Proton Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent in Different Tissue Systems : Implications for Imaging

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(16) Dissertation for the Degree of Doctor of Philosophy (Faculty of Medicine) in Radiology, presented at Uppsala University in 2002.. Abstract Bjørnerud A. 2002. Proton Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent in Different Tissue Systems - Implications for Imaging. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Medicine 1160. 79 pp. Uppsala. ISBN 91-554-5330-9.. Knowledge of the relationship between in vivo contrast agent concentration and magnetic resonance (MR) signal response is an important requirement in contrast enhanced MR imaging in general and in MR based perfusion imaging in particular. This relationship is a complex function of the properties of the contrast agent as well as the structure of the target tissue. The aim of the present work was to quantify the effects of the iron oxide nanoparticle based intravascular contrast agent, NC100150 Injection, on proton relaxation rates in different tissue systems in vivo in a pig model and ex vivo in phantoms containing whole blood. Methods that enabled accurate relaxation rate measurements in these organs were developed, and validated. From these measurements, trans-compartmental water exchange rates and blood volume could be estimated and the MR signal response could be predicted as a function of contrast agent concentration under relevant imaging conditions. Using a 1.5 Tesla clinical MR system, the longitudinal (R1 =1/T1 ) proton relaxation rates in blood, renal cortex, paraspinal muscle and myocardium were measured in vivo as a function of plasma concentration (C p ) of NC100150 Injection. The transverse (R2 * = 1/T2 * ) relaxation rates were measured in vivo in blood, renal cortex and muscle as a function of Cp and ex vivo in blood as a function of Cp and blood oxygenation tension. The proton nuclear MR (NMR) linewidth and lineshape were analysed as a function of Cp and blood oxygen tension ex vivo at 7.05 T. In muscle and renal cortex, there was a linear correlation between R2 * and Cp whereas R2 * increased as a quadratic function of Cp in blood. The NMR linewidth increased linearly with Cp in fully oxygenated blood whereas in deoxygenated blood the linewidth initially decreased with increasing Cp, reaching a minimum and then increasing again with further increase in Cp . R1 increased linearly with Cp in blood and. 2.

(17) from the slope of R1 vs. Cp the T1 -relaxivity (r1 ) of NC100150 Injection in blood at 1.5 T was estimated to be (mean ± SD) 13.9 ± 0.9 s-1 mM-1. In tissue, the maximum increase in R1 was limited by the rate of water exchange between the intravascular and interstitial tissue compartments. Using a two-compartment exchange-limited relaxation model, the permeability surface area (PS) product was estimated to be 61.9 ± 2.9 mL/min/g in renal cortex and 10.1 ± 1.5 mL/min/g in muscle and the total myocardial water exchange rate, k t, was 13.5 ± 6.4 s-1. The estimated blood volumes obtained from the same model were 19.1 ± 1.4 mL/100 g, 2.4 ± 1.4 mL/100 g and 11.2 ± 2.1 mL/100 g, respectively in renal cortex, muscle and myocardium. Current T2 * based first-pass MR perfusion methods assume a linear correlation between R2 * and Cp both in blood and tissue and our results therefore suggest that quantitative perfusion values can not easily be obtained with existing tracer kinetic models. The correlation between MR signal response and Cp is further complicated in the kidney by a significant first-pass increase in R1 which may lead to an underestimation of Cp . In T1 -based perfusion methods, low concentrations of NC100150 Injection must be used in order to maintain a linear dose-response relationship between R1 and Cp . The effect of blood oxygenation on the NMR linewidth in the presence of NC100150 Injection enabled accurate estimation of magnetic susceptibility of deoxyhemoglobin and the effect can potentially be used to determine blood oxygenation status. In conclusion, NC100150 Injection is well suited as a T2 * perfusion agent due to the large magnetisation and intravascular biodistribution of this agent. T1 -based perfusion imaging with this agent is limited by water exchange effects and large T2 * effects at higher contrast agent concentrations. Quantitative perfusion assessment is unlikely to be feasible with any of these approaches due to the non-linear dose response. Key words: Iron oxide nanoparticles, USPIO, NC100150 Injection, water exchange limited relaxation, MR perfusion imaging.. Atle Bjørnerud, Department of Oncology, Radiology, and Clinical Immunology, Section of Radiology, Uppsala University Hospital, SE-751 85 UPPSALA, Sweden. © Atle Bjørnerud, 2002 ISSN 0282-7476 ISBN 91-554-5330-9. Printed in Sweden by Uppsala University, Tryck & Medier, Uppsala 2002. 3.

(18) Acknowledgements The experimental work of this thesis was, with the exception of Paper I, carried out at the Department of Oncology, Radiology and Clinical Immunology at Uppsala University Hospital. The initial work leading to the first paper was carried out at Nycomed Imaging in Oslo (now Amersham Health). Experimental research is never a one-man show – this thesis being no exception. I am grateful to many people who have supported and helped me in different ways in my PhD work over the past two years: Håkan Ahlström, my mentor, for your support both scientifically and economically. The economic part became particularly important when I decided to leave Nycomed and financing of my PhD work and frequent trips to Uppsala became an issue. I appreciate your ability to not waste time on trivialities, thereby keeping the amount of noise down to a minimum. Your input was always to the point and your guidance along the way has been of great importance to the outcome of my work. Lars Johansson for being a great source of inspiration. Always full of ideas and with a never-ending source of energy. You have a common-sense approach to science, which is uncommon among scientist (and frightening to some). Combined with your positive attitude, sense of humour and social intelligence, these qualities make you a unique person to work with. Karen Briley Sæbø for all your support in many experimental aspects of my work. You are by far the most skilful analytical relaxometry person on this planet. Your systematic and tidy approach to experimental research have made me realise the truth in the saying that: if an experiment hasn’t been documented it hasn’t been done. Ken Kellar for sharing with me some of your immense knowledge in the field of relaxometry in particular and physics in general. Thanks for all the fun, both scientifically and otherwise, during our Nycomed years. I also appreciate you taking the time to read my thesis and suggesting important last-minute changes. (I never learn). 4.

(19) Tomas Bjerner for your important contributions to the last study. Your positive nature and structured personality made it a true pleasure to work with you. I also thank your for pleasant dinners and accompanying discussions during my frequent Uppsala stays in the dark autumn and winter months. Anders Ericsson for stimulating discussions around water exchange and for digging out obscure but important references from your impressive archive. Monica Hall for all your help with the animal preparation and handling. Christl Richter-Frohm for efficiently taking care of all the administrative work – a big task especially due to my absence from Uppsala most of the time. Former colleagues at Nycomed, Anita Haldorsen and David Grace, for helping me with relaxometry and NMR analysis and Svein Olaf Hustvedt for supporting my work during my last year at Nycomed. My current employer, Jarl Jakobsen and colleagues at the Department of Radiology, National Hospital in Oslo who have shown great flexibility and given me time to complete my thesis. Family and friends for support and help, especially during the many weeks when I had to attend courses in Uppsala. Without your help I would either have been divorced or without a thesis today. Thank you Hilde for your presence in my absence. To my children, Jeppe, Herman Julius and Maren who have courageously dealt with rather chaotic domestic circumstances at times. To Janne, my companion in life for supporting me and coping with my absence - both physically and mentally – over the last year. I hope I can make up for this ego trip.. 5.

(20) Original Papers Paper I Bjørnerud A, Briley-Saebo K, Johansson LO, Kellar KE. Effect of NC100150 injection on the 1H NMR linewidth of human whole blood ex vivo: dependency on blood oxygen tension. Magn Reson Med 2000;44:803-807. Paper II Bjørnerud A, Johansson LO, Briley-Sabo K, Ahlstrom HK. Assessment of T1 and T2* effects in vivo and ex vivo using iron oxide nanoparticles in steady state: dependence on blood volume and water exchange. Magn Reson Med 2002; 47:461-471. Paper III Bjørnerud A, Johansson LO, Ahlstrom HK. Renal T2* perfusion using an iron oxide nanoparticle contrast agent - influence of T1 relaxation on the first-pass response. Magn Reson Med 2002; 47:298-304. Paper IV Bjørnerud A, Bjerner T, Johansson LO, Ahlstrom HK. Assessment of myocardial blood volume and water exchange. Theoretical considerations and in vivo results. (Submitted).. Til Janne - det skulle vært deg -. 6.

(21) Contents 1. Abbreviations ........................................................................................................ 9. 2. Introduction.........................................................................................................11 2.1 Basics of MRI...................................................................................................... 11 2.1.1. Image generation ..............................................................................................................................13. 2.1.2. Proton relaxation...............................................................................................................................14. 2.1.3. Relaxation and MR signal behaviour............................................................................................16. 2.2 Contrast Agents in MRI ...................................................................................... 20 2.2.1. Paramagnetic agents ........................................................................................................................21. 2.2.2. Superparamagnetic agents ..............................................................................................................21. 2.2.3. Proton relaxation in the presence of magnetic agents................................................................22. 2.3 Contrast Agent Relaxivity In Vivo....................................................................... 28. 3. 2.3.1. Susceptibility effects........................................................................................................................28. 2.3.2. Water exchange effects ...................................................................................................................35. 2.3.3. T2 * perfusion imaging ......................................................................................................................40. 2.3.4. Tracer kinetic modelling .................................................................................................................41. 2.3.5. Correlation between MR signal intensity, relaxation rates and tracer concentration...........44. Study Aims ...........................................................................................................48 3.1 Main Aim ............................................................................................................ 48 3.2 Specific Aims ....................................................................................................... 48 3.3 Purpose of Individual Studies.............................................................................. 48. 4. 3.3.1. Study I ................................................................................................................................................48. 3.3.2. Study II...............................................................................................................................................49. 3.3.3. Study III..............................................................................................................................................49. 3.3.4. Study IV.............................................................................................................................................50. Methods ................................................................................................................51 4.1 Test Systems ........................................................................................................ 51 4.2 Animal Model (Studies II, III and IV) ................................................................. 51 4.3 MR Imaging (All Studies).................................................................................... 52 4.4 NMR Analysis (Study I) ...................................................................................... 53 4.5 Ex Vivo Blood Oxygenation /Deoxygenation (Study I)......................................... 53 4.6 Contrast Agent (All Studies)................................................................................ 53 4.7 Determination of Contrast Agent Concentration in Plasma (Studies I and II)..... 53 4.8 Data Analysis (All Studies) .................................................................................. 54 4.8.1. NMR analysis (Study I)...................................................................................................................54. 7.

(22) 4.8.2. Relaxation rate analysis (Studies I, II and IV).............................................................................54. 4.8.3. Quantification of tissue water exchange effects (Studies II and IV)........................................55. 4.8.4. Monte Carlo simulations (Study IV) .............................................................................................56. 4.8.5. Dynamic first-pass image analysis (Study III).............................................................................56. 4.8.6. Simulation of error in first-pass T2* response as a function of contrast agent dose and sequence parameters (Study III).....................................................................................................57. 5. Results and Discussion......................................................................................58 5.1 Study I................................................................................................................. 58 5.1.1. Effects of blood oxygenation .........................................................................................................58. 5.1.2. Implications for imaging .................................................................................................................60. 5.2 Studies II and III................................................................................................. 61 5.2.1. T2 * effects in steady state (Study II)..............................................................................................61. 5.2.2. T1 effects in steady state (Study II)................................................................................................62. 5.2.3. PS product and blood volume in renal cortex and muscle (Study II) ......................................63. 5.2.4. First-pass response in the kidney (Study III)...............................................................................64. 5.2.5. Implications for imaging (Studies II and III)...............................................................................65. 5.3 Study IV .............................................................................................................. 67 5.3.1. Myocardial water exchange and blood volume ...........................................................................67. 5.3.2. Chi-square maps ...............................................................................................................................68. 5.3.3. Monte Carlo simulations .................................................................................................................69. 5.3.4. Implications for imaging .................................................................................................................69. 5.4 Summary of Relaxation Properties ..................................................................... 70. 6. Conclusions ..........................................................................................................72. 7. References ............................................................................................................74. 8.

(23) 1 Abbreviations ζ. Fractional blood volume.. λ. Ratio of proton spin densities of tissue and blood.. µ0. Permeability of free space = 4π x 10-7 H/m.. χ2-map. A parametric image where each pixel represent the goodness-of-fit (in terms of the chi-square of the non-linear fit) of the underlying data to a model function. Also referred to as a chi-square map.. τe. Correlation time in ms associated with the average residence time of a water molecule in the extravascular compartment.. τi. Correlation time in units of ms associated with the average residence time of a water molecule in the intravascular compartment.. AIF. Arterial input function.. B. Magnetic flux density = µ0(H+M) (commonly referred to as ‘magnetic field’) in units of Tesla.. BV. Blood volume in units of mL/100 g tissue.. Cp. Contrast agent concentration in plasma.. ECF. Extracellular fluid.. ECF agent. A contrast agent which distributes to the extracellular fluid after i.v. administration.. H. Magnetic field in units of A/m.. k. Slope of linear correlation between contrast agent concentration in plasma and change in R2* in tissue in units of s -1mM-1.. ke. Water exchange rate 1/τe in units of s -1.. ki. Water exchange rate 1/τi in units of s -1.. kt. Total water exchange rate = ki + ke in units of s -1.. M. Magnetisation of a medium in units of A/m.. Pixel. Picture element.. PS product. Permeability surface area product = λ.ke/(ki+ke) in units of mL/g/min. 9.

(24) R1. Longitudinal relaxation rate = 1/T1 in units of s -1.. r1. DipolarT1 relaxivity of a contrast agent in units of s -1 mM-1 (s-1 mmol-1L). The increase in R1 in a given medium per unit concentration of the contrast agent.. R2. Transverse relaxation rate = 1/T2 in units of s -1.. r2. DipolarT2 relaxivity of a contrast agent in units of s -1 mM-1s-1 (mmol-1L). The increase in R2 in a given medium per unit concentration of the contrast agent.. R2*. Effective transverse relaxation rate in gradient echo sequences =1/T2* in units of s -1.. RF. Radio frequency.. ROI. Region of interest.. SD. Standard deviation.. SE. Standard error.. SI. Signal intensity.. SPIO. Small particles of iron oxide.. χ. Susceptibility of a medium (unitless in SI units). The slope of the linear correlation between induced magnetisation and applied magnetic field.. T1. Longitudinal relaxation time in units of ms.. T2. Transverse relaxation time in units of ms.. T2*. Effective transverse relaxation time in units of ms in gradient echo sequences.. TE. Echo time in units of ms. Time between excitation pulse and peak echo formation.. TI. Inversion time in ms. Time between 180° inversion pulse and image acquisition.. TR. Repetition time in units of ms. Time between consecutive RF excitation pulses.. USPIO. Ultra-small particles of iron oxide.. Voxel. Volume element.. 10.

(25) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. 2 Introduction 2.1 Basics of MRI Magnetic resonance imaging (MRI) is based on the discovery, made more than 50 years ago, that nuclei with a spin angular momentum (spin) can interact with a magnetic field (1,2). The essence of this interaction, known as nuclear magnetic resonance (NMR) is described by the simple linear relationship between the static magnetic flux density (magnetic field) B0 experienced by a nuclei and the resulting angular frequency of rotation ω0 of the nuclear spin: ω0 = γB0. [1]. where γ is the gyromagnetic ratio, which is a unique constant for each nuclear isotope possessing a spin. All current clinical use of MRI is based on proton NMR (with spin ½) and for protons γ/2π =.42.6 x 106 Hz/T. The angular frequency ω0 is referred to as the Larmor frequency, and is identical to the frequency of the electromagnetic radiation associated with the possible spin energy transitions induced by the magnetic field B0. Although the NMR phenomenon is purely a quantum mechanical process, its macroscopic manifestation is, under most circumstances, well described by classical physics. Each nuclear spin is associated with a dipolar magnetic moment µ 1. In fact, in the very first description of NMR the effect was used to accurately measure nuclear magnetic moment (3). The nuclear magnetic moment can be thought of as the magnetic energy per unit magnetic flux density induced by the current loop associated with the rotation, due to B 0, of the charged protons in a nucleus. Although the current loop of a single proton is negligible and has almost zero dimension, the sum of the individual magnetic moments of all the. 1. Vectors and matrices will be denoted by bold typeface.. 11.

(26) Atle Bjørnerud. protons contained in a macroscopic sample is finite and observable and is referred to as the macroscopic magnetisation of the sample, M. The behaviour of the macroscopic magnetisation vector as a result of magnetic interactions is described classically by the Bloch equation (1,4), which in a general form is given by: dM / dt = γ ( M × B ). [2]. Eq. [2] states that the vector describing the rate of change of M is perpendicular to both B and M. In other words, the macroscopic magnetisation vector M precesses about the direction of the magnetic field – in analogy to the precession of a gyroscope about the gravitational field. When the spin system is in a state of equilibrium the net magnetisation points in the direction of the main magnetic field, referred to as the z-direction with a magnitude given by Mz . MRI is based on the detection of the magnetisation vector M. However, in order to get any information about M, the vector needs to be moved away from its equilibrium orientation parallel to B 0. This is achieved by applying a second magnetic field, B 1, perpendicular to B 0. The Bloch equation describing the motion of the magnetisation vector in the presence of both the B 0 and B 1 fields can then be written as dM / dt = γM × ( B0 + B1 ). [3]. Contrary to the static field B 0, B 1 is made to oscillate at the Larmor frequency. Seen from a ’rotating frame of reference’ the magnetisation vector (which also rotates at the Larmor frequency) therefore experience B 1 as a ’static’ field perpendicular to Bo, causing the magnetisation vector to rotate about the B 0 axis with a precession frequency given by ω1=γB1. The angle of rotation of the magnetisation vector at time t during the application of B 1 is then given by α = γB1t. This angle is referred to as the flip angle and is typically between a few degrees and 180o. Since the duration t needed to flip the magnetisation by the required amount is typically very short (100 µs to a few ms), the application of 12.

(27) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. the B1-field is referred to as an RF-pulse where the term RF reflects the fact that the frequency of oscillation of the electromagnetic radiation associated with the field is in the radio frequency range. The term excitation pulse is also used to describe the process of applying the B1-field, reflecting the fact that the spin system will be in a higher energy state when the net magnetisation of the system is moved away from its equilibrium orientation. A 180o flip angle is an excitation pulse where the magnetisation is inverted to point along the –z-axis whereas a 90o pulse causes the net magnetisation vector to point in a plane perpendicular to the z-direction, referred to as the xy-plane. During, and immediately after the application of an excitation pulse, there will be a component of M present in the xy-plane, Mxy that rotates about the zaxis. The oscillating nature of Mxy makes it possible to detect the presence of this magnetisation component through the induction of a current in a coil placed within the oscillating field. The observed signal due to Mxy is referred to as the MR signal or the free induction decay (FID). The term decay refers to the fact the signal rapidly disappears due to proton relaxation processes, as discussed further below. 2.1.1 Image generation So far, only the gross behaviour of the net magnetisation in a sample is described. In order to create a MR image, the object needs to be decomposed into several sub-volumes where the magnitude of Mxy of each sub-volume must be resolved from the measured MR signals. The detailed process of spatial encoding of the MR signal is outside the scope of this introduction and the topic is covered in great depth in many standard textbooks on MRI (e.g. Ref. 5). In short, in order to spatially encode the MR signals additional magnetic fields are introduced where the magnitude of the fields varies as a function of position. These field gradients are applied in all three directions and cause the proton Larmor frequency to vary as a function of position within the object. By applying frequency selective excitation pulses at the same time as the field gradients are 13.

(28) Atle Bjørnerud. applied it is possible to selectively excite a limited volume in the object. However, the MR signal still contains information from the whole excitation volume and a single combination of the field gradients does not provide enough spatial information to uniquely resolve the magnetisation component of each individual volume element (voxel). In order to resolve individual voxels in the object, the excitation process must therefore be repeated multiple times using different magnetic gradient conditions for each excitation. The time between each successive excitation pulse is referred to as the repetition time, TR. Following each excitation pulse, the MR signal is sampled after a given delay. The delay time between the excitation pulse and the signal sampling is referred to as the echo time, TE. Several different methods exist whereby the MR signal is manipulated and sampled in different ways. The combination of multiple excitation pulses and the corresponding sampling process required to generate a MR image is referred to as a pulse sequence and a large variety of different pulse sequences exist which are tailor made to generate a certain type of image contrast and where the trade-off between image quality and acquisition time is optimised for a given application. 2.1.2 Proton relaxation If the induced electrical signal due to Mxy from a single excitation pulse is observed on an oscilloscope one will notice that the signal rapidly decays to zero, as discovered by Bloch already in his first nuclear induction experiment (6). This signal decay is due to what is generally referred to as proton relaxation and is the result of proton interactions and consequent exchange and loss of the excitation energy (7). The macroscopic effect of relaxation is that Mxy gradually disappears whereas Mz gradually recovers following an excitation pulse.. 2.1.2.1 T1 relaxation Excited protons either can go from their high-energy state to the low-energy state through spontaneous emission or stimulated emission. In MRI, only 14.

(29) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. stimulated emission is of importance and this requires the protons to experience a fluctuating magnetic field containing a frequency component at or near the Larmor frequency. In tissues, such random fields are generated by the magnetic moment of protons in thermal motion and by chemical exchange. The macroscopic effect of the energy transitions caused by stimulated emission results in a gradual recovery of the longitudinal component of the magnetisation, Mz , following an excitation pulse. The rate of recovery of Mz is described by a time constant that is referred to as the T1 relaxation time. The inverse of the relaxation time, 1/T1 is referred to as the relaxation rate, R1. The T1 relaxation times in different tissues vary from several seconds in body fluids like cerebrospinal fluid to less than 300 ms in fat, and these differences in T1 give rise to the image contrast when using pulse sequences which are sensitive to variations in T1 relaxation times; referred to as T1-weighted sequences. In T1-weighted sequences, TR is short (compared to the longest T1 to be observed) and tissues with a short T1 will then give more signal than tissues with a long T1 since more magnetisation is recovered in the TRinterval.. 2.1.2.2 T2 relaxation The term T2 relaxation is used to describe the decay of the transverse component of the magnetisation, Mxy, following an excitation pulse. This time constant is also referred to as the transverse relaxation time (and the corresponding relaxation rate 1/T2=R2). One might expect from the discussion of T1-relaxation above that the transverse component of the magnetisation will decay at the same rate as Mz is recovered so that T1=T2. However, in any medium (except pure water) the decay of Mxy occurs significantly faster than the recovery of Mz due to additional relaxation effects affecting the net magnetisation in the transverse plane. T2 relaxation is caused by local field inhomogeneities on a microscopic scale. These field variations are introduced by various ‘shielding effects’ at the molecular level as well as macroscopic field 15.

(30) Atle Bjørnerud. inhomogeneities in the field due to variations in the local susceptibility, as discussed later in the chapter. Immediately following an excitation pulse all the protons in a voxel precess in phase and their individual magnetic moments will collectively contribute to the transverse magnetisation vector. However, the presence of field variations on a molecular level will introduce variations in the Larmor frequency with consequent loss of phase coherence among the spins in a voxel. The loss of phase coherence therefore causes Mxy to decay faster than Mz is recovering so that T2 is always shorter than T1 in vivo. Transverse relaxation times in vivo can vary significantly depending on tissue composition and local field homogeneity and T2 is generally longer in fluids than in solid tissues. Changes in T2 relaxation times are therefore in many instances a sensitive marker for tissue pathology because many pathological processes are associated with changes in the tissue water content. In order to make the pulse sequence sensitive to T2 differences, TR needs to be as long possible (to minimise the sensitivity to T1 differences) and TE should be sufficiently long to ensure that a large enough difference in the transverse magnetisation has been established between the tissues of interest before the MR signal is acquired. 2.1.3 Relaxation and MR signal behaviour The Bloch equations can now be extended to include the proton relaxation time constants, T1 and T2 (8) to give dM = γM × B eff − R ( M − M 0 ) dt. [4]. where 1   T2 R=0   0 . 0 1 T2 0.  0  0  M x        0 and M 0 =  0  , M =  M y    M 0   M z  1  T1 . 16. [5].

(31) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. B eff is the effective field due to B 0 and B 1 and M0 is the equilibrium magnetisation. Additional terms are often added to the Bloch equations to account for the effects on the magnetisation of specific tissue phenomenon, for instance the effect of water exchange between different tissue compartments as will be discussed later in the chapter. Disregarding such additional effects, Eq. [4] can be solved to give the evolution of the two components of the magnetisation vector following an excitation pulse M z (t ) = M 0 [1 − exp( −t / T1 )] + M z (0) exp( −t / T1 ) M xy (t ) = M xy ( 0) exp( −t / T2 ). [6]. and M xy (t ) = M x (t ) + iM y (t ). where M(0) describes the magnitude of the respective magnetisation components immediately after the completion of the excitation pulse. Eq. [6] can be written in matrix notation as  M x (t )   E 2 M (t ) =  0  y    M z ( t )   0. 0 E2 0. 0   M x ( 0)   0     0  ⋅  M y ( 0)  + (1 − E1 ) ⋅  0   M 0  E1   M z (0) . [7]. where E1=exp(-t/T1) and E2=exp(-t/T2). Eq. [7] forms an important basis for all calculations of the magnetisation behaviour, and consequently the signal behaviour in MRI. However, these expressions only describe the magnetisation behaviour following a single excitation pulse. As discussed briefly above, all MR pulse sequences are based on multiple excitation pulses. Multiple excitations (typically 50-500) are needed in order to acquire enough spatial information about the magnetisation (and relaxation) distribution in the entire imaging volume to create an image. Each consecutive excitation pulse will in general affect both the transverse and the longitudinal components of the magnetisation and the effect of each RF 17.

(32) Atle Bjørnerud. excitation pulse can collectively be described by a rotation matrix R given by (5). 0,55. Spoiled Not spoiled Steady state (spoiled). 0,5 0,45 0,4 Mxy +. 0,35 0,3. 0,25 0,2 0,15 0,1 1. 6. 11 16 21 Number of RF pulses. 26. 31. Figure 1. The approach to steady state following multiple RF excitations in a tissue with T1 =100 ms and T2 =30 ms using a TR of 10 ms and a flip angle of 30o . The black solid line shows the magnetisation progression when the remaining transverse magnetisation Mxy is not eliminated prior to each new RF-pulse. The grey solid line shows the magnetisation when Mxy is removed by spoiling giving a smoother approach to the steady state magnetisation level. The dotted line indicates the relative magnetisation level in steady state calculated using Eq. [9], which is valid for spoiled sequences. In the nonspoiled case, the steady state level is somewhat higher due to a contribution from Mxy . The y-axis shows the magnitude of the transverse magnetisation immediately following each new RF pulse.. 18.

(33) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. 0 1  R = 0 cosα 0 − sin α. 0  sin α  cos α . [8]. so that the magnetisation vector immediately following each excitation pulse, M+, is related to the situation immediately prior to the pulse, M- by the relationship M+=R.M- . Applying both the relaxation matrix and the rotation matrix, one can then predict the evolution of the magnetisation in all three directions following multiple excitations. In general, one will observe that the transverse magnetisation components go through a transient stage of variable and falling magnitude before they reach a ‘steady state’ level. In a steady state situation the amount of magnetisation in each direction is the same immediately after each consecutive RF-pulse and is determined by the relaxation times as well as the sequence parameters TR and flip angle α. The two solid curves in Fig. 1 shows examples of how the relative magnitude of the transverse magnetisation, Mxy, changes following multiple RF excitations according to Eqs. [7] and [8]. The smoother approach to steady state, and the lower steady state magnetisation level for the grey curve is a result of the assumption that the transverse magnetisation vector is zero before each new excitation pulse. When this situation is met, it can be shown that the transverse steady state magnetisation is given analytically by the expression (5) M xy = ρ ⋅. sin α ⋅ [1 − exp( −TR / T1 ) ] 1 − cos α ⋅ exp( −TR / T1 ). [9]. where ρ is the proton density. Eq. [9] is only valid when TR >> T2 or when any remaining component of Mxy is effectively removed prior to each new excitation pulse. If this criterion is not met, a part of Mxy will be tilted back into the z-plane and hence contribute to the Mxy magnetisation of subsequent excitation pulses. This effect complicates the signal behaviour, as shown by the black curve in Fig 1, but can be avoided in short TR sequences by using a technique generally 19.

(34) Atle Bjørnerud. referred to as spoiling whereby any remaining Mxy is removed prior to each RFpulse. The resulting MR signal intensity (SI) then scales with the transverse magnetisation in steady state but is modulated by the amount of T2-relaxation which occurs during the echo time, TE; i.e. the time between the excitation pulses and the registration of the MR signal. The relative steady state SI in a spoiled gradient echo sequence is then given by SI (TE) ∝ ρ ⋅. sin α ⋅ [1 − exp( −TR / T1 )] * ⋅ exp( −TE / T2 ) 1 − cos α ⋅ exp( −TR / T1 ). [10]. The term T2*, rather than T2 is used here to denote the transverse relaxation time. The total amount of transverse relaxation is often divided into a proton diffusion sensitive and a diffusion insensitive (static) component and T2* is used to describe the total effect of both components. Gradient echo sequences (which are used in all studies reported here) are sensitive to both the static and the diffusion dependent components (rotational and translational diffusion as well as chemical exchange) of T2* and this is therefore the appropriate notation to use. Other types of pulse sequences, called spin echo (SE) or fast spin echo ( FSE) apply what is called refocusing pulses (usually 180o RF pulses) which tend to cancel out the component of relaxation which is due to static effects, thereby significantly reducing transverse relaxation effects in vivo (5). The effective transverse relaxation in SE and FSE sequences is therefore commonly denoted by T2 to indicate the lack of sensitivity of these sequences to the static dephasing component of T2*.. 2.2 Contrast Agents in MRI In spite of the excellent soft tissue contrast of MRI, the application of contrast enhancing agents in clinical MRI was proposed already more than 15 years ago (9) and contrast agents are today an integral part of this image modality. MR contrast agents work by enhancing the relaxation rate of the 20.

(35) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. protons in tissue, thereby altering the signal intensity in the image relative to areas not affected by the contrast agent. The principle of relaxation rate enhancement is as old as NMR itself. Bloch and coworkers published already in 1946 how the addition of paramagnetic ions such as ferric nitrate enhanced the relaxation rate of water (6). A MR contrast agent can be thought of as a catalyst that decreases the proton relaxation times of tissue water. In this respect, MR contrast agents are fundamentally different from X-ray contrast agents where the agent is directly visualised in the X-ray image. In contrast enhanced MRI, the effect of the agent on proton relaxation is observed; not the contrast agent directly. MR contrast agents can be divided into different classes according to their magnetic properties, in vivo relaxation effects and biodistribution. 2.2.1 Paramagnetic agents Paramagnetic agents contain water-soluble metal ions with one or more unpaired electrons. The most common paramagnetic metal used as MR contrast agent is gadolinium (Gd3+) which has seven unpaired electrons (10). For in vivo use, the gadolinium ions must be chemically linked to a carrier molecule, called a ligand, in order to reduce toxicity and alter the pharmacokinetic properties of the metal (11). The resulting gadolinium containing molecule is referred to as a chelate, and currently available gadolinium based chelates are known as extracellular fluid (ECF) agents because they are distributed in the extracellular space following intravenous injection. Gd-ECF agents are eliminated by renal excretion and the half-life of the agent is therefore determined by the glomerular filtration rate. 2.2.2 Superparamagnetic agents Superparamagnetic contrast agents are based on magnetite (Fe 3O4) or maghemite (γ-Fe 2O3) water insoluble iron oxide crystals with a core diameter in the range 5 – 10 nm (12,13). These crystals are often referred to as nanoparticles, and each nanoparticle contains several thousand paramagnetic Fe ions (Fe 2+ and 21.

(36) Atle Bjørnerud. Fe3+). If the Fe ions are magnetically ordered within the crystal, the net magnetic moment of the nanoparticle is so large that it greatly exceeds that of typical paramagnetic ions (14). This effect is referred to as superparamagnetism and is characterised by a large magnetic moment in the presence of an external magnetic field but no remnant magnetic moment when the field is zero - contrary to ferromagnetic substances which have remnant magnetic moment at zero field once magnetised. Unlike Gd-ECF agents, iron oxide nanoparticles do not leak into the interstitium and therefore act as intravascular contrast agents. Intravascular agents are also known as blood pool agents, reflecting the fact that these agents are contained within the intravascular space. Iron oxide agents are eliminated from blood by uptake into the reticuloendothelial cells in the liver, spleen and bone marrow and the half-life of these agents in blood varies significantly depending on particle size and physical chemical properties of the particle and its coating. Accordingly, iron oxide nanoparticles are commonly sub-divided into two groups, depending on the overall size of the particle, which may be substantially larger than the core size since the crystals are covered by a biodegradable coating which prevents particle aggregation and which may also be used to modify the biodistribution of the particles (15). Nanoparticles with a total particle size less that about 50 nm are referred to as ultrasmall particles of iron oxide (USPIO) whereas particles with a total size in the range 50-200 nm are referred to as small particles of iron oxide (SPIO). The particle used in the present work, NC100150 Injection belongs to the USPIO class (16). 2.2.3 Proton relaxation in the presence of magnetic agents The net magnetic moment of an unpaired electron spin is roughly 650 times greater than the magnetic moment of a proton. Consequently, all current MR contrast agents have magnetic properties and the corresponding magnetisation will introduce a significant fluctuation of the local magnetic field experienced by the water protons with a resulting increase in relaxation rate. Proton relaxation in the presence of a magnetic complex can be divided into two processes; dipolar relaxation and susceptibility induced relaxation. 22.

(37) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. 2.2.3.1 Dipolar relaxation Dipolar relaxation is caused by a direct interaction between the water protons and the magnetic moment of the unpaired electrons of the contrast agent, and is commonly subdivided into inner-sphere and outer-sphere relaxation (10). The inner-sphere component of dipolar relaxation requires a rapid proton exchange between the bulk solvent and the inner co-ordination sphere of the magnetic agent. The magnitude of this relaxation effect is therefore proportional to the number of water binding sites in the inner co-ordination sphere of the contrast agent molecule. All current gadolinium chelates have one inner-sphere co-ordination site for water (the other sites are occupied by the metal binding ligand). Inner-sphere relaxation accounts for approximately 50% of the relaxation effect in Gd-ECF agents (17). Iron oxide nanoparticles have no innersphere relaxation and the dipolar relaxation of this class of agents is only due to outer-sphere effects. Outer-sphere relaxation is caused by a fluctuation in the magnetic field sensed by the water protons due to fluctuations in the direction of the magnetic moment of the contrast agent as well as the diffusion of the protons in the vicinity of the magnetic centres. The theory of dipolar relaxation has been known for many decades (18,19) and has more recently been refined for specific applications to iron oxide nanoparticles (14,20,21).. 2.2.3.2 Contrast agent relaxivity The efficiency by which a contrast agent can enhance the proton relaxation rate in a homogeneous medium is called the dipolar relaxivity of the agent and is defined by R1, 2 = R1, 2 + r1, 2 ⋅ C 0. [11]. where R1,2 is the respective T1- or T2 proton relaxation rates (unit: s -1) in the presence of the contrast agent, R1,20 are the same relaxation rates in the absence of the contrast agent and C is the concentration of the contrast agent (unit: millimol/L=mM). The constant of proportionality r 1,2 is called the relaxivity (r1 or 23.

(38) Atle Bjørnerud. r2) of the agent (unit: s -1mM-1) and is a measure of how much the proton relaxation rate is increased per unit concentration of contrast agent. The two relaxivity constants are also commonly referred to as T1-relaxivity (r1) and T2 relaxivity (r2). The dipolar relaxivity of a given contrast agent can readily be measured by titrating a water solution with known amounts of the agent and measure the corresponding change in the water relaxation rate on a spectrometer. The measured relaxivities are generally dependent on magnetic field and on temperature and these parameters should always be specified when the relaxivity values of an agent are given. The relaxivities of Gd-ECF chelates as well as some iron oxide nanoparticles under development have been measured at relevant field strengths and temperatures (11,15-17,22). In general, ultrasmall iron oxide nanoparticles have higher relaxivity values at clinical field strengths, and especially the T2-relaxivity is much higher (by a factor of about 10 to several hundred) for iron oxides than for gadolinium based agents. The T1-relaxivity of iron oxides can also be higher than that of gadolinium ECF agents, but their r 1 value is dependent on field strength and particle size and can vary substantially, whereas r 1 of Gd-ECF agents is fairly constant at clinical field strengths, with a value of about 4 s -1mM-1 in water at 20 MHz (23). By comparison, the T1relaxivity of the iron oxide nanoparticle NC100150 Injection at 20 MHz is about 22 s -1mM-1 (16). The expressions for relaxivity given in Eq. [11] imply that the proton relaxation rate increases linearly with contrast agent concentration. This is an attractive feature in many dynamic MRI applications where the observed effect of the agent in the image needs to be correlated to the concentration of the contrast agent in tissue. This topic will be discussed in more detail later in the chapter. In many situations, however, the change in vivo relaxation rate is not a linear function of contrast agent concentration due to additional relaxation effects. In particular, the relaxivity equations given above only apply when proton relaxation is due to dipolar interactions. The term ‘dipolar’ here implies a 24.

(39) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. direct interaction between each individual magnetic atom or particle and the water molecules in the medium. In order for a pure dipolar relaxation to take place, the contrast agent must be evenly distributed in the medium. A further requirement is that all water protons in the medium are equally affected by the relaxation effects of the agent in the solution. These requirements are not commonly met in vivo since the biodistribution of all available contrast agents is restricted to certain tissue compartments. The so-called compartmentalisation of the contrast agent in vivo can have a profound influence on its effective relaxivity. Both the T1- and the T2-relaxivity can be influenced by contrast agent compartmentalisation, but the two mechanisms are affected in different ways as discussed further below.. 2.2.3.3 Susceptibility and induced magnetisation The relaxation effect, called the susceptibility effect of the contrast agent can make up a substantial part of the total transverse relaxivity of an agent in vivo. As will be discussed further below, the amount of susceptibility induced transverse relaxation is strongly dependent on the magnitude of the magnetisation (or more correctly magnetisation difference) induced by the contrast agent in tissue. For paramagnetic substances, the induced magnetisation is proportional to the applied field at clinically relevant fields M =χH. [12]. where M is the induced magnetisation (unit: A/m), H is magnetic field (unit: A/m) and χ is the susceptibility (unitless) of the paramagnetic agent. Note the distinction between magnetic field H with units of A/m and magnetic flux density B with units of Tesla. The magnetic field density B is commonly referred to as the ‘field strength’ in the MRI literature and it should be noted that B is really the magnetic induction, which is proportional to the magnetic field: B = µ0(H+M) ≈ µ0H where µ0 is the permeability of free space = 4π x 10-7 H/m.. 25.

(40) Atle Bjørnerud. For superparamagnetic agents like iron oxide nanoparticles, the linear relationship between M and H no longer applies at clinical field strengths due to magnetic saturation which occurs when the applied field is strong enough to cause complete alignment of all individual atomic magnetic moments of the. 5 NC100150 Injection gadolinium. 4,5. Magnetisation (A/m). 4 3,5 3 2,5 2 1,5 1 0,5 0 0. 0,2. 0,4. 0,6. 0,8. 1. Magnetic Field (Tesla). Figure 2. Magnetisation curves of NC100150 Injection and gadolinium.. crystal. Magnetic saturation occurs also for paramagnetic agents but at much higher fields (>50T). The general dependence between induced magnetisation M and magnetic field H, valid at all fields, is expressed classically by the Langevin function (24) M.  µ 0 mH   kT   = coth   −  Nm  kT   µ 0 mH . [13]. where N is the number of atoms per unit volume, m is the magnetic moment per atom, k is the Boltzmann’s constant and T is the temperature in Kelvin. For values of µ0 mH/kT<<1 this leads to the approximation 26.

(41) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent M = Nm2 µ0 H / 3kT χ=. [14]. Nm2 µ 0 3kT. where the expression for χ is known as the Curie law. For paramagnetic agents, the criterion µ0mH/kT<<1 is always true at clinical fields and temperatures. The susceptibility is therefore proportional to the concentration of paramagnetic atoms in tissue and the square of the magnetic moment of the agent. For iron oxide nanoparticles in current development as MR contrast agents, the saturation magnetisation is approached at around 1 Tesla (16), and M is therefore not a linear function of H at clinical fields. Figure 2 shows the plot of M vs. H (known as magnetisation curves) for a gadolinium chelate and the iron oxide nanoparticle NC100150 Injection. The curve for gadolinium was calculated from its susceptibility value whereas the curve for NC100150 Injection was measured using the method previously described (16). NC100150 Injection approaches full saturation already at 1 Tesla whereas the magnetisation of gadolinium increases linearly with the magnetic field with a slope given by the susceptibility χ. It is also evident that the magnetisation is much higher for the iron oxide particles compared to the gadolinium chelate due to the larger magnetic moment of the iron oxide crystal.. 2.2.3.4 Magnetisation of iron oxide nanoparticles versus gadolinium The susceptibility of gadolinium has been estimated experimentally by several investigators. Weiskoff et al reported at value of χ=2.7 x 10-2 cgs/mole Gd (25) whereas Kennan et al reported a value of χ=2.55 x 10-2 cgs/mole Gd (26). In order to compare the susceptibility effects of gadolinium to that of iron oxide nanoparticles, it is convenient to calculate the magnetisation per unit concentration of the two classes of contrast agent at a given field strength. Using χ Gd=2.7 x 10-2 cgs/mole, this equals a volume susceptibility of 2.7 x 10-2 cgs/mole x 10-6 mole/cm3 = 2.7 x 10-8 cgs/cm3. The volume cgs unit is related to. 27.

(42) Atle Bjørnerud. the (unitless) SI unit by χ SI=4πχcgs =3.4 x 10-6. The magnetisation per mmol/L (mM) gadolinium at 1.5 T is then given by M Gd/mM = χ SI B/µ0 = 3.4 x 10 -6 x 1.5 x 107/4π = 0.4 Am -1mM-1 The corresponding magnetisation for NC100150 Injection is obtained directly from the magnetisation curve at the appropriate field strength. The magnetic moment of this iron oxide nanoparticle is 4.38 x 10-20 Am2, and by fitting the magnetisation curve to the Langevin function (Eq. [13]), a magnetisation at 1.5 T of 8.06 x 10-2 Am2/g Fe is obtained for NC100150 Injection (Paper I). The corresponding magnetisation per mM of substance is then MFe/mM = 8.06x10-2 Am2/g Fe x 55.84 g Fe/ mole x 10-3 mole/10-3 m3 = 4.5 Am -1mM-1 At 1.5 Tesla, the magnetisation per unit concentration of contrast agent is therefore a factor of 11 higher for the iron oxide nanoparticle NC100150 Injection compared to that of gadolinium ECF agents. The large magnetisation of NC100150 Injection has important implications for its in vivo relaxation effects, as discussed below.. 2.3 Contrast Agent Relaxivity In Vivo 2.3.1 Susceptibility effects Because of the large magnetisation of iron oxides, susceptibility effects contribute significantly to the transverse relaxivity of these agents in vivo. The susceptibility effect is a result of contrast agent compartmentalisation whereby the agent is contained within only a fraction of the total tissue volume. The contrast agent containing compartment can then be considered as a secondary ‘contrast agent’, with a total magnetisation given by the bulk sum of the individual magnetisation of each contrast agent atom/particle contained in the 28.

(43) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. compartment. The contrast agent containing tissue compartment will be referred to as a ‘field perturber’ in the following discussion. The local field variations, induced by presence of the field perturber, will tend to enhance the transverse relaxation rate of protons experiencing these variations. The susceptibility effect does not affect the longitudinal relaxation times in tissue because the size of the field perturbing compartments in vivo are so large that the T1-relaxivity has dispersed to zero at clinical fields (27). This is an important point because it reflects a fundamental property of the proton relaxation enhancing process induced by contrast agents; a contrast agent can induce T2/T2* relaxation without affecting T1 if the combination of field strength, the magnetisation due to the perturber and the size of the perturber is such that T1-relaxivity has dispersed to zero. Any reduction in T1 does, however always cause a reduction in T2/T2* since T2 relaxation is caused by the same relaxation mechanisms which cause T1 relaxation – but includes an additional term which is independent of field fluctuations so that the T2 relaxation does not disperse to zero at high fields (20). The signal loss as a function of TE due to the susceptibility effect can be expressed in terms of the frequency distribution within the voxel (26,28) ∞. S (TE ) = S0 ∫ P (ω ) exp (− i ωTE )dω. [15]. −∞. where TE is the echo time, S0 is the signal at TE=0 and P(ω) is the frequencydistribution within a voxel. The distribution of frequencies gives rise to a intravoxel phase dispersion given by TE. φ = ∫ ω p ( r (t )) dt. [16]. 0. where ωp = γBp is the Larmor frequency variation, due to the presence of the perturber, experienced by the diffusing protons. Eq. [16] is only valid in a gradient echo experiment without the use of RF-refocusing pulses. In spin echo sequences the phase dispersion is refocused every TE/2 with a consequent 29.

(44) Atle Bjørnerud. B0 B0. a. b. Figure 3. Field distribution around a cylinder oriented perpendicular to B0. reduction in the total dispersion at time TE. Since only gradient echo sequences have been investigated in the present work, the discussion here will be limited to such sequences. If proton diffusion effects can be neglected (see below) r is approximately constant within the TE period and Eq. [15] then describes the signal attenuation in terms of the Fourier transform of the intravoxel frequency distribution. From this, the field distribution within the voxel must be known in order to determine the magnitude of the susceptibility-induced relaxation. The determination of the magnetic field distributions in non-uniform media is a complex function of the geometry of the field perturber. The distribution can, in theory, be determined for any geometrical shape by application of classical electromagnetic theory (29), but can in practice only be determined for simple idealised geometries. Two types of geometries are commonly assumed when modelling tissue susceptibility effects; spheres and cylinders of infinite length. For an infinite cylinder at an angle α to the direction of the main magnetic field B 0, the field distributions due to the cylinder is given by (30) 30.

(45) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent 2. R ∆B p ( r ,ϕ ) = µ 0∆M p   cos 2ϕ sin 2 α ; r ≥ R r and. [17]. ∆B p = µ 0∆M p (3 cos 2 α − 1) ; r < R. where ∆Mp is the magnetisation difference between the inside of the cylinder and the magnetisation of the bulk medium in the absence of the perturber, R is the radius of the cylinder, r and ϕ are the polar co-ordinates relative to the centre of the cylinder in a plane perpendicular to the cylinder axis. As expected, we see that the magnitude of the external field perturbations scales with the intravascular magnetisation due to the presence of the contrast agent. A similar expression can be derived for spherical geometries (31) yielding a similar dependence on ∆Mp. Figure 3a shows and example of the field distribution due to a cylinder oriented perpendicular to B0 with an internal magnetisation Mi larger than the external magnetisation Me so that ∆Mp>0. Notice the constant and negative field shift inside the cylinder due to the negative internal ∆Bp and the large field fluctuations at the cylinder-medium interface. Figure 3b shows the same field distribution as a contour plot. The presence of a constant internal field shift in cylindrical objects (e.g. blood vessels) with a magnetisation that differs from the surrounding medium can give rise to geometrical displacements of the object in the image; the magnitude of the displacement depending on the magnitude of ∆Mp relative to the strength of the magnetic field gradients used to generate the image (32). Two important parameters related to the susceptibility effect are the proton diffusion correlation time, τD, and the equatorial field, Be q, of the perturber (33). Beq is the magnetic field at the ‘centre’ of the field perturber and the corresponding Larmor frequency δωp=γBp is called the characteristic frequency. τD is the average time for a proton to diffuse a distance equal to the size of the perturber and is given by. 31.

(46) Atle Bjørnerud τD = R 2 / D. [18]. where R is the effective radius of the perturber. The characteristics of the susceptibility effect will be different, depending on the magnitude of the product τDδω. When τDδω << 1 the condition is referred to as a motional-narrowing regime (33) and when τDδω >> 1 the condition is referred to as static dephasing regime or static line broadening (34). In the static dephasing regime, the susceptibility effect is insensitive to proton diffusion and is only dependent on the distribution of magnetic fields within a voxel. In a motional narrowing situation, each proton experiences on average the entire range of frequencies due to the field perturber which tend to ‘average out’ part of the phase dispersion. It can here be instructive to make a rough calculation of the order of magnitude of τDδω in tissue systems containing the iron oxide nanoparticle NC100150 Injection. Assuming an intravascular concentration of 1 mM of NC100150 Injection (a relevant concentration in our work) the resulting intracapillary magnetisation due to the agent is about 5 A/m (from the magnetisation of the agent at 1.5 T: 4.5 Am-1mM-1). Assuming a capillary radius of 5x10-6 m and an extracellular diffusion constant of 1 x 10-9 m2/s (35) we then get τD=R2/D = 50 ms. The equatorial field of the capillary due to the contrast agent is Be q=µ0M=4πx10-7 x 5 ≈ 6 x 10-6 T and δω=γBe q= 2π x 42x106 x 6x10-6≈1.6 x 103 Hz. The product τDδω is therefore of the order of 50 x 1.6 ≈ 80 >> 1, suggesting that static line broadening is a plausible assumption at relatively moderate concentrations of NC100150 Injection in plasma. For larger vessels, the product τDδω will be even larger. Restricting the discussion to gradient echo sequence in the static dephasing regime, the resulting signal decay function obtained from the solution of Eq. [15] to the appropriate intra-voxel field distributions can generally be expressed as S = S 0 ⋅ exp( −∆R2 (σ 2 p , TE ) ⋅ TE ) *. [19]. 32.

(47) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. where ∆R2* is the increase in transverse relaxation rate due to susceptibility effects and σ2p is the variance of the field distribution within the voxel. The variance σ2p is related to the linewidth of the NMR spectrum of the sample tissue (or, from a single tissue voxel in imaging) which again is a function of the magnetisation induced by the perturber. Following the discussion above, the shape of the NMR spectrum describing the field distribution is generally not known, but by assuming that the distribution of fields is random, standard statistical models can be applied whereby the field is assumed to have a symmetrical distribution with either a Gaussian or a Lorentzian shape or a combination of the two (26). The exact shape of the frequency distribution will influence how the susceptibility effect scales with contrast agent concentration in tissue and whether the magnitude of the susceptibility induced relaxation rate is time dependent or time independent. In the case of a Gaussian lineshape, the intravoxel frequency distribution can be expressed as  −ω2 p (ω ) ∝ exp   2σ p 2 .    . [20]. where the linewidth is given by ν1/2 = 2ln(2)σp. From the discussion above (Eq. [17]) it would seem that ν1/2 scales with ∆Mp, and hence with the contrast agent concentration in tissue. We did indeed show in Paper I that ν1/2 increased linearly with contrast agent concentration in fully oxygenated blood. However, in spite of the linear relationship between ν1/2 and ∆Mp, the corresponding relationship between ∆R2* and ∆Mp is not linear if the intravoxel field distribution is Gaussian. From Eq. [15] and using the relationship σp =k∆Mp where k is a constant the signal attenuation is given by ∞  ω2   exp (− iωTE )dω = S 0 exp − k 2γ 2 ∆M p 2TE 2 S (TE ) = S 0 ∫ exp  2   −∞  (k∆M p ) . (. 33. ). [21].

(48) Atle Bjørnerud. Defining the relaxation rate according to Eq. [19] we then get ∆R2 = k 2γ 2 ∆M p TE *. 2. [22]. For a Gaussian field distribution, ∆R2* therefore scales linearly with TE and quadratically with the magnetisation, and hence the concentration of the contrast agent in tissue. The Gaussian field distribution in blood with a substantial intraextracellular ∆M (due to deoxyhemoglobin or contrast agent in plasma) was confirmed in Paper I and the quadratic dependence of ∆R2* in blood on contrast agent concentration was confirmed in Papers I and II. Eq. [22] also explains the observed initial reduction in R2* in deoxygenated blood with increasing plasma concentration of NC100150 Injection. When the increase in plasma magnetisation due to NC100150 Injection equals the intracellular magnetisation due to deoxyhemoglobin, ∆M and hence ∆R2* tend to zero. At this concentration, the susceptibility effect is effectively cancelled and only dipolar relaxation effects of the agent remain in blood. Under these conditions, the corresponding NMR lineshape was found to be purely Lorentzian (Paper I), in agreement with theory for a random distribution of point dipoles (36). A Lorentzian field distribution can be expressed as  σp  p (ω ) ∝  2  2 σ p + ω . [23]. Taking the Fourier transform according to Eq. [21] but using the Lorentzian expression for the field distribution term we then get S = S 0 exp (− γσTE ). [24]. and the relaxation rate is thus given by ∆R2 = γσ *. [25]. 34.

(49) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. In the case of a Lorentzian distribution, the relaxation rate is therefore independent of TE and proportional to the linewidth of the field distribution. The linewidth is also here proportional to contrast agent concentration C and ∆R2* therefore increases linearly with C. Many investigators have estimated the susceptibility effect in vascularised tissues by modelling the capillaries as cylinders of random orientation. The transverse relaxation has been determined analytically in the special situation of static dephasing (34,37). Kiselev and Posse recently extended the theory to include the effects of water diffusion (38,39) on transverse relaxation in tissue. These theoretical models generally predict the transverse relaxation to follow a mixed Gaussian and Lorentzian decay curve where the relative contribution from the two distributions depend on the magnitude of the product TE.δωp. Statistical methods based on Monte Carlo simulations have also been successfully employed to simulate the susceptibility effect for different tissue systems (26,28,30,40-42). Most of this work has focussed on the susceptibility effects due to deoxyhemoglobin in the physiological range of oxygen tensions where the maximum change in blood magnetisation is much smaller than what is anticipate from clinical doses of the iron oxide nanoparticle investigated here. Kiselev has however, in a recent article concluded that susceptibility-induced relaxation is governed by the same physiological and microanatomical parameters whether the effect is due to deoxyhemoglobin or due to a bolus of contrast agent (39). 2.3.2 Water exchange effects In addition to the influence of compartmentalisation on the transverse relaxation rate, compartmentalisation of the contrast agent in tissue can also affect the longitudinal relaxation rate by restricting water access to the contrast agent site. The dipolar relaxivity defined in Eq. [11] assumes that all water protons in the solution have equal and unrestricted access to the contrast agent on a time-scale equal to the T1 relaxation time of the medium. This condition is. 35.

(50) Atle Bjørnerud. referred to as ‘fast exchange’ (43) and the requirement for fast exchange can be expressed in term of a correlation time τ, so that 1 1 2 >> R1 − R1 τ. [26]. where 1/τ is the rate of water exchange between the compartments with longitudinal relaxation rates R11 and R12, respectively. Considering the water exchange between the intravascular compartment and extravascular compartment after contrast administration the requirement for fast exchange then becomes 1 0 >> R1i + r1C p − R1e τ. [27]. where Cp is the concentration of the contrast agent in plasma, r 1 is the T1relaxivity of the agent, R1i0 is the intravascular relaxation rate prior to contrast administration and R1e is the extravascular relaxation rate. The iron oxide nanoparticle NC100150 Injection has a T1-relaxivity at 1.5 T of about 14 s -1mM-1 (see section 5.2.2). At a contrast agent concentration in plasma of 1 mM, fast exchange between the intravascular and extravascular compartments therefore require that 1/τ>>14 s -1 (assuming that R1i0 ≈ R1e). The proton exchange rate between different tissue compartments has been measured by many investigators. Intra- extracellular water exchange in blood has been reported to be of the order of 60 s -1 – 100 s -1 (43,44) whereas intra-extravascular exchange has been measured to be about an order of magnitude slower in many tissues (43,45-47), although no values have been specifically reported for in vivo water exchange rates in the renal cortex or myocardium. Water exchange rates in these tissues were investigated in the present work. For applications of NC100150 Injection at plasma contrast agent concentrations in the range 0-2 mM Fe it is therefore expected that the intraextracellular water exchange in blood remains fast whereas the intra- extra vascular exchange can no longer be assumed to be fast at higher contrast agent concentrations. Under intermediate and slow water exchange conditions the correlation between R1 and Cp becomes 36.

(51) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. non-linear and in the slow exchange extreme when 1/τ << r 1Cp the observed tissue R1 reaches a plateau and is independent on further increase in Cp. The effect of limited water exchange on proton relaxation can be addressed by addition of a two-site water exchange term to the Bloch equations describing the rate of change of the magnetisation between the intra- and extracellular compartments (45,48) M − Mi d M i = 0i − ki M i + ke M e dt T1i. [28]. d M − Me M e = 0e + ki M i − k e M e dt T1e. where 1/T1e is the extravascular relaxation rate, 1/T1i is the intravascular exchange rate, M0 is the equilibrium magnetisation and ki and ke are the firstorder exchange rates between the two compartments and are given by PS BV PS ke = λ − BV ki =. [29]. where PS is the permeability surface area product, BV is the tissue blood volume and λ is the ratio of proton spin densities of tissue and blood. The exchange rate 1/τ introduced in Eq. [26] is then the sum of the two rate constants ki + ke so that 1/ki (τi) and 1/ke (τe) describe the average lifetime of the spins within the intravascular and extravascular compartments, respectively. The general solution to Eq. [28] is described by a biexponential function of the form (45) M (t ) = M 0 + c1 ⋅ exp( −u1t ) + c 2 ⋅ exp( −u 2t ). [30]. where c 1,c 2 and u1,u2 are given by c1 =. 2M 0 u1 − u2.   R k + R1i ke ⋅  u 2 −  1e i  k e + ki .    . [31] 37.

(52) Atle Bjørnerud   R k + R1i ke    ⋅  u1 −  1e i  k + k  e i  . c2 =. − 2M 0 u1 − u 2. u1 =. 1 (a + b) 2. [33]. u2 =. 1 (a − b ) 2. [34]. [32]. a = R1 i + k e + R1e + ki. b=. [35]. (R1i + k e − R1e − k e )2 + 4 ⋅ k i k e. [36]. and R1i, R1e are intra- and extravascular relaxation rates, respectively, ke = 1/τe, ki = 1/τi and kt = ki+ke. It can be shown that, for small blood volumes or in the fast exchange regime Eq. [30] is well approximated by a single exponential relaxation curve (45) following an inversion (180°) RF-pulse M m (t ) = M 0 − 2 ⋅ M 0 exp( −R1t ). [37]. where R1 is the tissue relaxation rate which is then given by R1 ≈ u2 =. 1 (R1i + k e + R1e + ki ) − 1 2 2. ( (R. 1i. + k i − R1e − k e ) + 4 ⋅ ki k e 2. ). [38]. The correlation between R1 (R1 in tissue) and R1i (R1 in blood) according to Eq. [38] is shown in Fig. 4 at different water exchange rates ki, using a relative blood volume of 10% and R1e=1s-1. From Eq. [29] the corresponding values of ke are then given by ki.BV/(λ-BV). R1 asymptotically approaches a maximum value given by: R1max ≈ R1e + ke when R1i-R1e >> ki; i.e. in the slow exchange limit.. 38.

(53) Relaxation Properties of a Particulate Iron Oxide MR Contrast Agent. Eq. [37] describes the recovery of the magnetisation following a single inversion (180o) pulse and the corresponding value of tissue R1 as a function R1i can then be determined using an inversion recovery sequence where the signal. ki=100 s -1. R 1 in tissue (1/s). 3.3. 2.8. 2.3. 1.8. ki=10 s -1. 1.3. ki=3 s -1 ki=1 s -1. 0.8 1. 6. 11. 16. 21. 26. 31. R1 in blood (1/s). Figure 4. R1 in tissue as a function of R1 in blood at different intra- extravascular water exchange rates (k i) with a blood volume of 10%.. intensity as a function of the inversion time, TI, between the 180o pulse and the signal readout is given by SI (TI ) = K (1 − 2 exp( −TI ⋅ R1 ) ). [39]. where K is a constant. By applying multiple small flip-angle excitation pulses which are individually phase encoded at intervals TI following a single inversion pulse, the magnetisation curve can be effectively sampled with a short overall scan-time. One implementation of such a sequence, referred to as a Look-Locker sequence was used in the present work to quantify R1 (49). From the measured R1 response in tissue as a function of R1i, the values of PS, BV and R1e can thus be estimated using a non-linear least squares fitting routine, provided the water partition. 39.

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