Degradation, Metabolism and Relaxation Properties of Iron Oxide Particles for Magnetic Resonance Imaging

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(1)Comprehensive Summaries of Uppsala Dissertations from the Faculty of Medicine 1362. Degradation, Metabolism and Relaxation Properties of Iron Oxide Particles for Magnetic Resonance Imaging BY. KAREN BRILEY SAEBO. ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2004.

(2) Uppsala University Department of Oncology, Radiology and Clinical Immunology Section of Radiology Akademiska sjukhuset SE-751 85 Uppsala, Sweden.

(3) Dissertation in Radiology to be publicly examined in Gröwallsalen, Akademiska sjukhuset, Uppsala, Thursday, June 3, 2004, at 13:15, for the degree of Doctor of Philosophy (Faculty of Medicine). The examination will be conducted in English. Abstract Briley Saebo, K. Degradation, Metabolism and Relaxation Properties of Iron Oxide Particles for Magnetic Resonance Imaging. Acta Universitatis Upsaliensis. Comprehensive summaries of Uppsala Dissertations from the Faculty of Medicine 1362. 92 pp. Uppsala. ISBN 91-554-5998-6. Whereas the effect of size and coating material on the pharmacokinetics and biodistribution of iron oxide based contrast agents are well documented, the effect of these parameters on liver metabolism has never been investigated. The primary purpose of this work was to evaluate the effect of iron oxide particle size and coating on the rate of liver clearance and particle degradation using a rat model. The magnetic and relaxation properties of five different iron oxide contrast agents were determined prior to the onset of the animal studies. The R2* values and the T1-enhancing efficacy of the agents were also evaluated in blood using phantom models. The results of these studies indicated that the efficacy of these agents was matrix and frequency dependent. Correlations between the R2* values and the magnetic properties of the agents were established and a new parameter, Msat/r1, was created to enable better estimations of contrast agent T1-enhancing efficacy in blood. The bio-distribution of one of the agents was also evaluated to assess the importance of sub-cellular particle distribution, using an isolated rat liver cell model. Phantom models were also used to verify that materials with magnetic properties similar to the particle breakdown products (ferritin/hemosiderin) may induce signal reduction when compartmentalized in a liver cell suspension. The results revealed that the cellular distribution of the agent did not influence the rate of particle degradation. This finding conflicted with current theory. Additionally, the study indicated that the compartmentalization of magnetic materials similar to ferritin may induce significant signal loss. Methods enabling the accurate determination of contrast agent concentration in the liver were developed and validated using one of the agents. From these measurements the liver half-life of the agent was estimated and compared to the rate of liver clearance, as determined from the evolution of the effective transverse relaxation rate (R2*) in rat liver. The results indicate that the liver R2* enhancement persisted at time points when the concentration of contrast agent present in the liver was below method detection limits. The prolonged R2* enhancement was believed to be a result of the compartmentalisation of the particle breakdown products within the liver cells. Finally, the liver clearance and degradation rates of the five different iron oxide particles in rat liver were evaluated. The results revealed that for materials with similar iron oxide cores and particle sizes, the rate of liver clearance was affected by the coating material present. Materials with similar coating, but different sizes, exhibited similar rates of liver clearance. In conclusion, the results of this work strongly suggest that coating material of the iron oxide particles may contribute significantly to the rate of iron oxide particle clearance and degradation in rat liver cells. Key words: Magnetic Resonance Imaging; contrasts agents, iron oxide particles, metabolism, relaxation mechanisms. Karen Briley Saebo, Department of Oncology, Radiology and Clinical Immunology, Akademiska sjukhuset, Uppsala University, SE-751 85 Uppsala, Sweden © Karen Briley Saebo 2004 ISSN 0282-7476 ISBN 91-554-5998-6 urn:nbn:se:uu:diva-4311 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4311).

(4) ˜ To my loving husband Jan Eystein. To love someone deeply gives you strength. Being loved by someone deeply gives you courage. ˜.

(5) ORIGINAL PAPERS I.. Characterisation of The Relaxation and Magnetic Properties of Five Different Iron Oxide Particles: Evaluation of T1-enhancing Efficacy. Karen Briley-Saebo, Yves Gossuin, Alan Roch, Håkan Ahlström, Robert N Muller and Atle Bjornerud Submitted MRM. II.. Hepatic Cellular Distribution and Degradation of Iron Oxide Nanoparticles Following Single Intravenous Injection in Rats: Implications For Magnetic Resonance Imaging. Karen Briley-Saebo, Atle Bjornerud, Derek Grant, Håkan Ahlström, Trond Berg and Grete Mork Kindberg In press Cell Tissue Res. 2004. III.. Long-Term Imaging Effects in Rat Liver Following a Single Injection of an Iron Oxide Nanoparticle Based MR Contrast Agent. Karen Briley-Saebo, Svein Olaf Hustvedt, Anita Haldorsen and Atle Bjornerud Accepted JMRI 2004. IV.. Temporal Changes in Liver R2* Values of Various Superparamagnetic Iron Oxide Contrast Agents: Importance of Hydrated Particle Size and Coating Material on The Rate of Liver Clearance. Karen C. Briley-Saebo, Lars O. Johansson, Svein Olaf Hustvedt, Anita Haldorsen, Atle Bjornerud and Håkan Ahlström Submitted Invest Radiol. 5.

(6) CONTENTS Abstract ...................................................................................................... 3 Original papers............................................................................................ 5 1. Abbreviations ........................................................................................ 8 2. Introduction ....................................................................................... 11 Summary ................................................................................................................11 2.1. Basics of MRI ........................................................................................... 12. 2.1.1. Historical Overview.................................................................................. 12. 2.1.2. Classical Physics of MRI............................................................................13. 2.1.3. Magnetic Properties of Molecules .............................................................17. 2.1.4. Contrast Agents and Measurement of Relaxation Times .......................... 24. 2.1.5. Relaxation of water protons by iron oxide particles: Relaxation theory ......35. 2.2. Iron metabolism ....................................................................................... 46. 2.2.1. Transferrin ................................................................................................ 48. 2.2.2. Ferritin ......................................................................................................51. 2.2.3. The Liver and Cells of the RES ..................................................................53. 3. Study Aims ......................................................................................... 57. 6. 3.1. Main Aims ................................................................................................57. 3.2. Specific Aims .............................................................................................57. 3.3. Purpose of individual studies .....................................................................57. 3.3.1. Study I .......................................................................................................57. 3.3.2. Study II .................................................................................................... 58. 3.3.3. Study III ................................................................................................... 58. 3.3.4. Study IV ................................................................................................... 58.

(7) 4. Methods .............................................................................................. 59 4.1. Test systems ...............................................................................................59. 4.2. Ex vivo Models (All studies).......................................................................59. 4.3. Animal Models (Studies II, III and IV) .....................................................61. 4.4. Contrast Agents ........................................................................................ 62. 4.5. MR Imaging (All studies) ......................................................................... 63. 4.6. Determination of R2* values (All studies) ................................................ 64. 4.7. Relaxation Analysis................................................................................... 64. 4.8. Magnetisation and core size (Study I) ....................................................... 66. 4.9. Particle size (Studies I and IV).................................................................. 66. 4.10. Total Iron determination (All studies) ...................................................... 66. 4.11. Phantom preparation (Studies I and II) .................................................... 66. 5. Results and Discussions ...................................................................... 67 5.1. Study I .......................................................................................................67. 5.2. Study II .................................................................................................... 72. 5.3. Study III ....................................................................................................76. 5.4. Study IV ................................................................................................... 78. 6. Conclusions ........................................................................................ 83 7.. Acknowledgements ............................................................................. 85. 8. References ........................................................................................... 87 9.. Colour supplement ............................................................................. 89. 7.

(8) 1.. ABBREVIATIONS. List of terms and abbreviations in alphabetical order: A. Distance of closest approach between the protons and the paramagnetic metal ion. a. Radius of the hydrated iron oxide particle. α. Angle of rotation of the magnetization vector (Greek symbol alpha). B0. Magnetic flux density, commonly referred to as the applied magnetic field. β. Bohr magneton (Greek symbol beta). C. Curie constant per unit mass. c. Concentration of the magnetic center. CA. Contrast agent. χ. Magnetic susceptibility (Greek symbol chi). CPMG. Carr-Purcell-Meiboom-Gill spin echo sequence. D. Diff usion coefficient that is proportional to the temperature divided by the radius of the molecule times the viscosity of the matrix.. d. Distance of proton from the center of the paramagnetic ion. Calculated based on the assumption that the magnetic center is spherical. <d>p. Total mean hydrated particle diameter. η. Viscosity of the liquid (Greek symbol eta). ex vivo. Tissue analyzed after removal from the body. FFE. Fast field echo sequences. A vendor specific term for gradient echo (GRE) sequence. FID. Free Induction Decay. γ. Gyromagnetic ratio of the proton (Greek symbol gamma). GRE. Gradient echo sequence. H. Applied magnetic field. in vivo. Tissue in the living organism. IR. Inversion recovery sequence. JA. Ayant spectral density function. JF. Freed spectral density function. k. Boltzmann constant = 1.3181x10-23 JK-1. KV. Anisotropy energy often defined as KV where K is the anisotropy constant and V is the crystal volume. M. Macroscopic magnetization. 8.

(9) NM. Number of metal ions per cubic centimeter. NMR. Nuclear Magnetic Resonance. ω0. Larmor frequency or precessional frequency of the proton (Greek symbol omega). ωs. Precession frequency of the electrons. ∆ω. Shift in the Larmor frequency of the protons in the hydration sphere. g. Landè factor. P. Spin angular momentum. P(ω). Frequency-distribution within a voxel. q. Number of water molecules in the hydration sphere of the paramagnetic ion. r. Radius of a paramagnetic molecule. R1. Longitudinal relaxation rate equal to 1/T1 (unit=1/s). r1. Dipolar longitudinal relaxivity of a contrast agent describing the increase in R1 per unit concentration of the contrast agent (unit=s-1mM-1). R2. Transverse relaxation rate equal to 1/T2 (unit=1/s). r2. Dipolar transverse relaxivity of a contrast agent describing the increase in R2 per unit concentration of the contrast agent (unit=s-1mM-1). RES. Reticuloendothelial system. rf. Radio frequency. S. Electronic spin quantum number. SE. Spin Echo sequence. SI. Signal intensity. σ. 2. σ. 2. p. Variance of the field distribution within the voxel (Greek symbol Sigma). Ml. Variance related to the line width of the NMR spectrum of the sample tissue. SPIO. Superparamagnetic iron oxide particles made up of particles with aggregated iron oxide cores (not single crystals) and <d>p greater than 50 nm.. SR. Saturation Recovery sequence. T. Absolute temperature (unit=Kelvin). Tc. Transition temperature often referred to as the Curie temperature for ferromagnetic materials and the Nèel temperature for ferrimagnetic materials. T1. Spin-lattice or longitudinal relaxation time (unit=ms). T2. Spin-spin or transverse relaxation time (unit=ms). T2*. Effective transverse relaxation time (unit=ms). τ. Time between the 180° and 90° pulses. τc. Modulation of the dipolar coupling. 9.

(10) τD. Modulation of the relative translational diff usion time where τD = d2/3(Dwater + Dparamagnetic complex) D is the diff usion coefficient. τE. Modulation of the scalar coupling. τm. Exchange correlation time describing the exchange rate of water molecules in and out of the hydration sphere of a paramagnetic ion. τN. Nèel relaxation time that describes the rate of the flipping of electrons along the easy anistropic axis. τo. Pre-exponential factor relating the anistropic energy to the Nèel relaxation time. τr. Rotational correlation time. τs1. The electron relaxation. TE. The echo time associated with a SE sequence. TE equals 2 times the τ value or the time between the 90° and the 180° pulses in a SE experiment.. TR. Repetition time or time between the 90° pulses. µ. Magnetic moment. µ0. Permeability of free space = 4πx10-7 H/m.. <µ Z>. The resultant mean magnetization. USPIO Ultrasmall iron oxide particles made up of single crystal iron oxide cores with a total mean hydrated particle diameter that is less than 50 nm ħ. 10. Planck’s constant (Latin letter wit).

(11) 2.. INTRODUCTION. Summary Magnetic Resonance Imaging (MRI) is a diagnostic tool used to visualize the structure (morphology) and function of intact tissue in living organisms (in vivo). The contrast associated with MRI is due the response of water protons to an external magnetic field. Energy is applied to the protons (in the radio frequency range), exciting the water protons. When the radio frequency source is removed, the water protons relax or return to a state of equilibrium. During the relaxation process energy is emitted, and it is this energy that gives the signal that is observed in MRI. The relaxation of the water protons is dependent upon the local environment of the protons, so that different tissue will relax at different rates. The difference in relaxation rates and proton densities within the various tissues is responsible for the native soft-tissue contrast that is characteristic for MRI. Despite the inherent contrast of MRI, there are situations where contrast agents are required to enhance the relaxation of water protons in specific tissues. Contrast agents may be water soluble paramagnetic complexes, or superparamagnetic particles. Most water soluble contrast agents used today are excreted intact by the kidneys and are not metabolised within the body. Superparamagnetic contrast agents are made up of iron oxide particles that are metabolised by cells of the reticuloendothelial system (RES). Despite the initial biodistribution of these contrast agents, a portion of the injected dose will be taken up by the RES cells of the liver. Within the liver RES cells, the iron oxide particles are degraded, and the iron from the particles eventually enters the normal iron pool of the body. The effect of particle size on the biodistribution of iron oxide particles has been well documented. Generally, smaller particles circulate longer than larger particles and can be taken up by RES cells of the lymphatic system and bone marrow. Larger particles (> 50 nm) are generally taken up quickly by the RES cells of the liver, and have limited uptake into lymph and bone. The effect of coating material on biodistribution has also been explored in the relevant literature. If has been observed that the circulation times and cellular uptake can be manipulated by altering the coating material of small particles. However, the effect of coating material on liver clearance and particle degradation within RES cells has never been addressed. Prolonged liver clearance may result in decreased signal intensity over extended periods of time. Slow liver clearance may interfere with subsequent liver examinations, if methods that rely on signal enhancement are employed. Additionally, there may be safety issues related to the prolonged storage of iron within certain cell types of the liver. The purpose of this thesis is to address the influence of iron oxide particle coating material and size on the rate of liver clearance and particle degradation using a rat model. The following introduction is designed to provide the theoretical background of MRI physics, relaxation, and liver metabolism that is central to this work.. 11.

(12) 2.1 Basics of MRI 2.1.1 Historical Overview “History is the short trudge from Adam to atom.” --Leonard Louis Levinson The existence of nuclear spin was first suggested by Pauli in 1924 in order to explain hyperfine structure in atomic spectra. Pauli’s experiments demonstrated that nuclei of different elements (and different isotopes of the same element) differ in spin angular momentum. Like neutrons and electrons, protons (1H) have spin quantum numbers of ½. For nuclei other than protons, the spin angular momentum is a sum of all individual nucleons. For example, nuclei with an odd mass number exhibit half-integral spins (e.g. 1 H , 13C, 17O, 19F, 23Na, 31P) and nuclei with even mass numbers, but odd charge numbers have integral spin (e.g. 14N, 2H). Nuclei with both even mass and charge numbers do not exhibit spin angular momentum (e.g. 12C, 16O, and 32S). In 1946 two American scientists, Felix Bloch and Edward M. Purcell, independently published the first manuscripts related to the potential application of Nuclear Magnetic Resonance (NMR) (1, 2). Bloch and Purcell discovered that there is a linear relationship between the magnetic field experienced by nuclei with non-zero quantum spin, and the resulting angular frequency of rotation, known as the Larmor frequency. Bloch and Purcell found that when these nuclei were placed in an external magnetic field they absorbed energy in the radio frequency (rf) range, and re-emitted the energy when the rf source was removed. This discovery was the first step towards the development of Nuclear Magnetic Resonance Imaging (MRI); and both Bloch and Purcell were awarded the Nobel Prize in Physics in 1952 for these important discoveries. Following the work of Bloch and Purcell, two groups led by Proctor and Dickinson discovered the chemical shift effect in 1950 (3, 4). The discovery of chemical shift turned NMR into a powerful analytical tool, since it was shown that the resonance frequency is dependent upon the structure or chemical environment of the nuclei. In 1953 the first commercial NMR spectrometers became available and groups began experimenting with the use of linear gradients. In 1971 Damadian began experimenting with ex vivo cancer tissue and found differences between the relaxation properties of normal tissue and cancer tissue (5). Damadian then went on to develop field focussing NMR (FONAR) in 1972 (6). FONAR was used to selectively measure the relaxation time of tissue in vivo, and images were obtained as the patient was manually moved. As a result, Damadian was the first to show that the relaxation properties of tissues may be used to differentiate tissue types (7). In 1972 Paul C. Lauterbur submitted a manuscript to Nature describing a new imaging technique called zeugmatography. After first being rejected, the manuscript was printed in Nature in March 1973 (8). This manuscript was entitled: “Image formation by induced local interactions: examples of employing nuclear magnetic resonance” and is considered to be the foundation of MRI. In this pioneering work, Lauterbur presented 2-dimensional 12.

(13) images of water filled objects. The images were reconstructed from a number of NMR measurements each obtained in the presence of a linear field gradient applied in different directions. Lauterbur was awarded the Nobel Prize in Medicine and Physiology in 2003 for his contribution to the development of MRI. In 1974, Hinshaw building on the two-gradient concept of Lauterbur, introduced the “sensitive point” technique that utilises three alternating gradients to allow signal selection by suppressing all NMR signals from defined areas in the object, except from areas or points where all gradient fields are zero (9). Later, Hinshaw developed the multiple sensitive point technique, which is the foundation of imaging acquisition and slice selection used in MR scanners today. In this technique a frequency encoding direction is defined along the sensitive line by the application of a stable gradient (10). Scanning is then performed by a parallel shifting of the sensitive line within selected planes. In 1977, Hinshaw published the first detailed cross-sectional image of a human wrist using the multiple sensitive point technique (11). Since the first crude images generated in the early 1970s, MRI has grown to become a powerful tool for both diagnostic and functional imaging, with more than 20,000 MRI scanners operating worldwide. MRI is unique, in comparison to PET, SPECT or ultrasound, in that it offers high soft-tissue contrast combined with a flexibility that allows for the evaluation of both morphology and function.. 2.1.2 Classical Physics of MRI “All science is either physics or stamp collecting”. --Ernest Rutherford in J. B. Birks “Rutherford at Manchester” (1962) A correct description of MRI physics relies on quantum mechanics, since quantum physics is needed to describe the transition of nuclei with non-zero spin quantum numbers between different energy states. However, classical physics can be used to give an adequate introduction into MRI theory. According to the classical model, protons (or other nuclei having non-zero spin quantum numbers) can be considered small magnets, as shown in Fig. 1. Protons are charged particles that spin around their axis (Fig. 1). Since the motion of a charged materials results in the generation of electromagnetic fields, protons possess a characteristic dipolar magnetic moment (µ) that is associated with the spin angular momentum (P). In classical terms, the magnetic moment is described by the product of the gyromagnetic ratio (γ) that is unique for each nucleus and reflects the charge number and mass number of the nuclei, and the angular momentum µ = γP. Currently, most magnetic resonance imaging (MRI) is based on proton NMR, where γ/2π =.42.6 x 106 Hz/T. In the absence of an applied magnetic field, the magnetic moment associated with an individual proton is randomly orientated in space. However, when a magnetic field of strength B0 is applied in a direction defined as z, the individual magnetic moments associated with each proton will align either parallel µ+z or anti-parallel µ-z to the applied field. 13.

(14) Fig. 1: Classical description of the magnetic moment associated with a proton. (Colour print available in the supplement - page 89). The orientation of the individual magnetic moment reflects the energy level or state of the nuclei, with parallel orientation representing the low energy state and anti-parallel orientation representing the high energy state. If a sample consists of many identical molecules (e.g. water), each with a magnetic nucleus of spin ½, then population of the two energy states can be estimated using Boltzmann’s equation (13):. Nl/Nh = exp(ǻE/kT). [1]. where Nl is the number of protons in the low energy state (µ+z) and Nh is the number of protons in the high energy state (µ-z). ∆E is the energy difference between the two levels, T is the absolute temperature (Kelvin) and k is a constant (Boltzmann constant = 1.3181x10-23 JK-1) From Equation 1 it is evident that as the energy separation between the levels increases, the difference in the populations between low and high energy nuclei increases. In addition, the change in energy (∆E) is proportional to the applied field strength so that the population difference increases linearly with the applied field. For proton MRI, the population difference between the high and low energy states (Nl/Nh) is 8x10-6 at 2.35 Tesla and 300 Kelvin. The NMR signal is directly related to the population difference defined by Equation 1, since it is only the small excess of nuclei aligned with the applied field (Nl with µ+z) that can emit signal. As a result, more signal (or greater signal-to-noise ratios) is observed at higher applied field strengths when ∆E is larger and there is a larger population difference. It is also apparent from Equation 1, that MRI is not a very sensitive method, since only a small population of the nuclei are able to emit a signal. Fortunately, 14.

(15) living organisms have a high natural abundance of water protons that increase the sensitivity of the method thereby allowing for the inherent soft-tissue contrast that is observed with proton MRI. The sum of the individual magnetic moments aligned with the magnetic field (based on Nl/Nh) is finite and is often referred to as the macroscopic net magnetization, M, of the sample. The macroscopic magnetization is characterised by a vector with both magnitude, depending upon the number of protons per cubic centimetre, and a direction. The behaviour of the macroscopic magnetization vector may be described classically by the Bloch equations (2). These equations show that the macroscopic magnetization vector M precesses or rotates about the direction of the applied magnetic field. Bloch and Purcell’s experiments from 1946 revealed that there is a simple linear relationship between the magnetic field, B0, experienced by protons, and the resulting angular frequency of rotation (precession), ω0, of the magnetization (1, 2):. Z0 = JB0. [2]. where γ is the gyromagnetic ratio that is a unique constant for each nuclei possessing a spin. ω0 is the Larmor frequency and is identical to the frequency of the electromagnetic radiation associated with the possible spin energy transitions (∆E) induced by the magnetic field. When the spin system is in a state of equilibrium the net magnetization is aligned with the applied magnetic field (z-direction) with a magnitude given by Mz. The net magnetization vector Mz is small compared to the applied field. Bloch and Purcell showed that in a steady-state NMR experiment, the spin system (Mz) can absorb energy from radio frequency (rf) radiation (1, 2). Radio waves that oscillate at the Larmor frequency, so that the energy delivered equals ∆E (Equation 2), will cause a transition between the spins that are aligned with the applied field (µ+z) to the higher energy state anti-parallel to the field (µ-z). Once the rf source is removed, the spins will return to a state of equilibrium aligned parallel to the applied magnetic field. In the process of returning to a state of equilibrium, the effected spins will emit energy equal to ∆E. It is the emitted energy that results in the signal observed by NMR. The perturbation of Mz from equilibrium is therefore performed by applying an rf pulse that oscillates at the Larmor frequency of the nuclei. The Bloch equations can be used to describe the motion of the magnetization vector in the presence of both the applied field B0 and the rf pulse, often defined as B1 (2). A rotating frame is often employed to help visualise the effect of B1 on the magnetization vector Mz. In this frame of reference, one needs to imagine the x, y and z coordinate system rotating at the Larmor frequency (13). In this frame, the nuclei that are rotating at the Larmor frequency will appear static or stationary as long as magnetic field is exactly equal to B0. Nuclei that are precessing at other frequencies will appear to be rotating at a rate 15.

(16) equal to the difference between their precessional frequency and the Larmor frequency. When an rf pulse is applied at the Larmor frequency, a static field is created (in the rotating frame) perpendicular to Bo, causing the magnetization vector Mz to rotate or precess about the B0 axis. The precessional frequency of this rotation is given by ω1=γB1 (note that this is the same as Equation 2, except now the spins have a frequency that is relative to B1 and not Bo). In addition, the angle of rotation (α) of the magnetization vector at time t is given by α = γB1t. Since the net magnetization is a vector, it can have components in both the xy and z planes of a three dimensional coordinate system. Following an rf pulse, the magnetization is defined by components of both Mz and Mxy. As the magnetization returns to a state of equilibrium, the component aligned with the magnetic field will increase (Mz increases) and the component in the xy-plane (Mxy) will decrease, as shown in Fig. 2. When a state of equilibrium is reached Mz is at a maximum value and Mxy is zero. Traditionally the duration of the rf pulse is used to change the angle of rotation often. Fig. 2: Magnetization after the application of an rf 90° pulse. (Colour print available in the supplement - page 89). 16.

(17) denoted as α (14). If the rf is applied so that the entire net magnetization Mz is inverted to point along the –z-axis, then a 180o pulse was applied. A 90o pulse can also be created that will cause the entire net magnetization vector Mz to point along the xy, or transverse plane. In this situation, the Mz component of the vector is zero and the Mxy component is at a maximum value. According to Faraday’s law of induction, the Mxy component of the magnetization can induce a current (at the Larmor frequency) in a coil placed on the x-axis. Therefore, one can measure the loss of the Mxy component as a function of time after removal of the rf pulse. The signal induced in the coil is a free precession signal and is called the free induction decay (FID).. 2.1.3 Magnetic Properties of Molecules “One of the problems in magnetism is that there are serious mathematical difficulties in tackling parts of the subject with theories that are very realistic.” -John Crangle in Solid-State Magnetism 1991 Following the application of an rf pulse, the net magnetization is perturbed from equilibrium and is in a high energy state. In order for the net magnetization of the proton to return to equilibrium (as shown in Fig. 2), the energy within the spin system must be transferred or emitted. Due to the large magnetic moment of electrons (658 times greater than that of protons), the electron spin-orbit associated with certain atoms or molecules may absorb energy from the proton spin system, thereby inducing proton relaxation (12). The rate by which the magnetization returns to equilibrium along the direction of the applied field, Mz, is the spin-lattice or longitudinal relaxation, and is defined by the longitudinal relaxation time, T1, or the longitudinal relaxation rate (R1=1/T1). The rate by which the magnetization decays in the xy-plane, or Mxy goes to zero, is defined by the spin-spin or transverse relaxation time, T2, or transverse relaxation rate (R2=1/T2). A single unpaired electron is a charged particle and therefore has angular momentum (similar to that of the proton). In addition, however, an electron in an atom may have two different kinds of angular momentum, its orbital angular momentum and its spin angular momentum (15). These two magnetic moments may interact (like any pair of dipoles). It this interaction that is often referred to as the spin-orbital coupling that gives rise to the magnetic properties of atoms and molecules. If the spin and orbital momenta are oriented in the same direction, then the total angular momentum (often denoted as j or j-coupling) takes the largest energy value. When the two magnetic moments are antiparallel, or oriented in different directions, the orbital and spin momenta is in the lowest energy state. Like in any other physical system, the low energy state is preferred and the energy required to cause a transition to a higher energy level is defined by a discrete value. The difference between spin-orbital energy levels is known as Zeemann splitting, and is important for the relaxation of water protons interacting with the electron spin orbitals of nearby molecules or atoms (15). In addition to the spin-orbital coupling, the electrons in an atom may also interact with each other (paired) or they may be alone. The magnetic moments of paired electrons are opposed and the total magnetic moment associated with 17.

(18) the pair is zero. If only paired electrons are present, then the material will be diamagnetic (16). When placed in an external magnetic field, diamagnetic materials will try to oppose the field. Traditionally, the response of a material to an applied field is defined by the magnetic susceptibility (16):. M=ȤH. [3]. where χ is the magnetic susceptibility of the molecules, H is the applied magnetic field, and M is the net magnetization of the material. It should be noted, however, that the magnetic field used to determine the magnetic susceptibility of various materials is different from the magnetic flux density B0 (unit: Tesla) from Equation 2. The magnetic field density B0 is commonly referred to as the ‘field strength’ in MRI literature and is the magnetic induction that is proportional to the magnetic field: B = µ 0 (H+M) ≈ µ 0H where µ0 is the permeability of free space = 4πx10-7 H/m. The magnetic susceptibility value for diamagnetic materials is small and negative. Most tissue, biological fluids, and proteins are diamagnetic, so that the relaxation times obtained in pure water or tissue solutions are long (T1 and T2 of pure water is approximately 4 seconds). For atoms that have unpaired electrons located in their outer spin-orbitals, the magnetic moment is non-zero and when placed in an external magnetic field these materials acquire a magnetization (in a similar fashion as that observed for protons). For example gadolinium, (Gd3+) has seven unpaired electrons in the 4f orbital, dysprosium (Dy3+) has 5 unpaired electrons in the 4f orbital, and iron (Fe3+) has 5 unpaired electrons in the 3d orbital (12). The molar bulk magnetic susceptibilities of gadolinium and dysprosium ions measured at room temperature are 2.54 x 10-2 and 4.94 x 10 -2 cm3mol-1 (19). Paramagnetism is generally defined by the following two magnetic properties: First, a positive magnetic susceptibility that is directly proportional to the external field (16). This means that the induced magnetization increases or decreases linearly with the applied magnetic field. Second, in the absence of an external magnetic field the individual magnetic moments are randomly oriented so that the net resultant magnetization is zero. Therefore, paramagnetic materials have no remenant magnetization. When individual magnetic moments do not interact, every single spin will react to an external magnetic field, independently of neighbouring spins. The spins will always try to orient themselves in the direction of the external magnetic field, since this is the low energy state. However, thermal shaking or the thermal energy of the system acts as sort of an entropy factor in that it tries to force the spin back into a random orientation. Since thermal energy is directly related to the temperature of the system, the observed susceptibility (that describes the net magnetization as a function of the external field) becomes dependent upon the temperature as described by the Curie Law (16):. 18.

(19) Ȥ=C/T. [4]. where χ is the susceptibility as described in Equation 3, C is curie constant per unit mass, and T is temperature. At low temperatures paramagnetism is never observed. This is due to the cooperative behaviour between the spins (or spin-coupling) below a specified transition temperature, defined as Tc. Below the transition temperatures of paramagnetic materials, the interactions between spins (or spin-coupling) can result in one of three different types of magnetism: ferromagnetism, ferrimagnetism and antiferromagnetism. In ferromagnetic systems, the spins are aligned in the same direction following placement into an external field. In addition, strong spin-coupling persists after the external magnet is removed, resulting in permanent magnetism of the material or remenant magnetization. Above the transition temperature, Tc (often referred to as the Curie temperature of ferromagnetic material) the system becomes paramagnetic with susceptibility defined by the Curie-Weiss law (16):. Ȥ=C/(T - Tc). [5]. where χ is the susceptibility as described in Equation 3, C is curie constant per unit mass, and T is temperature, and Tc is the transition or Curie temperature. Metallic iron is ferromagnetic at all temperatures below 1000 Kelvin. Ferrimagnetism results when paramagnetic materials are placed in an external field at temperatures below the transition temperature causing, some of the spins to aligned with the applied field (S1 position) and some to aligned against the field in the high energy state (S2 position). For ferrimagnetic material, the difference between the spin populations in the S1 and S2 energy levels is not equal, so that a net resultant magnetization is present. The spin-coupling is not very strong, so that when the external magnetic field is removed, thermal shaking causes the spins to return to a random state. Thus, there is no remenant or permanent magnetization present. Above the transition temperature the system becomes paramagnetic and the evolution of the susceptibility may be defined by Curie-Weiss Law (Equation 6). However, for ferrimagnetic systems, the transition temperature is often referred to as the Nèel temperature. The Nèel temperature is the same as the Curie temperature used to describe ferromagnetism. All iron oxide particles based on magnetite are either ferro- or ferrimagnetic at physiological temperatures (transition temperature is 850 Kelvin) (16). If there are equal populations in the S1 and S2 energy states following application of an external field below the transition temperature, then the system is antiferromagnetic and there is no resultant net magnetization. Above the transition temperature the system is 19.

(20) paramagnetic and the susceptibility may be described by (16):. Ȥ=C/(T + Tc). [6]. where χ is the susceptibility as described in Equation 3, C is curie constant per unit mass, and T is temperature, and Tc is the transition = Curie temperature = Nèel temperature. Some important biological materials are antiferromagnetic (for example deoxyhaemoglobin and ferritin). In order to fully understand superparamagnetism, the concept of anisotropy must be addressed. If a large number of paramagnetic ions are arranged in an orderly fashion (as in a crystal lattice) the spins will interact (via spin-coupling) so that when placed in an external field, the resultant magnetization is no longer isotropic. Anisotropy, therefore, describes the fact that the coupled-spins may align in more than one direction relative to the external field (15-18). These directions are often referred to as the anistropic axes and are determined by the symmetry of the crystal. The difference between isotropic and anistropic systems is that in isotropic materials all spins (or individual magnetic moments) align in the z direction (with the field), and in anistropic materials spins can assume other directions relative to the field. For crystals of magnetite there are six possible anisotropic axes (16). If it were possible to freeze a crystal of magnetite and measure the energy along the six anistropic axes (referred to as the anistropic energy), the result would be six different energy values, with lowest energy obtained in the “easy” direction that is parallel to the external field, and the highest energy obtained perpendicular to the external field. Normally, only the “easy” anisotropic axis is important, since in solution the movement or motion of the crystals causes an averaging of the anistropic energy. For materials made up of large crystals (diameters greater than 14 nm), the spins are divided and aligned within small magnetic domains called Weiss-domains (16). The direction of individual spins in the various domains is random prior to exposure to an external field. Once exposed to an external field, all the spins adopt the same direction along the anisotropic axes; the anisotropic energy is at a minimum value and the system may be considered isotropic. This explains why ferromagnetic crystals of magnetite must be magnetised by placement into an external field in order to gain remenance or permanent magnetism. If the crystals of magnetite become smaller then the Weiss-domains then superparamagnetism may be observed, as shown in Fig. 3. In order for the spins to move from one anistropic axes to another requires the input of energy that is equal to the desired transition. The anisotropy energy is often referred to as KV and is proportional to the following physical and chemical properties of the crystal (17, 18): 1) The larger the volume (or crystal size) the greater the values of KV. 2) The ions making up the crystal influence KV so that crystals made of materials other than Fe(II) and Fe(III), as in magnetite, will have different energies. 3) The shape of the crystal influences KV, with energy increasing as 20.

(21) Fig. 3: Superparamagnetic crystals. The anisotropy energy, E=KV, increases as the spins move away from the easy axis parallel to the external field. Fig. courtesy of Dr. Alan Roch, University of Mons- Hainut, Belgium. (Colour print available in the supplement - page 90). the crystals become less spherical. 4) The surface of the crystal effects KV since the different spin-orbital couplings can change the symmetry at the boarder of the crystal. Therefore, the coating material of iron oxide particles may be important if the layer of coating directly at the surface of the particles is different. Alterations in the coating further away from the surface are not expected to influence KV. 5) The distance between various crystals influences the KV since crystals in close proximity to each other (as in aggregates) may allow interactions between the spins resulting in dramatic increases of KV. If we only consider the flipping of the spins (or magnetic moment) along the easy axis (from parallel to antiparallel relative to the external field) then the rate of the flipping is defined by the Nèel relaxation time, τN, and is a result of the thermal agitation of the crystals (18). At low temperatures, the system does not have enough energy to make the transition from parallel to antiparallel, and the spins become locked along the anistropic axis. This is the transition temperature shown in Equation 5 and is referred to as the Nèel temperature for ferrimagnetic materials, and the Curie temperature for ferromagnetic 21.

(22) materials. For practical applications, the systems are always above the transition temperature at physiological temperatures. Therefore, the rate of flipping or fluctuation of the spins is critical for the relaxation properties of small iron oxide particles, especially in the low to mid-field frequency range. The Nèel relaxation time, τN, may be expressed as (18):. ĲN = Ĳo e(KV/kT). [7]. where K is the anisotropy constant, V is the crystal volume (proportional to the radius of the crystal cubed) and τo is the pre-exponential factor. From Equation 7 it is evident that as the crystal volume decreases the exponential term goes to 1, and the pre-exponential factor becomes increasingly important. Note that the pre-exponential term is not a constant value and is dependent upon the spin-orbital coupling of the system. For large crystals, however, the Nèel relaxation time is very long, so that the magnetic moment does not flip, and is essentially locked along the easy anistropic axis. For small crystals (< 6 nm in diameter) the transitions are fast and on the order of nanoseconds. When small ferrimagnetic crystals are in aqueous solution the fluctuations are modulated not only by the Nèel relaxation time, but also by the rotation of the crystals. The rotation time, τr, of the spin system is given by:. Ĳr = 4ʌa3Ș/3kT. [8]. where a is the radius of the particle, η is the viscosity of the liquid, T is the temperature and k is the Boltzmann constant. In summary there are two factors that cause re-orientation of the anisotropy: the fluctuation of the spins as defined by τN, and the rotation of the spins as defined by τr. If the Nèel relaxation times are long, then the spins may still re-orient along the anistropic axes if the rotation is adequate (1/ τr small so that a is small and T is large). For a system of superparamagnetic crystals the macroscopic or resultant magnetization, M, may be determined by (16):. M = Msat · L(Į). [9]. where L(α)=coth(α) –(1/α) and α=µBo/kT. µ is the total magnetic moment of the crystal, Bo is the external magnetic field, k is the Botlzmann constant, T is temperature and Msat defines the field at which the magnetization is locked or saturated along the easy axis. Based on the discussions above, it is possible to define superparamagnetism based on the magnetic moment of the crystal (which is much greater than the individual magnetic moments associated with the paramagnetic ions that make up the crystal) and by the fact 22.

(23) Fig. 4: Probability of finding the anistropic in energy as function of direction.Figure courtesy of Dr. Alan Roch, University of Mons- Hainut, Belgium. (Colour print available in the supplement - page 90). that in the absence of the magnetic field, the mean magnetic moment of the crystal is zero (due to averaging caused by the Nèel relaxation and rotation of the crystal lattice). As a result, the separation between superparamagnetism and ferromagnetism for iron oxide particles is primarily related to the size and structure of the crystal lattice. Fig. 4 shows that the anistropic energy is reduced for small crystal systems. Superparamagnetic iron oxide crystals of magnetite with core sizes smaller than a Wiess domain exhibit low anistropic energy compared to particles composed of larger iron oxide cores. As a result, the energy barrier that allows individual magnetic moments to align in different anisotropy directions is low for small iron oxide particles. As a result, the probability of finding spins in different anistropic directions is greater for small particle when the energy required to move the spins away from the easy axis is relatively small as shown Fig. 4. The high probability of finding spins in other anistropic directions (non-easy axes) greatly influences the low field relaxation properties of small iron oxide particles.. 23.

(24) 2.1.4 Contrast Agents and Measurement of Relaxation Times ”Contrast itself is a quite controversial term in imaging.” -Peter Rinck, Contrast and contrast agents in MRI, European Workshop on MR in Medicine, 1989. Contrast is a term used to describe the relative difference between the signal intensity of two adjacent regions by using a colour scale (normally the grey scale for MRI). For imaging modalities, such as conventional X-ray and CT, the image contrast is based on electron density difference that can be altered by the presence of a contrast agent (such as barium or iodinated complexes). The contrast is therefore directly related to the concentration of contrast agent in the tissue. For MRI, contrast is a complex, since the signal emitted by water protons is dependent upon both intrinsic and extrinsic factors. The most important intrinsic factors are proton relaxation and the proton densities of the tissue. External factors capable of influencing contrast include the field strength of the MRI scanner, the pulse sequence and pulse sequence parameters chosen, and whether or not contrast agents are present during imaging generation. One of the main advantages of MRI, in comparison with other modalities, is the ability to change contrast by manipulation of the pulse sequence and pulse sequence parameters. However, despite the good softtissue contrast of MRI, there are situations that require contrast agents (CA) to enhance the relaxation properties of a specific tissue (aid in diagnosis) or to act as perfusion or permeability marker (to evaluate tissue function). In 1946 Bloch showed how the addition of a paramagnetic material enhanced the longitudinal relaxation of water proton. Since then, several different types of contrast agents have been developed that enhance the relaxation times of water protons. Contrast agents are normally defined based on their relaxation properties (ability to relax a water proton), their magnetic properties and their bio-distribution. When defining a contrast agent based on relaxation properties, the efficacy is described by the longitudinal and transverse relaxivity r1 and r2, respectively. The relaxivity reflects the change in the relaxation rate as a function of contrast agent concentration. If a linear correlation is assumed, then the relaxivities are calculated as:. y. rc n b. [10]. where y is the relaxation rate of the sample containing the contrast agent (1/s), c is the concentration of contrast agent in the sample (mM per magnetic centre), r is the slope of the linear regression, n is the factor of curvature associated with the fit, and b is the relaxation rate of the sample without the addition of contrast agent (1/s). Once calculated, the r value is the r1 or r2 relaxivity (s-1mM-1). Most relaxivity values are obtained in aqueous solution or in ex vivo tissue samples. The r1 and r2 values are determined using calibrated spectrometers that measure the signal from the magnetization in the time domain (pulse NMR spectrometers). 24.

(25) Longitudinal relaxation, T1 Following the application of an rf pulse, the time that is required for the net magnetization Mz to reach a state of equilibrium is defined by the spin-lattice or longitudinal relaxation time, T1. Starting from zero magnetization in the +z direction, the z magnetization will increase to 63% of its maximum value with a time of T1. Any change in Mz is accompanied by an energy flow between the proton spin system and other degrees of freedom (electron spin-orbitals) in nearby molecules of the matrix known as the lattice. In tissues, the lattice is made up of the random fields that are generated by the magnetic moment of protons due to thermal motion of the molecules. Interaction of the spins with these fields results in a stimulated emission of energy (equal to ∆E in Equation 1) with a gradual recovery of the longitudinal component of the magnetization, Mz. Since all biological tissues are made up of a variety of molecules, the T1 values of tissue will be different, as shown in Fig. 5. From this figure it is apparent that the contrast, or difference in T1 values between tissues, is dependent upon the repetition time (TR) used to generate the image. If the environment is heterogeneous, then the T1 value obtained will reflect the average properties of the material, and multi-exponential recov-. Fig. 5: Relative signal intensity (SI) observed for three tissues (CSF, grey and white brain matter) with different T1 relaxation times. The contrast, or difference in T1 values, is dependent upon the TR used. Figure courtesy of Atle Bjornerud. 25.

(26) ery of the longitudinal magnetization may be observed. In addition, since the net magnetization M is a vector, the magnetization will always have components of both Mz and Mxy following the application of a 90° rf pulse (or any pulse less than180°). Therefore, T1 and T2 can be considered interrelated processes, with dephasing of the magnetization in the xy-plane and recovery in the z direction. In all matrices (e.g. tissues, blood, plasma, ect.) except pure water, the decay of Mxy occurs faster than the recovery of Mz so that T2 is always shorter than T1. The in vivo T1 values can be measured clinically using partial saturation pulse (SR) sequences (used to generate Fig. 4). This sequence may be defined as (13):. 90ºx - [ - TR - 90º x (FID) – TD] n. [11]. where 90°x is the rf pulse applied in the x-plane, TR is the repetition time (or time between the 90° pulses) followed by measurement of the FID along the x axis. TD is a delay time that normally is longer than T1 value to be measured, and n illustrates that the sequence can be repeated several times. In a SR sequence a 90° rf pulse rotates Mz to the xy-plane (resulting in maximum Mxy). The spin system is then exposed to a second 90° rf pulse that rotates all the individual spins that have relaxed (recovered Mz) during the TR time back to xy-plane. Once in the xy-plane the FID signal is measured. Any residual Mxy magnetization that is present during the second 90° rf pulse is flipped down to the –z axis and is not measured during acquisition of the FID. If TR values are greater than 5 times the T1 value of the sample, the magnetization measured after the second 90° rf pulse is equal to the amplitude of the net magnetization at time zero Mz(0). If TR is less than 5 times the T1 of the sample, then incomplete relaxation occurs and the measured signal amplitude is less than Mz(0). In each experiment the TR values can be changed to generate a plot of signal intensity versus time. The T1 value can then be calculated according to (13):. Mz (TR ). Mz (o) 1 exp> TR / T 1)@

(27). [12]. where Mz (TR) is the amplitude of the magnetization at a time equal to TR and T1 is the longitudinal or spin-lattice relaxation time (ms). The dependence of the observed signal amplitude on the repetition time may be used to enhance contrast in clinical MRI scans. As seen in Fig. 5, the contrast between the CSF and grey and white matter is at a maximum when long TR values are used. At a TR of 2200 ms, the longitudinal magnetization of grey and white matter has recovered more than the magnetization of CSF. As a result, these tissues appear relatively bright. Additionally, T1 relaxation times may also be determined clinically using inversion pulses rather than saturation pulses (examples include the Philips Look-Locker sequence or sim26.

(28) ilar magnetization prepared rapid GRE sequences from other vendors). Analytical spectrometers also use inversion-recovery (IR) sequences for the determination of T1. The advantages of using IR sequences are related to gains in accuracy and precision. In the IR sequence a 180° pulse is applied and the net magnetization is rotated to the –z direction. No signal is observed as the spins return to a state of equilibrium, since no magnetization is produced in the xy direction. However, at any time τ (known as the inversion time, TI) following the 180° pulse, the state of the magnetization can be monitored by applying a 90° pulse (known as the read pulse). The IR pulse sequence can be summarized as (13):. [180º - Ĳ - 90º (FID) – TD] n. [13]. where τ is time between the 180° and 90° pulses (TI), the signal of the FID is read immediately after the 90° pulse, TD is a delay time (normally five times longer than T1 to be measured), and n illustrates that the sequence can be repeated several times. A 180° pulse is succeeded only by spin-lattice relaxation. The experiment is repeated several times by changing the time τ between the 180° and 90° pulses and measuring the signal amplitude. From these recovery curves the T1 value is calculated as:. Mz (W ). Mz (0)>1 2 exp(W / T 1)@. [14]. Whereis the signal amplitude of the magnetization in the z direction at time , is the amplitude of the net magnetization in the z direction at time zero, is the time between the 180° and 90° pulses, and T1 is the longitudinal or spin-lattice relaxation time.. Transverse relaxation, T2 The loss of signal observed in the FID is a result of spin dephasing. Immediately following a 90° rf pulse (time=0 after the rf pulse is removed) all individual spins precess at the same frequency (equal to ω1) and Mxy is at a maximum value (Fig. 2). As the time after removal of the rf pulse increases, the individual spins start to loose their phase coherence. Phase coherence means that all individual spins rotate or precess at the same ω1 frequency. The loss of phase coherence, called dephasing, is primarily due to the following two effects: First, other spins and local magnetic fields generated by macromolecules in the tissue (Bm) alter the magnetic field experienced by different individual spins as they randomly diff use through the endogenous Bm fields. The precessional frequencies of these spins (ωm) are no longer equal to ω1 and are now precessing at a frequency ωm=γBm. Since the precessional frequency of each spin is randomly changed, there is a loss of phase coherence (dephasing), and the net Mxy transverse magnetization decays at a rate defined by the spin-spin or the dipolar transverse relaxation time T2. The T2 values are measured in milliseconds (ms) and are usually on the order of 50 to 200 ms, depend27.

(29) ing upon the sample measured and the experimental conditions (e.g. type of tissue, presence of a contrast agent, and/or pulse sequence parameters used). Second, inhomogeneities in the macroscopic magnetic field in the sample (Bs) cause an increase in the rate of spin dephasing, and thereby a reduction in the T2 values. Macroscopic variations in the magnetic field may occur due to differences in the magnetic properties within the tissue (susceptibility differences), or due to systematic field inhomogenities within the external applied field Bo, or within the rf coil B1. Spin dephasing occurs when the magnetic field is not constant over the normal diff usion distance of the proton (or spins). As a result, the individual spins that randomly diffuse into Bs will precess at frequencies that are not equal to ω1, and a loss of phase coherence is observed. The reduction in the Mxy magnetization by inhomogeneous macroscopic fields is called T2* and is known as T2*-effects or susceptibility effects. T2* decay is normally much faster than the dipolar T2 decay. T2*effects reflect the net loss of Mxy magnetization and are dependent upon both dipolar T2 relaxation (discussed in the next chapter), and the inhomogeneous macroscopic fields as described by (13):. 1/T2* = 1/T2 + JǻBs. [15]. where γ∆Bs is the spread in the Larmor frequencies due to the field inhomogenities in the sample, over then normal diffusion distance of the proton within a specified time frame (normally the echo time, TE, of the sequence). 1/T2 is the dipolar spin-spin transverse relaxation time that is characteristic of the magnetization decay of the individual spins without any field inhomogenities. If field inhomogenities were absent, then T2* would equal T2. In 1950 Hahn discovered a method of measuring dipolar T2 values by reducing the effect of the applied field inhomogenities on spin coherence. His discovery was known as the Hahn echo, and was later expanded into the spin-echo (SE) sequences that are used today. SE sequences are used either to accurately measure T2 values by spectroscopy methods, or utilised in MRI to weight the observed images with respect to T2 (by minimizing T2* effects). The MRI SE pulse sequence is currently the most commonly used pulse sequence for clinical diagnosis. The spin echo sequence is described by a 90° pulse that moves the magnetization to the xy-plane and generates Mxy . After the 90° pulse a 180° pulse is applied that refocuses the spins that have dephased due to macroscopic field inhomogenities. The 180° pulse is applied along the y-axis after a time τ, following the 90° rf pulse, as shown in Fig. 3. The 180° pulse (often referred to as the refocusing pulse) has the effect of rotating all individual magnetizations by 180°, and reflecting them into the yz-plane. Any magnetization along the z direction is inverted to the –z direction and does not produce signal. Since the spins continue to move in the same direction after the 180° pulse is applied, the spins will refocus and be in phase in the y-direction after a time τ. The process can be repeated 28.

(30) by applying several successive 180° pulses along the y-axis. The application of successive echoes is called a Carr-Purcell-Meiboom-Gill (CPMG) spin echo sequence. The CPMG SE can be described as:. 90ºx - [ - ½TE - 180º y – ½TE – echo-]n. [16]. where one half of an echo time (½TE) is the time between the 90° and 180° pulses, and n reflects the fact that the 180° pulse can be repeated n times to produce an echo train. The echo time (TE) associated with a SE sequence is the time between 180° pulses (for echo trains) or the time between the 90° pulse and the formation of the echo. If one immediately repeats the SE sequence to generate a new echo train, then the time between the successive 90° pulses is the repetition time known as TR in clinical applications, and as the relaxation delay (RD) in spectroscopy applications. Often, SE sequences are repeated several times in order to obtain a signal average, allowing for increased signal-to–noise ratios (MRI), or more accurate T2 measurements (spectroscopy). As shown in Fig. 6, at the centre of the echo, the effects of macroscopic inhomogenities (causing differences in precessional frequency) are cancelled out and the amplitude of the echo reflects the dipolar T2 dephasing of the spins. The dephasing that occurs after the 90° pulse, and on either side of the echo centre (time τ) is due to T2* effects, that are elimi-. Fig. 6: Transverse relaxation. Dephasing and rephasing of the spins following a 90° and 180° pulses, respectively. Figure courtesy of Atle Bjornerud. (Colour print available in the supplement - page 91). 29.

(31) nated when the echo amplitudes are used to calculate T2. The amplitude of successive spin echoes decays exponentially, and the dipolar T2 value(s) can be calculated as a function of time, t, according to (13):. My (t ). My(0) exp(t / T 2)

(32). [17]. where My(t) is the magnetization in the y plane at a given time t, My(0) is the amplitude at time zero, and T2 is the transverse relaxation time. Equation 17 describes a monoexponential decay of the transverse magnetization. However, if different water protons in the sample experience different microscopic or local magnetic fields during a given echo time, then the decay is no longer mono-exponential, and multi-exponential fitting functions should be employed. As mentioned previously, the decay of the net Mxy magnetization can be measured by placing a coil on the x-axis and measuring the FID. In Fourier Transform (FT) NMR, the T2* values can also be determined directly from the line width of the proton peak obtained in the frequency spectra. It is also possible to determine the T2* of in vivo tissue using commercially available MRI scanners. The 1/T2* relaxation rate (R2*) may be quantified using gradient echo (GRE) double echo, or multiple echo sequences. GRE sequences use initial rf pulses that are less than 90° and echoes are formed by gradient switching. This method enables the use of very short TE and TR times that are required to evaluate the T2* in tissue. If the decay of the net Mxy magnetization is assumed to be mono-exponential, then R2* is then given by (20):. R 2*. § SI (TE1) · ¸¸ / 'TE ln¨¨ © SI (TE 2) ¹. [18]. where SI(TE1) and SI(TE2) are the measured signal intensities at the first echo time TE1 and the second echo TE2, respectively and ∆TE = TE2-TE1. The signal intensities (SI) can be measured from a region of interest (ROI), determined after the image is obtained.. Bio-distribution of contrast agents Currently contrast agents can be placed in one of five groups, based on their bio-distribution: I) Low molecular weight, water soluble materials that distribute into the extracellular space and are primarily renally excreted via glomular filtration with limited biotransformation. II) Water soluble materials that have some degree of interaction with the endogenous materials of blood, resulting in increased r1 efficacy. These materials are primarily renally excreted with limited uptake by the cells of the RES. III) Intravascular particulate contrast agents that are eliminated or degraded by the cells of the RES. IV) Seconardy bio-distribution mechanisms that rely on the contrast agents being seques30.

(33) tered into specific cells or tissue, using passive targeting mechanisms. This includes passive targeting due to variations in excretion kinetics (for low molecular weight materials) and passive targeting of particles into macrophages. V) Contrast agents that are actively targeted to specific cells or tissues. Most paramagnetic based contrast agents are water soluble extra-cellular agents made from the lanthanide metals gadolinium (Gd3+), manganese (Mn2+) and dysprosium (Dy3+). Although gadolinium and manganese agents are currently on the market, dysprosium based agents have been tested for various indications, but are not commercially available. Gadolinium and dysprosium metal ions are quite toxic if administered as free metal ions. As a result, these materials are chemically linked to carrier molecules that can safely transport them out of the body without any significant bio-transformation. These agents are eliminated intact by renal excretion so that the half-life of the agent in the blood is determined by the glomerular filtration rate. The carrier molecule is known as the ligand or chelating agent. For Group I materials, the ligand inhibits interactions between the metal ion and endogenous components in blood or tissue (limited protein binding), and has a high selectivity (log S) to the metal ion in order to avoid transmetallation with the multitude of endogenous in vivo cations. The Group I contrast agents were the first to be developed and used clinically for diagnostic imaging of the central nervous system. Examples of Group I compounds include GdDTPA, GdDTPABMA and GdDOTA. A complete list of the current Group I contrast agents are shown in Table 1. Whereas high molecular weight lanthanide agents are currently in development, the only commercially available agents today are low molecular weight chelates with relatively low in vivo efficacy. As a result, relatively large doses (0.1 to 0.3 mmol metal ion/Kg body weight) of Group I agents must be administered. Group I agents may also exhibit Group IV characteristics, since the excretion kinetics may be altered based on the morphology of the tissue. For example, gadolinium based agents may be used to access myocardial infarct, since the excretion of the material is delayed in infracted tissue, compared to normal tissue. By imaging at relatively late time points (10-15 minutes post injection) the areas of infarct that retain the agent will have increased signal intensity compared to normal tissue allowing for infarct detection (21). It is possible to intraveneously administer unchelated manganese (Mn2+) without serious toxic effects, as long as the injection rate is slow and the concentrations are low. The cardiotoxicity observed with manganese (Mn2+) is directly related to the speed of administration, since the free Mn2+ ions will compete with calcium for the calcium gated channels in myocytes (22). Manganese (Mn2+) that is administered as a free ion will bind immediately with serum protein albumin and will be eliminated via the portal system with excretion into the bile and eventually into the faeces, making this a Group IV agent. Since most vertebrates have an effective mechanism for eliminating Mn2+, contrast agents made using this ion do not require a strong chelating agent. In fact, the only Mn2+ agent currently in clinical use for liver imaging (see Table 1) relies on the small concentration of unbound transmetallated metal ions to cause signal enhancement in normal hepatocytes 31.

(34) of the liver. Although Mn2+contrast agents may be desirable from a safety point of view, they are not as effective as the lanthanides at enhancing the relaxation of protons. As a result, Mn2+contrast agents often require high doses, thereby increasing the risk of cardiotoxic side effects. The r1 of chelate bound Mn2+ (MnDPDP) is half that of GdDTPA and the r1 of protein bound Mn2+ is 1.5 times larger than that of GdDTPA at 20 MHz and 37° C. Currently there is only one paramagnetic Group V agent in clinical development (GdEOB-DTPA). However, an increasing number of targeted paramagnetic compounds are currently being developed and tested pre-clinically. Most paramagnetic contrast agents, with the exception of dysprosium, are called positive contrast agents, since they primarily increase R1, resulting in signal enhancement. However, all contrast agents will enhance both R1 and R2 of water protons. Whether or not the signal intensity is increased or decreased is dependent upon which effect predominates. Since most paramagnetic agents produce only weak local magnetic fields, the R1 enhancement is greater than R2* enhancement. As a result, the observed signal intensity (that reflects the average effect) increases. When gadolinium complexes are compartmentalised at high concentrations, or when T2* weighted sequences are used (long TE GRE sequences), the R2* effects predominate and signal decrease is observed. Superparamagnetic contrast agents are composed of a water insoluble crystalline magnetic core, usually magnetite (Fe3O4) or maghemite (γ-Fe2O3). The mean core diameters normally range from 4 – 10 nm, and the core is often surrounded by a polyoside layer based on dextran or starch derivatives. The total size of the particle is expressed as the mean hydrated particle diameter, since it includes water molecules that are associated with particle surface. Iron oxide particles are often characterized by their mean hydrated diameters <d>p as follows: Nanoparticles are mono-disperse iron oxide cores, where <d>p is less than 15 nm. Ultrasmall iron oxide particles (USPIO) are also made up of single crystal iron oxide cores with a total mean hydrated particle diameter <d>p that is less than 50 nm. In these samples there may also be a relatively larger distribution in particle sizes, so that a small percentage of the particles in the sample may have diameters significantly greater than 50 nm. A superparamagnetic iron oxide particle (SPIO) refers to particles with aggregated iron oxide cores (not single crystals) and <d>p greater than 50 nm. Iron oxide particles are classified in Group III with some of the nano-particles and USPIOs also exhibiting Group IV characteristics, since these materials may be passively taken up and excreted by other macrophages (see Table I). The r1 of iron oxide based agents is extremely dependent upon the Larmor frequency of the applied imaging field (as discussed in the next section). Generally r1 values are 4-5 times greater than that of GdDTPA at 20 MHz. The r2 values obtained for iron oxide agents are dependent primarily upon the size of the particle, and ranges from 5 to more than 20 times that of GdDTPA at 20 MHz in water. Most Group IV agents currently under development utilise the high R2* relaxation of iron oxides when trying to actively target a tissue or receptor. 32.

(35) Table 1: Summary of MRI contrast agents which have been reported to be undergoing clinical testing or which are clinically available. Acronym/ Company. Generic and Brand Name. Magnetic properties. Gd-DTPA Schering AG, Berlin, Germany. Gadopentated imeglumine Magnevist. Paramagnetic. I IV (infarct). Positive; R1 enhanced. Gd-DOTA Guerbet, Aulneysous-Bois, France. Gadoterate meglumine Dotarem. Paramagnetic. I IV (infarct). Positive; R1 enhanced. Gd-HP-DO3A Bracco SpA, Milan, Italy Gd-BOPTA Bracco SpA, Milan, Italy. Gadoteridol Prohance. Paramagnetic. I IV (infarct). Positive; R1 enhanced. Gadobenate dimeglumine MultiHance. Paramagnetic. II IV (infarct). Positive; R1 enhanced. Gadobutrol Gadovist. Paramagnetic. I IV (infarct). Positive; R1 enhanced. Gd-DTPA-BMA GdDTPABMA Amersham Health, Omniscan London, UK. Paramagnetic. I IV (infarct). Positive; R1 enhanced. Mn-DPDP Amersham Health, London, UK. Paramagnetic. I (renal clearance of bound Mn). Positive; R1 enhanced. Gd-D03A-butriol Schering AG, Berlin, Germany. MnDPDP Teslascan. Biodistribution Normal Enhance(Group No.) ment Pattern. IV (Uptake of transmetallated Mn into liver hepatocytes) Gd-EOB-DTPA Schering AG, Berlin, Germany. Gadoxetate Primovist. Paramagnetic. V (Uptake into liver hepatocytes.). Positive; R1 enhanced. MS-325 Epix, Cambridge, MA, USA. MS325 Angiomark. Paramagnetic. II. Positive; R1 enhanced. 33.

(36) AMI-25 Guerbet, Aulneysous-Bois, France. Ferumoxides Endorem Feridex. Ferrimagnetic at temp. < Nèel temp.. SPIO III. Negative; R2* enhanced in normal RES cells of the liver/spleen.. USPIO III, IV. Negative; R2* enhanced in normal RES cells of the lymph/bone marrow/ liver/spleen.. Superparamagnetic at temp. > Nèel temp.. AMI-227 Guerbet, Aulneysous-Bois, France. Ferumoxtran Sinerem Combidex. Ferrimagnetic at temp. < Nèel temp. Superparamagnetic at temp. > Nèel temp.. AMI-121 Guerbet, Aulneysous-Bois, France. Lumirem Gastromark. Ferrimagnetic at temp. < Nèel temp. Superparamagnetic at temp. > Nèel temp.. SHU 555 C Schering AG, Berlin, Germany. Ferucarotran Resovist. Ferrimagnetic at temp. < Nèel temp. Superparamagnetic at temp. > Nèel temp.. 34. SPIO IV (Orally or rectally administered). SPIO III. Positive; R1 enhancement observed in blood and highly perfused tissue at early time points. Negative; R2* enhanced in gastro-intestinal system.. Negative; R2* enhanced in normal RES cells of the liver and spleen. Positive; R1 enhancement observed in blood and highly perfused tissue at early time points..

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