Influence of molecular parameters and increasing magnetic field strength on relaxivity of gadolinium- and manganese-based T1 contrast agents

Abstract

Simulations were performed to understand the relative contributions of molecular parameters to longitudinal (r₁) and transverse (r₂) relaxivity as a function of field, and to obtain theoretical relaxivity maxima over a range of fields to appreciate what relaxivities can be achieved experimentally. The field dependent relaxivity of a panel of gadolinium and manganese complexes with different molecular parameters: water exchange rates, rotational correlation times, hydration state, etc were measured to confirm that measured relaxivities were consistent with theory. The design tenets previously stressed for optimizing r₁ at low fields (very slow rotational motion; chelate immobilized by protein binding; optimized water exchange rate) do not apply at higher fields. At 1.5T and higher fields, an intermediate rotational correlation time is desired (0.5 – 4 ns), while water exchange rate is not as critical to achieving a high r₁. For targeted applications it is recommended to tether a multimer of metal chelates to a protein-targeting group via a long flexible linker to decouple the slow motion of the protein from the water(s) bound to the metal ions. Per ion relaxivities of 80, 45, and 18 mM⁻¹s⁻¹ at 1.5, 3, and 9.4T respectively are feasible for Gd³⁺ and Mn²⁺ complexes.

Introduction

MR imaging is increasingly moving to higher fields. There is now a large installed base of 3T scanners that are used clinically. 7T whole body scanners are available from the major MRI equipment manufacturers and there are a number installed worldwide. Recently human imaging at 9.4T has been reported (1). Higher fields bring greater signal:noise (SNR) and its attendant benefits of higher spatial resolution and/or reduced acquisition times.

Contrast agents are widely used in clinical MRI, with about a third of clinical scans being contrast enhanced (2,3). Clinical contrast agent usage is dominated by gadolinium-based T₁-contrast agents which increase signal intensity on T₁-weighted images, shorten acquisition times, and improve diagnostic confidence. Contrast agents are characterized by their relaxivity (r₁ or r₂) which is defined as the change in relaxation rate (R_1,2 = 1/T_1,2 in units of s⁻¹) of solvent water protons upon addition of contrast agent, normalized to the concentration of contrast agent ([CA] in units of mM), equation 1:

$$r_i=\frac{\Delta (1∕T_1)}{\left[CA\right]};i=1,2$$ [1]

The longitudinal relaxation times (T₁) of tissue and blood increase with increasing field (4). For a contrast agent with equivalent relaxivity at two fields, the T₁ change would be greater at the higher field because the inherent tissue R₁ is slower at higher field. This is true of commercial extracellular fluid agents like Gd-DTPA whose relaxivity is fairly independent of field (5). However relaxivity is not a constant, but depends on external parameters such as applied field and temperature, and on molecular parameters such as the hydration state of the molecule and the molecular size. These molecular parameters can be tuned and optimized to create contrast agents with much higher relaxivities than conventional Gd-DTPA (6). High relaxivity contrast agents can be used at lower doses, or can be used in molecular imaging to detect low concentration targets.

There is an ongoing need to create new contrast agents. Molecular imaging agents bring additional specificity as a result of targeting (7-9). Recently, the incidence of nephrogenic systemic fibrosis (NSF) has highlighted the need for safe agents where the metal ion is completely eliminated from the body (10-13). While there are other contrast mechanisms available (T₂*, chemical exchange saturation transfer, hyperpolarized agents), T₁ relaxation has many salutary effects. For instance, T₁ agents provide positive image contrast, can shorten acquisition times, are shelf stable, and have a proven track record in the clinic.

It is well known that T₁ relaxivity typically decreases with increasing at high fields. Small, fast tumbling molecules like Gd-DTPA show a modest decrease in r₁ with field (5), while slow tumbling molecules like MS-325 bound to serum albumin have high relaxivity that peaks between 0.5-1.0T and then shows a sharp drop in r₁ with field (5,6). The strategy of markedly slowing rotational diffusion results in large gains in r₁ at 1.5T but at high fields this strategy is much less effective. As new T₁ agents are prepared, it would be valuable to design agents that have excellent relaxation properties over a broad range of imaging field strengths in order to take advantage of current 1.5T scanners and the increasing number of higher field scanners. This has been recognized in the recent work by Livramento et al. who have described new compounds with improved r₁ at high fields (14-18).

Transverse relaxivity, r₂, is static or increases with increasing field strength resulting in an increasing r₂/r₁ ratio with increasing field strength. Like r₁, transverse relaxivity is dependent on a range of molecular parameters. In addition, for paramagnetic contrast agents like those based on gadolinium or manganese, the magnetization of the complex increases linearly with field and this results in greater susceptibility contrast at higher fields. Since r₁ is decreasing with field but r₂ is not, increasing the dose to offset lower r₁ may not be effective at high field because of T₂* effects at high doses. In molecular imaging, high doses may also result in target saturation where the amount of contrast achieved at the targeted is limited. New T₁ reagents therefore should work effectively in high field imagers and provide high relaxivity over a range of field strengths and not be limited to 1.5T and lower fields.

The aims of this work are twofold. The first is to understand the relative contributions of the various molecular parameters to r₁ and r₂ as a function of field to determine what molecular factors are key in the design of high field, high relaxivity contrast agents. The second aim is to obtain theoretical relaxivity maxima over a range of fields to appreciate what can and cannot be achieved experimentally. Relaxivities greater than 100 mM⁻¹s⁻¹ per ion have been posited in the literature (2,19) and may be achieved at low fields (0.5T) but are such high values theoretically feasible at 3T and higher? If not, what represents “high relaxivity” at high fields? Here, we simulated the effect of different molecular parameters, including internal and anisotropic rotation, on the relaxivity of gadolinium and manganese complexes. We also measured field dependent relaxivities of a panel of gadolinium and manganese complexes with different water exchange rates, rotational correlation times, etc to ascertain if the measurements at high fields were consistent with theory.

Results

Theory

Solvation spheres

The metal complex can be viewed as having separate coordination spheres. The inner-sphere (IS) consists of ligands directly bonded to the metal ion. For contrast agents like GdDOTA, Figure 1, the inner-sphere is the DOTA ligand and a water molecule. The second coordination sphere (SS) is less well defined and consists of water molecules hydrogen bonded to the metal complex and possibly counterions. Beyond the second-sphere there is less organized structure and water freely diffuses, and this is referred to as the outer-sphere (OS). We define the 2^nd sphere in terms of water residency time, τ_m’, which must be longer than the diffusion correlation time of water. Relaxivity can be factored into contributions arising from water in each coordination sphere, eqn 2.

$$r_i^{obs}=r_i^{IS}+r_i^{SS}+r_i^{OS};i=1,2$$ [2]

Figure 1.

Factors influencing solvent water relaxation. The metal complex has an inner-sphere (IS) of nitrogen and oxygen atoms from the DOTA ligand and a coordinated water molecule. There is a distinct 2^nd hydration sphere (SS) with Gd-H distance r’, and water molecules from both spheres undergo exchange with bulk water at rates 1/τ_m and 1/τ_m^’ for 1^st and 2^nd sphere exchange

Inner-sphere relaxivity

The effect of chemical exchange on relaxation has been dealt with in terms of the Bloch equations by McConnell (20) and applied to the problem of water exchange at paramagnetic metal ions by Swift and Connick (21). Relaxation of bulk water arising from exchange of water molecules associated with a paramagnetic ion is given by:

$$R_{1p}=R_1-R_1^0=\frac{P_m}{T_{1m}+{\tau }_m}$$ [3]

$$R_{2p}=R_2-R_2^0=P_m\frac{1}{{\tau }_m}\lfloor \frac{R_{2m}({\tau }_m^{-1}+R_{2m})+\Delta {\omega }_m^2}{{({\tau }_m^{-1}+R_{2m})}^2+\Delta {\omega }_m^2}\rfloor$$ [4]

where R_i is the observed relaxation rate, R_i⁰ is the rate in the absence of paramagnetic species, R_im is the relaxation rate of the water bound to the metal ion (i=1,2), τ_m is the lifetime of the water coordinated to the metal ion (its reciprocal is the water exchange rate k_ex = 1/τ_m), Δω_m is the chemical shift of the coordinated water, and P_m is the mole fraction of water coordinated to the metal ion. This can be expressed in terms of the hydration number, q, which is the number of water molecules bound to the metal ion (M):

$$P_m=\frac{q\left[M\right]}{\left[H_{2}O\right]}$$ [5]

where square brackets denote concentration. For ions such as Gd³⁺ and Mn²⁺, the chemical shift of the bound water is small at most fields compared to its transverse relaxation rate and the Δω_m term can be neglected. Combining equations 1-4 and neglecting Δω_m, one arrives at expressions for two site exchange in terms of relaxivity, where the superscript “IS” is used to denote the relaxivity due to the inner-sphere (metal bound) water molecules:

$$r_i^{IS}=\frac{q∕\left[H_{2}O\right]}{T_{im}+{\tau }_m};i=1,2$$ [6]

where [H₂O] is the water concentration in millimolar (55,600 mM).

Paramagnetic relaxation is fairly well understood. There are three mechanisms that contribute: dipole-dipole (DD) coupling between the paramagnetic ion and the hydrogen of water, scalar (SC) or contact relaxation, and Curie spin (CS) relaxation. The first two mechanisms were described by Solomon (22) and Bloembergen (23). Curie spin relaxation, first described by Gueron (24), results from modulation of the permanent magnetic moment and can become important at high fields as the complex becomes increasingly magnetized. At the fields that we are concerned with (1.5T and higher), only dipolar relaxation contributes appreciably to T_1m for Gd(III) or Mn(II) induced nuclear relaxation whereas all three mechanisms can contribute to T_2m, i.e. 1/T_2m = 1/T₂^DD +1/T₂^SC+1/T₂^CS. The relevant expressions for 1.5T and above are:

$$\frac{1}{T_1^{DD}}=\frac{2}{15}\left(\frac{{\mu }_0}{4\pi }\right)\frac{{\gamma }_H^2{g}_e^2{\mu }_B^{2}S(S+1)}{r_{MH}^6}\lfloor \frac{3{\tau }_c}{1+{\omega }_H^2{\tau }_c^2}\rfloor$$ [7]

$$\frac{1}{T_2^{DD}}=\frac{1}{15}\left(\frac{{\mu }_0}{4\pi }\right)\frac{{\gamma }_H^2{g}_e^2{\mu }_B^{2}S(S+1)}{r_{MH}^6}\lfloor 4{\tau }_c+\frac{3{\tau }_c}{1+{\omega }_H^2{\tau }_c^2}\rfloor$$ [8]

$$\frac{1}{T_2^{SC}}=\frac{1}{3}\left(\frac{A}{\hslash }\right)S(S+1)\left[{\tau }_{SC}\right]$$ [9]

$$\frac{1}{T_2^{CS}}=\frac{1}{5}{\left(\frac{{\mu }_0}{4\pi }\right)}^2\frac{{\omega }_H^2{g}_e^4{\mu }_B^4{S}^2{(S+1)}^2}{{\left(3k_{B}T\right)}^2{r}_{MH}^6}\left[4{\tau }_{CS}\right]$$ [10]

Here, S is the spin quantum number, r_MH is the ion-proton distance, ω_H is the Larmor frequency of the proton (rad/s), ω_S is the Larmor frequency of the electron, γ_H is the proton magnetogyric ratio, g_e is the electronic g-factor (g_e = 2 for Gd(III) and Mn(II)), μ_B is the Bohr magneton, μ₀ is the permittivity of vacuum, A/ħ is the hyperfine coupling constant between the ion and the hydrogen nucleus, k_B is the Boltzmann constant, and T is the absolute temperature.

The correlation time for each relaxation mechanism can have contributions from different processes: rotational motion (1/τ_R), longitudinal relaxation of the unpaired electrons (1/T_1e), and water exchange (1/τ_m). Dipole-dipole relaxation can be modulated by either of these three, but at high fields electronic relaxation is slow relative to rotational motion and T_1e does not contribute as a correlation time. By definition, scalar relaxation is independent of rotation, and Curie spin relaxation is independent of electronic relaxation:

$$\frac{1}{{\tau }_c}=\frac{1}{{\tau }_R}+\frac{1}{{\tau }_m}$$ [11]

$$\frac{1}{{\tau }_{sc}}=\frac{1}{{\tau }_m}+\frac{1}{T_{1e}}$$ [12]

$$\frac{1}{{\tau }_{cs}}=\frac{1}{{\tau }_R}+\frac{1}{{\tau }_m}$$ [13]

These simplified expressions differ from the more general forms that cover low fields. There are several dispersive terms with 1/ω_S²τ_c² dependence that are vanishingly small at 1.5T and these have been omitted for clarity. In addition electronic relaxation is slow at high fields. Values of T_1e directly measured for Gd³⁺ complexes at 0.34T were in the 1 – 5 ns range (25,26) and these times increase with increasing field. At very low fields T_1e can be quite short and under conditions where 1/T_1e is fast relative to rotational reorientation (slow motion regime) the description of electronic relaxation is complex and the simple analytical expressions of Bloembergen and Morgan do not hold (23). However at the fields we are considering (≥1.5T), the static zero field splitting of the complexes (<0.05T) is much less than the Zeeman energy and T_1e >> τ_R. Although in principle 1/T_1e is multiexponential, Belorizky and Fries showed that 1/T_1e could be well approximated by a simple analytical expression (27). As a result, the usual modified Solomon-Bloembergen-Morgan (MSBM) equations are applied here. In a full analysis of the nuclear magnetic relaxation dispersion (NMRD) profile of MS-325 bound to albumin we found that high field relaxation was adequately described by MSBM while the description of the entire curve required application of the slow motion theory.

Here we describe the field dependence of electronic relaxation for Mn²⁺ and Gd³⁺ by:

$$\frac{1}{{\mathrm{T}}_{1\mathrm{e}}}=\frac{{\Delta }^2[4S(S+1)-3]}{25}\left[\frac{{\tau }_v}{1+{\omega }_s^2{\tau }_v^2}+\frac{4{\tau }_v}{1+4{\omega }_s^2{\tau }_v^2}\right]$$ [14]

Electronic relaxation for Mn²⁺ and Gd³⁺ in solution at high fields is a result of transient distortions of the compound that result in a modulation of the crystal field interaction parameters (23), also referred to as zero-field splitting (ZFS). The magnitude of this transient ZFS is given by Δ² and this is related to crystal field terms D and E by Δ² = (2/3)D² + 2E². The correlation time for this modulation is denoted τ_v and is on the order of picoseconds.

Second- and outer-sphere relaxivity

For the water in the second-sphere, relaxivity can be described by the same mechanisms as for inner-sphere water. We denote second-sphere parameters with a prime:

$$r_i^{SS}=\frac{q^{\prime }∕\left[H_{2}O\right]}{T_{im}^{\prime }+{\tau }_m^{\prime }};i=1,2$$ [15]

Strictly, each water should have its own relaxation time and residency time, but we assume here that all waters in a given coordination sphere behave the same. The ion-hydrogen distance r’ is longer and the residency time τ_m’ is shorter for waters in the second-sphere.

The outer-sphere contribution to relaxivity has been described by Freed (28,29). This is dominated by the diffusion time of water and a distance of closest approach. This is not something that can be readily changed by modifying the contrast agent. For the range of fields considered here, r₁^OS should be constant. We assume a value of 2 mM⁻¹s⁻¹ for r₁^OS based on literature values (30).

Effect of internal motion

For multimeric contrast agents or protein-targeted agents, rotation about the ion-hydrogen vector may not be well approximated by an isotropic model. Most targeted agents are bifunctional molecules that contain a moiety that binds to a protein linked to a relaxation enhancing moiety. If there is flexibility between the targeting moiety and the relaxation moiety then the motion that the coordinated water proton “sees” will be a function of the slow global motion of the protein and the faster internal motion of relaxation moiety (metal part) (31). Similarly for metal complexes attached to the surface of a dendrimer, the rotational correlation time at a given field will have contributions from the slow overall motion of the dendrimer as well as from faster local motions because of internal flexibility (32,33). To look at the effects of internal motion on relaxivity we used a model-free approach originally described by Lipari and Szabo (34). They showed that for many complicated models of motion, the spectral density function could be approximated as:

$$J\left(\omega \right)=\frac{F^{2}3{\tau }_g}{(1+{\omega }_H^2{\tau }_g^2)}+\frac{(1-F^2)3{\tau }_l}{(1+{\omega }_H^2{\tau }_l^2)};\frac{1}{{\tau }_l}=\frac{1}{{\tau }_g}+\frac{1}{{\tau }_f}$$ [16]

for dipolar longitudinal relaxation, where F represents an order parameter (usually denoted S but here F to not to confuse with spin number) that can vary between 0 and 1, τ_g is the global correlation time (which is the same as τ_c above for DD relaxation or τ_cs for CS relaxtion) and τ_l is a local correlation time that takes into account fast local motion (τ_f). When F² = 1, motion is isotropic and the system is governed by the global relaxation time. When F² = 0, relaxation is governed by the fast local motion. This approach has been successfully applied to explain the field dependent relaxivity of certain contrast agents (31,35-38).

Simulations

Relaxivity due to inner-sphere water

We simulated relaxivity as a function of external field (B₀ = ω_H/γ_H), rotational correlation time, and water residency time for a water in the inner-sphere, i.e. directly bound to the metal ion, of a Gd³⁺ complex and a Mn²⁺ complex. For Gd³⁺, the metal ion – water hydrogen distance was set to 3.1Å and the isotropic hyperfine constant was set to 0.1 MHz based on previous EPR studies (39-43). For Mn we use a distance of 2.9Å based on the Mn-O_water bond length determined from X-ray crystallography (44) and assuming a similar orientation of the bound water as in the Gd³⁺ case (41). A/h for Mn²⁺ was set to 1.0 MHz, the value reported for the Mn²⁺ aqua ion (23). We used previously determined values of Δ² and τ_v for MS-325 and MnL1 for the simulations (35,38,45). Electronic relaxation was slow with respect to rotational diffusion for the field strengths that we are concerned with here (1.5 to 15T).

Effect of rotational dynamics on relaxivity due to inner-sphere water

The field dependent relaxivity for the inner-sphere water of a Gd complex with a water exchange rate similar to GdDTPA or GdDOTA (τ_m ~100 ns at 37 °C) is plotted in Figure 2 for 3 different isotropic rotational correlation times: 0.1, 1, and 10 ns. The short correlation time would be similar to a small metal complex like GdDTPA, while the long correlation time would reflect the protein-bound case like MS-325 bound to albumin. Protein binding (slow rotation, long τ_R) is an effective strategy at low field for increasing r₁. However by 3T, this strategy offers diminishing returns and the r₂/r₁ ratio balloons with increasing field strength. This suggests that increasing the dose of a slow rotation contrast agent to decrease T₁ has less effect at high field because of the large r₂ effect. The fast tumbling complex exhibits a relatively field independent, but low r₁ relaxivity. However by 7T, the r₁ relaxivity of the fast tumbling case is now higher than the slow tumbling case. The intermediate motion regime (1 ns) also shows a fall off in r₁ with field but this is less dramatic. The intermediate case offers the best combination of high r₁ and low r₂/r₁ over a wide range of fields. For r₂ the field dependence is rather flat and is proportional to the rotational correlation time. At very high fields, r₂ starts to increase and this is due to an increasing contribution from the Δω_m term in equation 3. Although this shift is relatively small, above 12 T it starts to approach the magnitude of R_2m.

Figure 2.

Effect of rotation on r₁ (A), r₂ (B), or the ratio r₂/r₁ (C) as a function of field for the inner-sphere water of a Gd³⁺ complex with a water residency time 100 ns. τ_R = 0.1 ns (•••), 1.0 ns (---), or 10 ns (—). Inset in A is a magnified view.

For Mn²⁺, we observe a similar effect for r₁ as a function of field and rotational correlation time, Figure 3a. Again, slow tumbling is a potent strategy at low fields, but not at high fields. The intermediate correlation time provides better high field relaxivity. For r₂ there are some differences. Because the hyperfine interaction between the metal ion and the water proton is about an order of magnitude higher for Mn²⁺ than for Gd³⁺, there is a significant scalar contribution to r₂ for Mn²⁺ complexes. This contribution is modulated by a correlation time that has contributions from τ_m and T_1e. T_1e increases with the square of the magnetic field and does not contribute significantly at high fields. In Figure 3b and 3c, the effect of the water residency time is shown for τ_m = 5 ns or 100 ns. For Mn²⁺ compounds, we see that r₂ increases with increasing τ_R like for Gd³⁺ but r₂ also increases with increasing τ_m.

Figure 3.

Effect of rotation on r₁ (A), r₂ (B and C) as a function of field for the inner-sphere water of a Mn²⁺ complex. Water residency times (τ_m) of 5 or 100 ns do not affect the r₁ result, but r₂ depends on τ_m because of a scalar contribution to r₂: τ_m = 5 ns (B) or 100 ns (C). τ_R = 0.1 ns (•••), 1.0 ns (---), or 10 ns (—). Inset in A is a magnified view.

Effect of water exchange dynamics on relaxivity due to inner-sphere water

Relaxivity depends inversely on the water residency time, τ_m, and the relaxation time of the bound water, T_1,2m. Obviously if τ_m becomes too long, there is little/no exchange of the relaxed water with the bulk and relaxivity will be limited. If τ_m becomes less than the rotational correlation time, then it starts to modulate the interaction energy, i.e. it becomes τ_c. A very short τ_m results in an increased T_1m (relaxation of the bound water is less efficient) and relaxivity suffers. There is some optimum range, then for τ_m.

It is apparent that there is an optimum correlation time for r₁ at each field. At high fields τ_c should be about 1/ω_H. We simulated the effect of water exchange (k_exchange = 1/τ_m) on the Gd³⁺ relaxivity at 3 field strengths: 0.47T, 3T, and 9.4T. We chose τ_R values that would give very high relaxivities for each field strength, 20, 1.5, and 0.5 ns respectively. The effect of water exchange on relaxivity is shown in Figure 4. Figure 4 demonstrates again, that maximum T₁ relaxivity falls off with increasing field strength and that there is an ideal range for water exchange kinetics. However this ideal range of water exchange rates is much broader at higher fields. Similar results are obtained for Mn²⁺ with the additional effect of τ_m on r₂ as shown in Figure 3.

Figure 4.

Effect of water residency time τ_m (ns) for an inner-sphere water on r₁ (—) and r₂ (---) under optimal rotational conditions at 0.47T (A, τ_R = 20 ns), 3T (B, τ_R = 1.5 ns), and 9.4T (C, τ_R = 0.5 ns). The optimal τ_m range increases as field increases.

In order to better appreciate the interplay between field strength, water exchange and rotational dynamics, we looked at τ_m vs τ_R for T₁ relaxivity at 4 different field strengths. In Figure 5, relaxivity is presented as a contour plot with each color representing 20% increments of the maximum relaxivity at that given field strength. Figure 5 reveals that while it is theoretically possible to achieve very high relaxivity at low fields, this is difficult to achieve because it requires a narrow combination of correlation times. At 0.47T the largest area is represented by the lowest quintile of relaxivity. Conversely, at higher field strengths the highest quintile of relaxivity can be achieved with a wider range of water exchange rates and rotational dynamics. At higher fields the values of τ_R giving rise to the highest relaxivity become increasingly shorter.

Figure 5.

Interplay between water residency time (τ_m) and rotational motion (τ_R) on maximum achievable r₁ or an inner-sphere water. Higher relaxivities can be achieved at lower fields, but at higher fields there is much larger dynamics space to achieve the top 20% of attainable r₁.

Effect of internal motion on relaxivity due to inner-sphere water

It is apparent from equation 16 that internal motion will reduce relaxivity. The best scenario is either when there is no internal motion and rotation is isotropic, or when the local motion is completely decoupled from the slow motion (F² = 1 or 0). This is illustrated in Figure 6 for relaxivity at 3T. At 3T, isotropic rotation with τ_R = 1.5 ns would lead to a high relaxivity. For a slow tumbling system (τ_global = 10 ns) with fast internal motion (τ_local = 0.1 ns), relaxivity is poor at all combinations of motion; slow and fast motion do not equal intermediate motion. When the internal motion is slower (τ_local = 1 ns, Figure 6b), then relaxivity is higher, but the relaxivity is highest when this internal motion is completely decoupled (F² = 0) from the slower global motion.

Figure 6.

Effect of internal motion on relaxivity due to one inner-sphere water molecule at 3T, τ_m =100 ns. A) Simulation for global correlation time, τ_global = 10 ns and local correlation time, τ_local = 0.1 ns. B) τ_global = 10 ns, τ_local =1 ns. r₁ is always highest at either F² = 0 or 1.

Effect of second-sphere hydration on relaxivity

Waters in the second-sphere typically have very short residency times (τ_m’) which limits their probability of being relaxed. However there is good evidence that τ_m’ can be increased through hydrogen bonding. For instance GdDOTP (tetraphosponate analog of DOTA) has similar relaxivity to GdDOTA even though the former has no inner-sphere water (46). We showed that a q=0 GdDOTP-fatty acid derivative could have very high relaxivity (40 mM⁻¹s⁻¹ at 0.47T) when bound to serum albumin (47). This is likely due to strong hydrogen bonding of 2^nd-sphere water to the anionic phosphonate oxygens. Relaxometry showed that there were 2^nd-sphere exchangeable proton(s) with a lifetime of 1 ns (47). This seems to be general to phosphonate complexes (30,48-50). For example replacing one acetate on DOTA with a phosphonate still results in a q=1 complex, but the phosphonate has a 28% higher relaxivity which can only be attributed to a 2^nd-sphere effect.

Using the q’/r’_GdH value obtained previously, we simulated 2^nd-sphere relaxivity for Gd³⁺ complexes using different correlation times for rotation and for the lifetime of the water in the 2^nd-sphere. Some of these are shown in Figure 7. As may be expected, the relaxivity effect from protons in the 2^nd-sphere can be significant if the residency time is relatively long, and if rotational motion is relatively slow. The effect is quite meaningful at high fields where shorter correlation times are preferred.

Figure 7.

Second-sphere relaxivities, r₁ (A) and r₂ (B) calculated for one water with r’_GdH = 3.5 Å at different water residency times and rotational correlation times. τ_R = 10 ns, τ_m’ = 0.1 ns (•••); τ_R = 1 ns, τ_m’ = 1 ns (---); or τ_R = 10 ns, τ_m’ = 1 ns (—).

Effect of hydration on relaxivity

The inner-sphere contribution to relaxivity scales linearly with the number of water molecules bound. The simulations in Figures 2-4 would result in double the relaxivity if there were two inner-sphere waters. Similarly for the 2^nd-sphere effect, more long-lived protons at an equivalent distance to the ion will increase the relaxivity.

Experimental Relaxivities

Field dependence on inner-sphere relaxivity

The compounds studied in this work are shown in Figure 8. These compounds provide a range of rotational correlation times and the correlation time can be altered further by protein binding. Relaxivities for these compounds determined at ambient temperature (21°C) and 3 field strengths are listed in Table 1.

Figure 8.

Compounds studied in this work.

Table 1.

Relaxivities (r₁, r₂) per metal ion determined at 1.4, 4.7, and 9.4T at 21 °C with units mM⁻¹s⁻¹ in either phosphate (10 mM) buffered saline (PBS) pH 7.4 or PBS+4.5% w/v human serum albumin (HSA), or 10 mg/mL human fibrin. Error estimated at ±10%.

Compound	r1 1.4T	r1 4.7T	r1 9.4T	r2 1.4T	r2 4.7T	r2 9.4T
MS-325	8.30	7.21	5.14	9.27	14.0	15.7
MS-325+HSA	24.3	11.20	7.16	55.8	93.6	105
GdDTPA-BSA	10.4	5.99	3.79	13.6	13.6	13.9
EP-2104R	15.6	9.43	6.39	19.3	14.2	13.0
EP-2104R+fibrin	16.3	10.0	5.94	23.5	32.8	36.7
MnL1	5.32	4.46	4.05	8.37	7.3	7.00
MnL1+HSA	27.2	5.78	3.48	96.7	80.6	94.6
MnCl2	6.63	5.92	5.14	60.2	110	117

Discussion

Comparison of measured relaxivities with simulations

The measured relaxivities and their field dependencies are in the range one would expect on the basis of what is known about the correlation times of these molecules. For MS-325 bound to the protein serum albumin, it was previously shown (45) that r₁ reaches a maximum between 0.5 and 1T and then declines, while r₂ increases above 1T. At much higher fields (4.7 and 9.4T), r₁ continues to decrease while r₂ is large. In the absence of protein, MS-325 has a τ_R of ~0.18 ns at room temperature. Its relaxivity, both r₁ and r₂, is rather field independent as predicted by theory. At 9.4T the T₁ relaxivity of MS-325 is about the same with or without albumin, but r₂ is an order of magnitude higher in the presence of albumin. The protein-binding strategy which works well at low field offers no benefit for improving r₁ at 9.4T.

We also looked at Gd-DTPA-BSA which has the Gd chelated by a diethylenetriaminetetraacetate-monoamide that is covalently attached to albumin. The monoamide complex is known to have about 3-fold slower water exchange rate than the diethylenetriaminepentaacetate (DTPA) chelator that is used in MS-325 (51). This slower water exchange rate mutes the r₂ effect. The slow exchange also limits r₁ but this is more important at low fields, see Figure 5. At 1.4T r₁ for Gd-DTPA-BSA is much lower than MS-325/HSA but this difference is reduced as the field strength is increased.

The complex MnL1 is a manganese analog of MS-325 (38). Analogous field dependent relaxivity is observed for MnL1 in the presence and absence of albumin, as was seen for MS-325. At low field, there is a benefit to albumin binding for r₁ but this falls off quickly with increasing field. At high fields MnL1 displays a relatively low r₁ and very high r₂ in the presence of HSA. In the absence of protein, the field dependence on r₁ and r₂ is again flat. As predicted by theory, at 9.4T r₁ is actually worse for the protein bound form of MnL1 than the unbound form.

The water exchange rate of MnL1 was previously measured (38) and the mean residency time of water at 20 °C is about 5 ns. This short residency time results in only a modest scalar contribution to r₂. We also measured relaxivity for the manganese aqua ion. The rotational correlation time of the aqua ion is very short (10's of picoseconds) while the water residency time was determined to be 50 ns at 20 °C (21). As a result of the very short rotational correlation time, the r₁ relaxivity for Mn²⁺ is very low per coordinated water (1.2 mM⁻¹s⁻¹ per bound H₂O). However the aqua ion has 6 waters bound so its T₁ relaxivity is reasonable. The very short rotational correlation time insures a flat field dependence on r₁. The short τ_R also means that the dipolar contribution to transverse relaxivity is small. However the relatively long residency time results in a large scalar contribution to r₂ and an r₂/r₁ of ~20 compared to r₂/r₁ < 2 for MnL1.

The molecular imaging probe EP-2104R is an example of a molecule with internal motion contributing to relaxivity. From the field dependence of fibrin-bound EP-2104R, there is clearly a significant slow motion contribution that has a positive effect on r₁ at 1.4T. However at 9.4T, the fibrin-bound T₁ relaxivity is slightly lower than that of the unbound EP-2104R. r₂ is higher for EP-2104R when it is bound to fibrin as we expect. However the impact of internal motion is such that r₂ is not as high as for MS-325/HSA because of the effect of the fast internal motion component on relaxation.

Taken together, the experimental results confirm the results of the simulations. The simulations in turn provide guidance for design of new probes.

Impact of high fields on T₁ probes

The simulations and measured high field relaxivities in this paper, along with other high field relaxivity data previously (5) reported highlight the challenges faced at high fields. The receptor induced magnetization enhancement (RIME) strategy (2,45,52) that is effective at low fields is counterproductive at very high fields. It leads to low r₁ and large r₂. Another factor not explored here is the increasing magnetization of paramagnetic complexes. Unlike iron oxide particles which are fully magnetized by 1T, Gd³⁺ and Mn²⁺ magnetize linearly with applied field (53). As a result, susceptibility effects of Gd³⁺ are higher at higher magnetic fields (susceptibility of Mn is 5/9 that of Gd). A consequence of these r₂ and R₂* effects is that increasing the contrast agent dose to shorten T₁ may not be effective because T₂ effects may dominate. This may be less of an issue for targeted probes where the concentrations at the target are relatively low. However as the relaxivities of EP-2104R demonstrate, r₁ is much lower at 4.7 or 9.4T than at 1.4T. Increasing the dose here to overcome poor high field relaxivity may also prove ineffective, because the molecular target can become saturated.

Strategies to improve high field relaxivity

The utility of T₁ contrast agents has been widely established clinically and in preclinical models. T₁ contrast agents can continue to provide benefits at high fields. For new probes, some consideration should be made to how the chelate and the dynamics affect relaxivity. From the simulations, the rotational correlation time should be intermediate between a fast tumbling small molecule like GdDTPA and a slow tumbling protein- or polymer-bound agent. The optimum correlation time will depend on the field strength, but for good relaxivity over the 1.5 to 9.4T range, a correlation time in the 0.5 to 1.5 ns range is effective. In order to achieve these intermediate correlation times, two approaches can be used. One is to place the metal complex at the barycenter of the molecule, Figure 9a. This approach has been employed by Port et al, and Fulton et al. (54,55). This minimizes any effects of internal motion as the chelate should tumble with the overall rate of motion of the molecule. Pendant groups can be added to modulate this rate. The other approach is to make the molecule larger by linking multiple chelates together in a fairly rigid fashion, Figure 9b. There are several examples of this approach and increased high field relaxivity has been noted (15,17,56,57).

Figure 9.

Strategies to achieve high relaxivity compounds at high fields. A) the metal ion is placed at the barycenter of the molecule limiting effects of internal motion; correlation time can be increased by adding pendant groups. B) correlation time and metal content increased by making a rigid multimer. Targeting groups should be linked via flexible linkers to decouple the motion at the metal ion from the macromolecule.

Examples of compounds with improved high field relaxivity have often focused on non-targeted molecules. However there is broader utility in expanding high relaxivity into molecular imaging probes. Protein binding and rotational immobilization is obviously to be avoided for high field, high relaxivity agents. The simulations suggest that the best solution is to decouple the slow rotational dynamics of the target from the internal motion of the metal chelator. The internal motion should be in this sweet spot of 0.5 to 1.5 ns. Targeted agents then should have chelates using the rotational dynamics strategy shown in Figure 9. A targeting vector (e.g. peptide) is tethered via a long flexible linker to metal chelators; upon protein binding, the internal motion of the chelators is decoupled from the slow motion of the protein.

Ideally the complex should have two inner-sphere water molecules (q = 2) since the gain in r₁ from multiple waters is independent of field. However, increasing q carries two risks: it can result in a less stable complex where the Gd³⁺ is more easily released; it can open up a site for anion (HCO₃⁻, HPO₄²⁻, citrate) coordination whereby the anion displaces the water molecules (58). However stable q = 2 complexes have been reported with higher relaxivity, e.g. the Gd-HOPO series (59,60) or pyridine analogs of DOTA (50,61). Recently Aime and colleagues reported the AAZTA ligand which forms a thermodynamically stable q=2 complex with Gd resulting in an increased relaxivity that is unaffected by the presence of anions like phosphate (62). An albumin binding version of this complex displayed very high relaxivity at low field (84 mM⁻¹s⁻¹ at 0.47T) (63).

Optimal relaxivity

Relaxivity is clearly field dependent and the correlation times that give the highest r₁ at 0.5T are not the same as those that provide the highest relaxivity at 3T. We performed simulations using reasonable molecular parameters to identify what one could expect from an “ideal” high field agent. Figure 10 shows the result of a simulation for a gadolinium complex with 2 inner-sphere water molecules with fast water exchange (τ_m = 50 ns) and a long lived (τ_m’ = 1 ns) water at 3.5 Å from Gd. These are reasonable values based on current literature. We assumed isotropic rotation and plotted results for 3 correlation times representing optimal relaxivity at 1.5T, 3T, and 9.4T. Rotational correlation times in the range 0.5 – 4.6 ns give excellent high field relaxivity. The short correlation time 0.5 ns which provides the highest r₁ at higher fields would still deliver a relaxivity greater than 30 mM⁻¹s⁻¹ at 1.5T which is better than almost all reported compounds. If the rotational correlation time increases are achieved by making a rigid multimer of n chelates, then the relaxivity of the molecule will be n-fold higher.

Figure 10.

Simulated r₁ for a Gd³⁺ complex with two rapidly exchanging (τ_m = 50 ns) inner-sphere waters and one water with r’_GdH = 3.5 Å, τ_m’ = 1 ns for three different isotropic rotational correlation times τ_R = 0.5 ns (•••), 1.6 ns (---), or 4.6 ns (—).

Because of the number of parameters involved, even higher relaxivities may be achievable with q>2 or greater 2^nd-sphere hydration. However Figure 10 represents a reasonable, practical upper range of r₁ that may be achieved through judicious molecular design, yet still resulting in complexes that are stable and inert enough for in vivo use.

Conclusions

Longitudinal relaxivity will decrease with increasing field but very high relaxivities may still be achieved by judicious molecular design. The design tenets stressed for optimizing r₁ at low fields (very slow rotational motion; protein binding with the Gd chelate tethered by short, rigid linker; narrow, optimal water exchange rate) do not apply at higher fields. At 1.5T and higher fields, an intermediate correlation time is desired (0.5 – 4 ns) and the water exchange rate is not as critical to achieving a high r₁. Although r₁ decreases with increasing field, the parameter space for identifying a compound with high relaxivity becomes greater as the field increases, and thus the likelihood of identifying high field, high relaxivity agents is increased. For targeted applications it may be best to use a multimer of metal chelates with an optimal rotational correlation time that is linked to a protein-targeting group via a long flexible linker to decouple the slow motion of the protein from the water(s) bound to the metal ions. Per ion relaxivities of 80, 45, and 18 mM⁻¹s⁻¹ at 1.5, 3, and 9.4T respectively are feasible for Gd³⁺ and Mn²⁺ complexes, making the future bright for T₁-contrast at high fields.

Experimental

The compounds EP-2104R (64) and MS-325 (gadofosveset) (45) were gifts of Epix Pharmaceuticals. The albumin binding MnEDTA derivative MnL1 (38) and Gd-DTPA-BSA (65) were prepared as previously described. Human serum albumin (Fraction V) was obtained from Sigma, human fibrinogen was from Calbiochem, and manganese chloride hexahydrate was purchased from Aldrich. Fibrinogen was dialyzed against 50 mM Tris buffered saline (TBS) containing 5 mM sodium citrate. Fibrin gels were prepared by mixing fibrinogen (12 μM final concentration), EP-2104R (0 – 40 μM), and calcium chloride (20 mM) and then adding 0.33 NIH units of human thrombin. All solutions were at pH 7.4.

Relaxation rate measurements were made at ambient temperature (21 °C) using a Bruker mq60 Minispec at 1.4T, or horizontal bore imagers at 4.7 and 9.4T (Bruker, Billerica MA). At 1.4T samples (200 μL) were prepared in small glass cylindrical vials and placed inside a 7.5mm NMR tube inside the Minispec. At 4.7 and 9.4T, samples were prepared in 0.5 mL plastic centrifuge tubes. Five of these tubes were placed in a holder and immersed in an aqueous solution of 10 mM MnSO₄ and imaged with a volume coil. T₁ was measured using an inversion-recovery sequence with 8 to 10 TI values and care was taken to set TR ≥ 5T₁. T₂ was measured using a multi echo spin echo sequence with typically 25 echoes.