numerical model, depending on the determined measure of quality of the reconstructed particle distribution. It is an advantage of embodiments according to the present invention that an automated and/or automatic optimization of the numerical model can be performed by the processing unit, thus allowing to derive the reconstructed particle distribution in a good, improved or even optimum way.
• the system may comprise a feedback loop comprising the quality determining means and wherein the feedback loop is adapted for controlling the system so as to obtain further electron paramagnetic resonance measurement data of the object.
• Altering of the electron paramagnetic resonance measurement data can comprise requesting alternative input data or can be performed in an automated and/or automatic way.
• the data obtaining means may comprise an EPR measurement system for measuring EPR measurement data, wherein the feedback loop is adapted for controlling the EPR measurement system for obtaining further measurement data with an altered measurement condition for the object. It is an advantage of embodiments of the present invention that systems allow to implement, e.g. in an automated and/or automatic way although not restricted thereto, improved measurement conditions allowing to obtain an improved reconstruction of the particle distribution.
• the feedback loop may be adapted for controlling the data obtaining means so as to obtain further EPR measurement data. It is an advantage of embodiments of the present invention that systems are provided that allow, adjusting the required measurement input, when the predetermined, e.g. desired, reconstruction quality is not obtained.
• the feedback loop may be adapted for controlling the data obtaining means so as to obtain further EPR measurement data of the object sampled at different or additional relative positions of a magnetic field of the EPR system with respect to the object, sampled using different or additional gradient magnetic fields applied to the object, or sampled using a different spatial sampling point distribution over the sample.
• Different parameters determining the EPR measurement data collection can be tuned for obtaining optimal reconstruction quality.
• the present invention also relates to a system for obtaining electron paramagnetic resonance data of an object, the system comprising a system for determining a reconstruction of a particle distribution in an object as described above.
• the present invention relates to a method for determining a reconstruction of a particle distribution in an object based on electron paramagnetic resonance (EPR) measurement data of the object comprising the distribution of particles, the method comprising obtaining electron paramagnetic resonance measurement data of the object under study, processing the obtained data by applying a numerical model for solving a numerical inverse problem of deriving from the electron paramagnetic resonance measurement data a reconstruction of the particle distribution, and outputting data based on the derived reconstruction of the particle distribution.
• EPR electron paramagnetic resonance
• Said processing may comprise deriving a reconstruction of the particle concentration profile.
• the processing may comprise determining a measure of the quality of the
• the method may comprise controlling the processing of the obtained data, as function of the determined measure of quality of the reconstructed particle distribution.
• Said controlling may comprise selecting a parameter of the numerical model.
• Selecting may comprise altering a set of eigenvalues of the numerical problem solved using the numerical model, depending on the determined measure of quality of the reconstructed particle distribution.
• the method may comprise obtaining further electron paramagnetic resonance measurement data of the object, based on the determined measure of quality of the reconstructed particle distribution.
• the method may comprise obtaining further measurement data for an altered measurement condition for the object.
• the method may comprise controlling the data obtaining means so as to obtain further EPR measurement data.
• the method may comprise obtaining further EPR measurement data of the object sampled at different or additional relative positions of a magnetic field of the EPR system with respect to the object, sampled using different or additional gradient magnetic fields applied to the object, or sampled using a different spatial sampling point distribution over the sample.
• the present invention also relates to an image or volumetric image obtained using a system as described above or using a method as described above.
• the present invention also relates to a computer program product for, if implemented on a processing unit, performing the method as described above.
• the present invention also relates to a data carrier comprising a computer program product as described above or the transmission thereof over a network.
• FIG. 1 shows a schematic representation of an exemplary system according to an embodiment of the present invention.
• FIG. 2 illustrates an electron paramagnetic resonance measurement system comprising a distribution reconstruction means as described in FIG. 1.
• FIG. 3 illustrates a schematic overview of steps in an exemplary method for reconstructing a particle distribution in an object, according to an embodiment of the present invention.
• FIG. 4 illustrates an example of an inverse modeling step as can be applied in a method for reconstructing a particle distribution in an object according to an embodiment of the present invention.
• FIG. 5 illustrates assumed concentrations in a volume, as used in simulations illustrating features according to embodiments of the present invention.
• FIG. 6 illustrates calibration functions for different concentration values and Field strengths as used in simulations illustrating features according to embodiments of the present invention.
• FIG. 7 illustrates examples of a set of different applied gradient fields in one direction, as used for simulations illustrating features according to embodiments of the present invention.
• FIG. 8 illustrates a linear net effect is obtained using the calibration functions as shown in FIG. 6.
• FIG. 9 illustrates the net effect measurements for certain concentrations using the conditions described in FIG. 5 to FIG. 8.
• FIG. 10 illustrates a reconstructed concentration profile, illustrating features of method embodiments according to the present invention.
• FIG. 11 illustrates an experimental setup whereby for the example shown movement of the sample was performed along the positive XY- axis, as used in the example illustrating features of embodiments of the present invention.
• FIG. 12 illustrates measured response functions for the situation shown in FIG. 11.
• FIG. 13 illustrates the natural response function, as used in an example illustrating features of embodiments of the present invention.
• FIG. 14A to FIG. 14D illustrates a comparison of the performed measurements and the simulated measurements, illustrating features of embodiments of the present invention.
• FIG. 15 illustrates the eigenvalue distribution for a measurement resolution of 1 mm and a reconstruction resolution of 1 mm, as used in an example illustrating features of embodiments of the present invention.
• FIG. 16 illustrates the influence of noise on the reconstruction quality for the case of 5 retained eigenvalues, illustrating features of embodiments of the present invention.
• FIG. 17 illustrates responses of a real measurement, simulated measurement without noise and a simulated measurement with noise, illustrating features of embodiments of the present invention.
• FIG. 18 illustrates the inclusion of measurements that also consider the insertion and removal of the concentration with respect to the magnetic field, illustrating features of embodiments of the present invention.
• FIG. 19 illustrates the effect of the inclusion of measurements according to FIG. 14 on the eigenvalue distribution.
• FIG. 20 illustrates the effect of the response function used on the reconstructed concentration profile, illustrating features of embodiments of the present invention.
• the drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes.
• particles presenting paramagnetic properties may be introduced in any suitable way such as for example by administering, by mixing, by pouring, etc. More particularly, the information gathered is based on or related to the distribution of the particles representing paramagnetic properties in the object.
• Particles comprising paramagnetic properties may be nano-particles, typically referring to particles having a critical dimension, e.g. diameter, in the range of 1 nm to 1000 nm.
• the nano- particles or magnetic nano-particles may be single domain particles.
• the particles may be magnetic particles with a broad line width, reference may be made to a line width of 3MHz or larger, e.g.
• embodiments of the present invention can be advantageously applied to spin systems with a broad line width, although embodiments of the present invention are not limited thereto and can be applied to spin systems with any line width, i.e. including spin systems with narrow line width.
• an object under study such an object may be a non-living object or a living object.
• the object may be a body of a living creature, such as for example an animal or human body.
• the object under study according to embodiments of the present invention are paramagnetic objects.
• Embodiments of the present invention can also be used for in- vitro testing, e.g. for the quantification of cells linked with the paramagnetic objects).
• Embodiments of the invention allow to reconstruct the distribution of the paramagnetic objects with a high sensitivity and accuracy. Examples of applications include 3D imaging.
• Objects under study may be paramagnetic objects as of nature or may be made at least partially paramagnetic by adding, e.g. through administering, paramagnetic particles, such as paramagnetic nanoparticles, to the object.
• the administering step may be performed prior to application of the method according to embodiments of the present invention for detecting electron paramagnetic resonance of the object under study.
• the present invention relates to a system for reconstructing or determining a reconstruction of a particle distribution in an object. Such determining is based on electron paramagnetic resonance (EPR) measurement data of the object comprising the distribution of particles.
• EPR electron paramagnetic resonance
• Embodiments according to the present invention can be used for all types of electron paramagnetic resonance (EPR) detection, such as for example for detecting paramagnetic particles with broad line width - embodiments of the present invention not being limited thereto.
• a data obtaining means for obtaining electron paramagnetic resonance measurement data of the object under study
• a processor for processing the obtained data by applying a numerical model for solving a numerical inverse problem of deriving from the electron paramagnetic resonance measurement data a reconstruction of the particle distribution
• an output means for outputting data based on the derived reconstruction of the particle distribution.
• a data obtaining means 110 for obtaining electron paramagnetic resonance measurement data Such a data obtaining means may be an input port via which previously recorded electron paramagnetic resonance measurement data is received. Alternatively, such a data obtaining means may include an electron paramagnetic resonance system for recording the measurement data.
• the measurement data as such may be data recorded through any suitable measurement technique.
• One example are the measurement techniques as described in the international patent applications WO 2010/037800 and/or in international patent application WO 2010/037801, or in particular techniques as described e.g. in international patent application PCT/EP2012/055042 or in GB patent application GB1104758.6.
• the system furthermore comprises a processing means 120.
• a processing means 120 typically may be adapted for processing the obtained data by applying a numerical model for solving a numerical inverse problem of deriving from the electron paramagnetic resonance measurement data a reconstruction of the particle distribution.
• a numerical model for solving a numerical inverse problem of deriving from the electron paramagnetic resonance measurement data a reconstruction of the particle distribution.
• the numerical modeling technique comprises input parameter values and output values.
• the input typically is the particle distribution, while the output of the system are the simulated signals in the sensors.
• the numerical inverse problem comprises using this numerical modeling so to determine the parameter values that correspond with the measured signals.
• the processing means comprises a quality determining means 122, allowing to determine a measure of the quality of the reconstructed particle distribution. Quality may e.g. express the way the reconstruction coincides or approaches the measurements.
• the system also comprises an output means for outputting information regarding the particle distribution, e.g. a concentration profile, of the particles in the object.
• an output means for outputting information regarding the particle distribution, e.g. a concentration profile, of the particles in the object.
• the reconstruction system 100 also comprises a controlling means for controlling the processing of the obtained data as function of the determined measure of quality of the reconstruction.
• a controlling may be adapted for controlling the processor, e.g. by adjusting the numerical modeling.
• One way of adjusting the numerical modeling may be by selecting different numerical modeling parameters and the processor therefore may be equipped with a parameter selecting means. Selection of different numerical modeling parameters may be performed based on predetermined algorithms, a neural network, look up tabels, according to predetermined rules, etc.
• One example of adjusting may be selecting the number or the specific set of eigenvalues used in the problem to be solved. For example, when the quality is insufficient, the number of eigenvalues used may be increased or decreased to deal therewith.
• rules may make use of the condition where the difference between measured and simulated signals is smaller than a certain tolerance or if the difference between the particle distribution in a certain iteration compared to the previous one is smaller than a certain tolerance.
• the difference can in one example be expressed as a least-squares difference (L.2-norm), another norm, correlation coefficients, etc.
• the system comprises a feedback loop, and controlling the system as function of the quality does not only affect the reconstruction process as such, but also the measurement data used.
• the control system may be adapted for controlling the system so as to obtain further electron paramagnetic resonance measurement data of the object.
• Such further electron paramagnetic resonance measurement data may for example comprise measurement data recorded with an altered measurement condition for the object.
• Such measurement data may be for example data sampled at different or additional relative positions of a magnetic field of the EPR system with respect to the object, sampled using different or additional gradient magnetic fields applied to the object, or sampled using a different spatial sampling point distribution over the sample.
• the invention also relates to an EPR system comprising a reconstruction system as described above.
• the EPR system as such may for example be a system as described in any of the international patent applications WO 2010/037800 and/or in international patent application WO 2010/037801, or in particular techniques as described e.g. in international patent application PCT/EP2012/055042 or in GB patent application GB1104758.6.
• embodiments of the present invention relate to a method for reconstructing or determining a reconstruction of a particle distribution in an object based on electron paramagnetic resonance (EPR) measurement data of the object.
• the reconstructed distribution may be or provide a concentration profile of the particles in the object.
• the particle distribution envisaged thereby is a distribution of particles comprising paramagnetic properties, as described above.
• Different steps of a method according to an embodiment of the present invention are further illustrated with reference to FIG. 3, embodiments of the present invention not being limited thereby.
• the method according to an embodiment comprises in a first step obtaining 310 electron paramagnetic resonance measurement data of the object under study. Such obtaining data may comprise merely receiving the data via an input port.
• obtaining the data may include performing the electron paramagnetic resonance measurements and receiving the data thereof in the reconstruction system.
• the method also comprises processing 320 the obtained data by applying a numerical model for solving a numerical inverse problem of deriving from the electron paramagnetic resonance measurement data a reconstruction of the particle distribution.
• FIG. 4 A schematic overview of an example of how to apply a numerical model for solving a numerical inverse problem is illustrated in FIG. 4.
• solving a numerical inverse problem comprises a step of applying an inverse reconstruction whereby based on the measurement data obtained a concentration is derived.
• a concentration is derived.
• a so-called forward model is applied, whereby starting from a determined concentration, the estimated measurement results are derived.
• Such forward calculation which needs to include information regarding the measurement conditions, can for the present case relate to deriving concentrations based on performed EPR measurements .
• the method furthermore comprises outputting 330 data based on the derived reconstruction of the particle distribution.
• the method may be implemented such that it operates automated and/or automatic. It may be implemented in a processor and may be based on predetermined algorithms, using predetermined rules and/or look up tables, make use of a neural network for its processing, ....
• the quality of the reconstruction can be monitored.
• the quality (or a measure/metric expressing the quality) of the reconstruction is not only monitored, but it is also tuned to reach a predetermined value, so that an accurate interpretation of the results obtained can be envisaged.
• different actions are possible.
• an internal feedback loop is installed and the quality can be improved or optimized by altering the processing of the obtained data.
• the latter may include using a certain numerical model, altering the numerical model used, e.g. by altering a set of eigenvalues of the numerical problem solved using the numerical model, etc.
• further electron paramagnetic resonance measurement data of the object are obtained or used.
• the method then may comprise obtaining further measurement data for an altered measurement condition for the object.
• Obtaining such further EPR measurement data thereby may for example comprise obtaining further EPR measurement data of the object sampled at different or additional relative positions of a magnetic field of the EPR system with respect to the object, sampled using different or additional gradient magnetic fields applied to the object, or sampled using a different spatial sampling point distribution over the sample.
• embodiments of the present invention also relate to computer- implemented methods for performing at least part of the methods as described above or to corresponding computing program products.
• Such methods may be implemented in a computing system, such as for example a general purpose computer.
• the computing system may comprise an input means for receiving data.
• the system may be or comprise a data processor for processing data, e.g. the electron paramagnetic resonance data of the single domain particles.
• the computing system may include a processor, a memory system including for example ROM or RAM, an output system such as for example a CD-rom or DVD drive or means for outputting information over a network.
• Conventional computer components such as for example a keybord, display, pointing device, input and output ports, etc also may be included.
• Data transport may be provided based on data busses.
• the memory of the computing system may comprise a set of instructions, which, when implemented on the computing system, result in implementation of part or all of the standard steps of the methods as set out above and optionally of the optional steps as set out above. Therefore, a computing system including instructions for implementing part or all of a method as described above is not part of the prior art.
• Further aspect of embodiments of the present invention encompass computer program products embodied in a carrier medium carrying machine readable code for execution on a computing device, the computer program products as such as well as the data carrier such as dvd or cd-rom or memory device. Aspects of embodiments furthermore encompass the transmitting of a computer program product over a network, such as for example a local network or a wide area network, as well as the transmission signals corresponding therewith.
• the gathering of information regarding the magnetic nanoparticles and its translation into a numerical problem typically includes the following :
• V m denotes the modeled responses.
• V mea s the intention is then to reconstruct the real concentrations C* in space using the following relationship.
• the accuracy of the reconstruction can be further optimized by a good, improved or optimal choice of the parameter r in the above formula and a good, improved or optimal system matrix choice A. It is to be noted that there exist a number of different methods for obtaining C*.
• the measured signal 5 can be expressed as (superposition):
• V the volume of the sample, Bhom, hom defined for the single voxel. It is proximated that the function F will also hold when using multiple voxels.
• the aim is to reconstruct Ck by using fields, i.e. Lk different from each other, and multiple measurements.
• a first possibility is to use a gradient coil configuration, i.e. instead of using Helmholtz coils, coils can be placed as Maxwell coils.
• I n a first example, illustrating numerical results, it is assumed that there is a certain test concentration that fluctuates ID (x-direction). If there is for example a volume of 20.4x12x16.8 mm, one wants to reconstruct the particles along the 20.4 side.
• FIG. 5 illustrates two test concentrations that were used in the simulations. The concentration thereby is defined here as the concentration in a volume 1x12x16.8m m 3 .
• FIG. 7 illustrates an example of 10 spatia lly varying applied magnetic inductions that are sequentially applied by using a gradient magnetic field of -lOmT to lOmT over the region of 20mm, yielding gradient of IT/m, and where a Helmholtz homogeneous field is applied with steps of 2.2mT.
• These 10 sequential gradient fields are necessary so to obtain different measurements for the reconstruction of the magnetic nanoparticles.
• results are illustrated using EPR measurements.
• a one dimensional reconstruction through screening was performed, i.e. the sample is moved in the vicinity of the excitation and measurement coils.
• the response function vs position was measured.
• Measurements of Resovist 18.8 (18.8 ⁇ ), Resovist J (0.29 ⁇ ), Resovist K (0.15 ⁇ ) and Resovist L (0.07 ⁇ ) were used to obtain the response function.
• the measurements were performed for the positive XY-axis with a discretization of 1 mm, as shown in FIG. 11.
• the response function was measured (i.e. measurements at different points in EPR) for the 4 different samples described above.
• the measured response functions are shown in FIG. 12.
• a forward model was developed. First the response function was extended to a 'natural response function', with a discretization ⁇ of 0.1 mm, using splines, as shown in FIG. 13.
• the forward model used in the present example is based on the above response functions.
• Fig. 14A to FIG. 14D shows measurements that are sensitive to the distribution of particles.
• the discrepancy between forward and real measurements is here mainly because of noise and changes in the system (for example temperature).
• FIG. 15 shows the distribution of the eigenvalues for the Leadfield matrix L used. These eigenvalues represent the sensitivities of the response function for a measurement resolution of 1 mm and a reconstruction resolution of 1 mm. In total there are 19 eigenvalues. The eigenvalue distribution is dependent on the reconstruction and measurement resolution.
• the selection of the optimal eigenvalue distribution can be obtained by proposing an internal optimization loop that determines numerically the best eigenvalues that give the best reconstruction quality.
• the correlation coefficient for different concentrations using different noise levels were compared.
• the obtained construction result is dependent on the number of used eigenvalues. For lower noise levels, one should use more eigenvalues. The latter can be explained by the fact that in this case most eigenvalues represent signal sources instead of noise sources.
• FIG. 17 shows an example of a measurement, a simulated measurement without noise and a simulated measurement with noise and the corresponding reconstructions. The differences between the responses cause errors on the reconstructions.
• a first used Leadfield matrix only considered the concentration distribution inside the magnetic field (meaning that for every element of the concentration distribution there exists a corresponding response function value). Initially a low condition number was obtained for the Leadfield matrix, however due to changes of the response function (more measurements) this condition number became higher. The condition number should be as low as possible, as a condition number shows the extent to which a calculated value (in our case the reconstruction) will change, when fixed parameters are changed (our Leadfield matrix). A high condition number means a big difference in reconstruction values for only a small change of the Leadfield values. This means that a response function with a small error, will have a major effect on the reconstruction. The Leadfield matrix was therefore extended with more measurements.

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