Compensation of magnetic field distortions from paramagnetic instruments by added diamagnetic material: Measurements and numerical simulations

A zirconia/tantalum biocermet: in vitro and in vivo evaluation for biomedical implant applications

A biocermet made of zirconia/20 vol% tantalum (3Y-TZP/Ta) is a new composite with exceptional capabilities due to a combination of properties that are rarely achieved in conventional materials (high strength and toughness, cyclic fatigue resistance and flaw tolerance, wear resistance, corrosion resistance, electrical conductivity, etc.). In this study, for the first time, the biomedical performance of a 3Y-TZP/Ta biocermet was evaluated in detail. Its in vitro biocompatibility was assessed using mesenchymal stem cell culture. The effectiveness of in vivo osteointegration of the biocermet was confirmed 6 months after implantation into the proximal tibiae of New Zealand white rabbits. In addition, the possibility of using magnetic resonance imaging (MRI) for medical analysis of the considered biocermet material was studied. The 3Y-TZP/Ta composite showed no injurious effect on cell morphology, extracellular matrix production or cell proliferation. Moreover, the implanted biocermet appeared to be capable of promoting bone growth without adverse reactions. On the other hand, this biocermet demonstrates artefact-free performance in MRI biomedical image analysis studies, making it more suitable for implant applications. These findings open up possibilities for a wide range of applications of these materials in orthopedics, dentistry and other areas such as replacement of hard tissues.

On the equivalence of demagnetization tensors as discrete cell size approaches zero in three-dimensional space

The calculation of the demagnetization field is crucial in various disciplines, including magnetic resonance imaging and micromagnetics. A standard method involves discretizing the spatial domain into finite difference cells and using demagnetization tensors to compute the field. Different demagnetization tensors can result in contributions from adjacent cells that do not approach zero, nor do their differences, even as the cell size decreases. This work demonstrates that in three-dimensional space, a specific set of magnetization tensors produces the same total demagnetization field as the Cauchy principal value when the cell size approaches zero. Additionally, we provide a lower bound for the convergence speed, validated through numerical experiments.

High-resolution simulation of B0 field conditions in the human heart from segmented computed tomography images

B₀ inhomogeneity leads to imaging artifacts in cardiac magnetic resonance imaging (MRI), in particular dark band artifacts with steady-state free precession pulse sequences. The limited spatial resolution of MR-derived in vivo B₀ maps and the lack of population data prevent systematic analysis of the problem at hand and the development of optimized B₀ shim strategies. We used readily available clinical computed tomography (CT) images to simulate the B₀ conditions in the human heart at high spatial resolution. Calculated B₀ fields showed consistency with MRI-based B₀ measurements. The B₀ maps for both the simulations and in vivo measurements showed local field inhomogeneities in the vicinity of lung tips with dominant Z3 spherical harmonic terms in the field distribution. The presented simulation approach allows for the derivation of B₀ field conditions at high spatial resolution from CT images and enables the development of subject- and population-specific B₀ shim strategies for the human heart.

Susceptibility artifacts induced by crowns of different materials with prepared teeth and titanium implants in magnetic resonance imaging

This study aimed to investigate the artifacts induced by crowns composed of different materials with prepared teeth and titanium implants. Resin, metal-ceramic, ceramic and zirconia crowns were fabricated and placed onto the prepared teeth on a human cadaver head or titanium implants with prosthesis abutments on a dry human mandible. The samples were scanned on a 1.5 T MRI apparatus, and artifact areas were defined as the signal intensity and signal loss adjacent to the prosthesis and measured by a threshold tool with ImageJ2x. Data were analyzed using SPSS 22.0. Resin, ceramic, zirconia, and precious metal-ceramic crowns barely produced artifacts on the cadaver skull (p > 0.999). By contrast, pure Ti and nonprecious metal-ceramic crowns created significant artifacts (p < 0.001). The average artifacts reduction of double Au-Pt and Ag-Pd metal-ceramic crowns combined with titanium implants and abutments was 79.49 mm² (p < 0.001) and 74.17 mm² (p < 0.001) respectively, while artifact areas were increased in double Co-Cr and Ni–Cr metal-ceramic crowns by 150.10 mm² (p < 0.001) and 175.50 mm² (p < 0.001) respectively. Zirconia, ceramic and precious metal-ceramic crowns induce less MRI artifacts after tooth preparation while precious metal-ceramic crowns alleviate artifacts in combination with titanium implants.

MRI magnetic compatible electrical neural interface: From materials to application

Neural electrical interfaces are important tools for local neural stimulation and recording, which potentially have wide application in the diagnosis and treatment of neural diseases, as well as in the transmission of neural activity for brain-computer interface (BCI) systems. At the same time, magnetic resonance imaging (MRI) is one of the effective and non-invasive techniques for recording whole-brain signals, providing details of brain structures and also activation pattern maps. Simultaneous recording of extracellular neural signals and MRI combines two expressions of the same neural activity and is believed to be of great importance for the understanding of brain function. However, this combination makes requests on the magnetic and electronic performance of neural interface devices. MRI-compatibility refers here to a technological approach to simultaneous MRI and electrode recording or stimulation without artifacts in imaging. Trade-offs between materials magnetic susceptibility selection and electrical function should be considered. Herein, prominent trends in selecting materials of suitable magnetic properties are analyzed and material design, function and application of neural interfaces are outlined together with the remaining challenge to fabricate MRI-compatible neural interface.

Dedicated holmium microsphere administration device for MRI-guided interstitial brain microbrachytherapy

Microbrachytherapy with radioactive holmium-166 (¹⁶⁶Ho) microspheres (MS) has the potential to be an effective treatment method for brain malignancies. Direct intratumoural delivery of ¹⁶⁶Ho-MS and dose coverage of the whole tumour are crucial requirements. However, currently no dedicated instruments for controlled intratumoural delivery exist. This study presents an administration device that facilitates this novel magnetic resonance imaging (MRI) -guided intervention. The bioceramic alumina oxide cannula creates a straight channel for a superelastic nitinol precurved stylet to control spatial deposition of Ho-MS. End-point accuracy of the stylet was measured during insertions in phantoms. Imaging tests were performed in a 3 Tesla MRI-scanner to quantify instrument-induced artefacts. Additionally, the feasibility of non-radioactive holmium-165 (¹⁶⁵Ho)-MS delivery with the administration device was evaluated in a brain tumour simulant. Absolute stylet tip error was 0.88 ± 0.61 mm, instrument distortion in MRI depended on needle material and orientation and dose delivery of ¹⁶⁵Ho-MS in a brain tumour phantom was possible. This study shows that the administration device can accurately place the stylet for injection of Ho-MS and that visualization can be performed with MRI.

Novel Composite Gold-Aluminum Electrode with Application to Neural Recording and Stimulation in Ultrahigh Field Magnetic Resonance Imaging Scanners

Traditional electrodes used for neural recording and stimulation generate large regions of signal void (no functional MRI signal) when used in ultrahigh field (UHF) MRI scanners. This is a significant disadvantage when simultaneous neural recording/stimulation and fMRI signal acquisition is desired, for example in understanding the functional mechanisms of deep brain stimulation (DBS). In this work, a novel gold-aluminum microwire neural electrode is presented which overcomes this disadvantage. The gold-aluminum design greatly reduces the magnetic susceptibility difference between the electrode and brain tissue leading to significantly reduced regions of signal void. Gold-aluminum microwire samples are imaged at ultrahigh field 16.4 Tesla and compared with gold-only and aluminum-only microwire samples. First, B0 field mapping was used to quantify field distortions at 16.4T and compared with analytical computations in an agarose phantom. The gold-aluminum microwire samples generated substantially less field distortion and signal loss in comparison with gold-only and aluminum-only samples at 16.4T using gradient echo imaging and echo planar imaging sequences. Next, the proposed gold-aluminum electrode was used to successfully record local field potential signals from a rat cortex. The newly proposed gold-aluminum microwire electrode exhibits reduced field distortions and signal loss at 16.4T, a finding which translates to MRI scanners of lower magnetic field strengths as well. The design can be easily reproduced for widespread study of DBS using MRI in animal models. Additionally, the use of non-reactive gold and aluminum materials presents an avenue for translation to human implant applications in the future.

Minimal artifact actively shimmed metallic needles in MRI

PURPOSE

Signal voids caused by metallic needles pose visualization and monitoring challenges in many MRI applications. In this work, we explore a solution to this problem in the form of an active shim insert that fits inside a needle and corrects the field disturbance (ΔB₀ ) caused by the needle outside of it.

METHODS

The ΔB₀ induced by a 4 mm outside-diameter titanium needle at 3T is modeled and a two-coil orthogonal shim set is designed and fabricated to shim the ΔB₀ . Signal recovery around the needle is assessed in multiple orientations in a water phantom with four different pulse sequences. Phase stability around the needle is assessed in an ex-vivo porcine tissue dynamic gradient echo experiment with and without shimming. Additionally, heating of the shim insert is assessed under 8 min of continuous operation with 1A current and concurrent imaging.

RESULTS

An average recovery of ~63% of lost signal around the needle across orientations is shown with active shimming with a maximum current of 1.172 A. Signal recovery and correction of the underlying ΔB₀ is shown to be independent of imaging sequence. Needle-induced phase gradients outside the perceptible signal void are also minimized with active shimming. Temperature rise of up to 0.9° Celsius is noted over 8 min of continuous 1A active shimming operation.

CONCLUSION

A sequence independent method for minimization of metallic needle induced signal loss using an active shim insert is presented. The method has potential benefits in a range of qualitative and quantitative interventional MRI applications.

Modeling of active shimming of metallic needles for interventional MRI

PURPOSE

Artifacts caused by large magnetic susceptibility differences between metallic needles and tissue are a persistent problem in many interventional MRI applications. The signal void caused by the needle can hide procedure targets and prevent accurate image-based monitoring. In this paper, a solution to this problem is presented in the form of an active shim insert inspired from degaussing coils used in naval vessels, that is designed to correct the field disturbance (ΔB₀ ) caused by the needle.

METHODS

The ΔB₀ induced by a 10 gauge hollow single-beveled titanium needle at 3T is modeled in different orientations. A set of 63 orthogonal coil pairs with unique tip paths are evaluated for shimming performance, and an optimal coil pair is chosen. Shimming performance and current demands are evaluated over a range of needle orientations.

RESULTS

Robust correction of the titanium needle induced ΔB₀ is predicted using a flat no-loop coil combined with an orthogonal 1½ turn loop coil angled at the bevel angle for most orientations, with currents well below 1 amp per coil. Reductions in ΔB₀ standard deviations with shimming ranged from ~49% to ~10% depending on needle orientation, with performance worsening as the needle is aligned more along B₀ .

CONCLUSION

Simulations predict that it is possible to minimize metallic probe induced ΔB₀ and signal losses using externally supplied direct current shim coil inserts in arbitrary orientations for potential benefits in many interventional MRI applications.

Computation of Magnetic Field Distortions and Impact on T2*-weighted MRI with Application to Magnetic Susceptibility Parameter Estimation

A two-step numerical computation of T₂* signal weighting maps in gradient echo magnetic resonance imaging in the presence of an object with varied susceptibility property is presented. In the first step, the magnetic scalar potential is computed for an arbitrary 2D magnetic susceptibility distribution using an algebraic solver. The corresponding magnetic field disturbance is computed from the magnetic scalar potential. In the second step, nonlinear operations are used to compute T₂* from the magnetic field disturbance and then to generate a map of T₂* signal weighting. The linearity of the first step of the solution process is used to implement a superposition of basis solutions approach that increases computational efficiency. Superposition of basis solutions, computed from a system composed of a single node of differing magnetic susceptibility from the surround, herein referred to as the base system, is found to provide an accurate estimation of the scalar potential for arbitrary susceptibility distributions. Afterwards, nonlinear computation of the T₂* signal weighting maps can be performed. The properties of the algebraic magnetic scalar potential solver are discussed in this work. Finally, the linearity of the magnetic scalar potential solver is used to estimate the magnetic susceptibility of various objects from in vitro MR-imaging data acquired at 9.4T.

Rapid, theoretically artifact-free calculation of static magnetic field induced by voxelated susceptibility distribution in an arbitrary volume of interest

PURPOSE

To demonstrate a computationally efficient and theoretically artifact-free method to calculate static field (B₀ ) inhomogeneity in a volume of interest induced by an arbitrary voxelated susceptibility distribution.

METHODS

Our method computes B₀ by circular convolution between a zero-filled susceptibility matrix and a shifted, voxel-integrated dipolar field kernel on a grid of size N_S +N_T - 1 in each dimension, where N_S and N_T are the sizes of the susceptibility source and B₀ target grids, respectively. The computational resource requirement is independent of source-target separation. The method, called generalized susceptibility voxel convolution, is demonstrated on three susceptibility models: an ellipsoid, MR-compatible screws, and a dynamic human heartbeat model.

RESULTS

B₀ in an ellipsoid calculated by generalized susceptibility voxel convolution matched an analytical solution nearly exactly. The method also calculated screw-induced B₀ in agreement with experimental data. Dynamic simulation demonstrated its computational efficiency for repeated B₀ calculations on time-varying susceptibility. On the contrary, conventional and alias-subtracted k-space-discretized Fourier convolution methods showed nonnegligible aliasing and Gibbs ringing artifacts in the tested models.

CONCLUSION

Generalized susceptibility voxel convolution can be a fast and reliable way to compute susceptibility-induced B₀ when the susceptibility source is not colocated with the B₀ target volume of interest, as in modeling B₀ variations from motion and foreign objects.

Aluminum-free low-modulus Ti-C composites that exhibit reduced image artifacts during MRI

Feasibility studies were performed to determine the suitability of a novel synthesis technique for fabricating multifunctional composite materials for orthopedic implants. By blending paramagnetic Ti powder with diamagnetic graphite and consolidating the resulting mixtures, Ti-C composites that cannot be feasibly obtained via conventional alloying techniques or ingot metallurgy were synthesized. The synthesized composite material exhibited extremely low magnetic susceptibility (χ=67.6×10(-6)), and, as a result, exhibited fewer artifacts during magnetic resonance imaging. The strength of the composite material (σ=770MPa) was such that it could support external loads to which the human body is subjected, but its Young's modulus was low (E=81.9 GPa) such that it could mitigate the stress-shielding effect. The material was also free from toxic elements such as Al and V and, thus, can be considered less harmful.

Evaluation of magnetic resonance imaging-compatible needles and interactive sequences for musculoskeletal interventions using an open high-field magnetic resonance imaging scanner

In this article, we study in vitro evaluation of needle artefacts and image quality for musculoskeletal laser-interventions in an open high-field magnetic resonance imaging (MRI) scanner at 1.0T with vertical field orientation. Five commercially available MRI-compatible puncture needles were assessed based on artefact characteristics in a CuSO4 phantom (0.1%) and in human cadaveric lumbar spines. First, six different interventional sequences were evaluated with varying needle orientation to the main magnetic field B0 (0 degrees to 90 degrees ) in a sequence test. Artefact width, needle-tip error, and contrast-to-noise ratio (CNR) were calculated. Second, a gradient-echo sequence used for thermometric monitoring was assessed and in varying echo times, artefact width, tip error, and signal-to-noise ratio (SNR) were measured. Artefact width and needle-tip error correlated with needle material, instrument orientation to B0, and sequence type. Fast spin-echo sequences produced the smallest needle artefacts for all needles, except for the carbon fibre needle (width <3.5 mm, tip error <2 mm) at 45 degrees to B0. Overall, the proton density-weighted spin-echo sequences had the best CNR (CNR(Muscle/Needle) >16.8). Concerning the thermometric gradient echo sequence, artefacts remained <5 mm, and the SNR reached its maximum at an echo time of 15 ms. If needle materials and sequences are accordingly combined, guidance and monitoring of musculoskeletal laser interventions may be feasible in a vertical magnetic field at 1.0T.

In vivo quantification of contrast agent concentration using the induced magnetic field for time-resolved arterial input function measurement with MRI

For pharmacokinetic modeling of tissue physiology, there is great interest in measuring the arterial input function (AIF) from dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) using paramagnetic contrast agents. Due to relaxation effects, the measured signal is a nonlinear function of the injected contrast agent concentration and depends on sequence parameters, system calibration, and time-of-flight effects, making it difficult to accurately measure the AIF during the first pass. Paramagnetic contrast agents also affect susceptibility and modify the magnetic field in proportion to their concentration. This information is contained in the MR signal phase which is discarded in a typical image reconstruction. However, quantifying AIF through contrast agent susceptibility induced phase changes is made difficult by the fact that the induced magnetic field is nonlocal and depends upon the contrast agent spatial distribution and thus on organ and vessel shapes. In this article, the contrast agent susceptibility was quantified through inversion of magnetic field shifts using a piece-wise constant model. Its feasibility is demonstrated by a determination of the AIF from the susceptibility-induced field changes of an intravenous bolus. After in vitro validation, a time-resolved two-dimensional (2D) gradient echo scan, triggered to diastole, was performed in vivo on the aortic arch during a bolus injection of 0.1 mmol/kg Gd-DTPA. An approximate geometrical model of the aortic arch constructed from the magnitude images was used to calculate the spatial variation of the field associated with the bolus. In 14 subjects, Gd concentration curves were measured dynamically (one measurement per heart beat) and indirectly validated by independent 2D cine phase contrast flow rate measurements. Flow rate measurements using indicator conservation with this novel quantitative susceptibility imaging technique were found to be in good agreement with those obtained from the cine phase contrast measurements in all subjects. Contrary to techniques that rely on intensity, the accuracy of this signal phase based method is insensitive to factors influencing signal intensity such as flip angle, coil sensitivity, relaxation changes, and time-of-flight effects extending the range of pulse sequences and contrast doses for which quantitative DCE-MRI can be applied.

Biopsy needle tips with markers--MR compatible needles for high-precision needle tip positioning

Needle tip visualization is of high importance in magnetic resonance imaging (MRI) guided interventional procedures, for example for taking biopsies from suspicious lesions in the liver or kidney. The exact position of the needle tip is often obscured by image artifacts arising from the magnetic properties of the needle. The authors investigated two special biopsy needle tip designs using diamagnetic coatings. For common interventional MR sequences, the needle tip can be identified in the MR image by several equidistant dark spots arranged along a straight line. A dotted instead of a solid line allows for an improved control of the movement of the needle, not only if the needle is tilted toward the imaging plane, but also if the needle leaves an empty canal with signal extinction, which cannot be distinguished from the needle material itself. With the proposed design the position of the needle tip can be estimated with a precision of approximately 1 mm using conventional FLASH, FISP, and TSE sequences, as used for interventional MR. Furthermore, the size of the biopsy probe can be estimated from the artifact. In using needles with a properly designed tip coating, taking biopsies under MR control is beginning to be greatly simplified. The approach to design artifacts using diamagnetic material in combination with paramagnetic material paves the way toward new instruments and implants, suitably tailored to the needs of the interventional radiologist.

Low magnetic moment PIN diodes for high field MRI surface coils

Positive-intrinsic-negative (PIN) silicon diodes are commonly used in magnetic resonance imaging (MRI) coils to perform active or passive blocking and detuning, or to disable circuit functions. However, diode packages with large magnetic moments are known to cause image artifacts in high field MRI systems. In this study, diode packages with low magnetic moment were designed by compensating components of ferromagnetic nickel and paramagnetic tungsten with diamagnetic silver. The new diodes have an initial positive susceptibility up to fields of 1 T and a negative susceptibility from 1 to 7 T. Their magnetic moments are one to two orders of magnitude smaller than those of standard diodes; moments as small as 20 nJ/T at 7 T were achieved.

Concerning the preparation and use of substances with a magnetic susceptibility equal to the magnetic susceptibility of air

In this work it is demonstrated that the susceptibility of diamagnetic substances, such as water and agarose gel, can easily be tuned to the susceptibility of air by the addition of a proper amount of strongly paramagnetic ions, in this case 16.6 +/- 0.1 mM holmium(III). The resultant air-equivalent substances are shown to allow the creation of objects that do not disturb the static magnetic field of the scanner and hence do not invoke susceptibility artifacts, regardless of the objects' shape, size, and orientation with respect to B(0), and regardless of the pulse sequence being used. The addition of the proper amount of holmium(III) to aqueous solutions and gels is further shown to exert a negligible influence on the chemical shift and to cause a moderate increase of the relaxation rates 1/T(1) and 1/T(2). The results indicate the potential of air-equivalent substances for many purposes, including construction of artifact-free test objects; experimental setups and accessory devices; investigation of systems that contain air cavities, gas bubbles, etc.; and monitoring of system-related and object-induced field disturbances.

Combined passive and active shimming for in vivo MR spectroscopy at high magnetic fields

The use of high magnetic fields increases the sensitivity and spectral dispersion in magnetic resonance spectroscopy (MRS) of brain metabolites. Practical limitations arise, however, from susceptibility-induced field distortions, which are increased at higher magnetic field strengths. Solutions to this problem include optimized shimming, provided that active, i.e., electronic, shimming can operate over a sufficient range. To meet our shim requirements, which were an order of magnitude greater than the active shim capacity of our 7T MR system, we developed a combined passive and active shim approach. Simple geometries of ferromagnetic shim elements were derived and numerically optimized to generate a complete set of second-order spherical harmonic shim functions in a modular manner. The major goals of the shim design were maximization of shim field accuracy and ease of practical implementation. The theoretically optimized ferro-shim geometries were mounted on a cylindrical surface and placed inside the magnet bore, surrounding the subject's head and the RF coil. Passive shimming generated very strong shim fields and eliminated the worst of the field distortions, after which the field was further optimized by flexible and highly accurate active shimming. Here, the passive-shimming procedure was first evaluated theoretically, then applied in phantom studies and subsequently validated for in vivo 1H MRS in the macaque visual cortex. No artifacts due to the passive shim setup were observed; adjustments were reproducible between sessions. The modularity and the reduction to two pieces per shim term in this study is an important simplification that makes the method applicable also for passive shimming within single sessions. The feasibility of very strong, flexible and high-quality shimming via a combined approach of passive and active shimming is of great practical relevance for MR imaging and spectroscopy at high field strengths where shim power is limited or where shimming of specific anatomical regions inherently requires strong shim fields.

Geometry and extension of signal voids in MR images induced by aggregations of magnetically labelled cells

The ability of magnetic resonance imaging (MRI) to visualize magnetically labelled cells has attracted much attention for revealing cellular events. The present study addressed the geometry and the extension of signal voids in static signal dephasing MRI induced by aggregations of magnetically labelled cells by means of a three-dimensional numerical model. The magnetic field distortions around spherical cell aggregations were treated as equivalent to those of a magnetic dipole. Intravoxel signal dephasing and respective signal voids attributed to these field inhomogeneities were computed. Effects of cell concentration on the signal void in the plane of view were evaluated in terms of dipole magnetization. Signal void characteristics were scrutinized systematically for fundamental sequence parameters including echo time, voxel size and plane-of-view orientation. For all variables examined, significant changes in geometry as well as extension of signal voids were demonstrated. The results are of crucial importance to optimize and interpret MR images with regard to spatial accuracy as well as sensitivity to detect aggregations of labelled cells in vitro or even in vivo. It is anticipated that the dependence of the extension of signal voids on the local magnetization may be valuable for quantifying labelled cells.

Numerical simulations of intra-voxel dephasing effects and signal voids in gradient echo MR imaging using different sub-grid sizes

Signal void artifacts in gradient echo imaging are caused by the intra-voxel dephasing of the spins. Intra-voxel dephasing can be estimated by computing the field distribution on a sub-grid inside each picture element, followed by integration of all magnetization components. The strategy of computing the artifacts based on the integration of the sub-voxel signal components is presented here for different sub-grids. The coarseness of the sub-grid is directly related to computational effort. The possibility to save memory space and computing time for the dipole model by computing the field only on a sub-grid is addressed in the presented article. It is investigated as to how far computational time and memory space can be reduced by using an appropriate sub-grid. Numerical results for a model of a partially diamagnetically coated needle shaft are compared to experimental findings. In the case of a pure titanium needle, it is shown as being sufficient to compute the field distribution on a sub-grid that is at least four times coarser in each direction than the grid used to discretize the object in the related MR image. Due to three nested loops over the 3D grid, the need for memory space and time is saved by a factor 64. Deviations between measurements and simulations for the broad side of the artifact (uncompensated) and for the small side of the artifact (compensated) were 15.5%, respectively, 19.1% for orientation parallel to the exterior field, and 22.7%, respectively, 23.1% for orientation perpendicular to the exterior field.

Effect of Spatial Distribution of Magnetic Dipoles on Lamor Frequency Distribution and MR Signal Decay – a Numerical Approach Under Static Dephasing Conditions

Cells loaded with superparamagnetic iron oxide (SPIO) cause relatively strong magnetic field distortions, implying that field position effects of neighboring SPIO loaded cells have to be accounted for. We treated SPIO loaded cells as magnetic dipoles in a homogeneous magnetic field and computed the 3D frequency distribution and the related signal decay using a numerical approach under static dephasing conditions. The volume fraction of dipoles was kept constant for all simulations. For larger randomly distributed magnetic dipoles we found a non-Lorentzian frequency distribution and a non-monoexponential signal decay whereas, for smaller dipoles, the frequency distribution was more Lorentzian and the signal decay was well fitted monoexponentially. Moreover, based on our numerical and experimental findings, we found the gradient echo signal decay due to a single SPIO labeled cell to be non-monoexponential. The numerical approach provides deeper understanding of how the spatial distribution of SPIO loaded cells affects the MR signal decay. This fact has to be considered for the in vivo quantification of SPIO loaded cells, implying that in tissues with different spatial distributions of identical SPIO concentrations, different signal decays might be observed.