Fast Field Cycling Nmr Relaxometry Biology Essay

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Field-Cycling NMR relaxometry is a technique for acquiring T1 dispersion curves (a plot of T1 (or relaxation rate R1, where R1 = 1/T1) against magnetic field strength) also known as Nuclear Magnetic Relaxation Dispersion (NMRD) curves. FFC-NMR Relaxometry, has proven to be an invaluable tool in relation to this project, as it allows rapid and accurate determination of the T1 dispersion curves of different contrast agents. This information can be used to select the magnetic field strengths at which to image in order to optimise contrast. This chapter gives an insight into the methods used to investigate the T1 time constant of samples. First a brief history is given of the different instruments used for relaxometry. This is followed by a more detailed description of the commercial relaxometer used in this project, along with the methods in which relaxometry data is acquired.

2.1 History:

The very first NMR experiments carried out (separately) by Bloch and Purcell in 1946 (Bloch, 1946; Bloembergen, et al., 1948) investigated the relaxation times of protons in aqueous solutions. These experiments were carried out on home built RF transmitter/detector circuits in magnetic fields. The magnetisation behaviour was observed following an RF pulse and the T1 values of different samples could be measured using equation 1.4. It was only a few years later that field cycling techniques were used to determine T1 relaxation rates of proton magnetisation precessing in the Earth's magnetic field (Packard, et al., 1954). The first field-cycling technique involved physically shuttling the sample between areas with different field intensities (Ramsey, et al., 1951; Packard, et al., 1954). From these initial relaxometry experiments information regarding both the physical and chemical environment of the protons in the sample could be deduced. However, this method was inherently slow, as mechanical shuttling proved unstable and time consuming requiring up to 250 ms to move samples between fields (Kimmich, et al., 2004; Stork, et al., 2008).

As the technique developed so too did the range of applications and FC-NMR became an important tool for studying molecular structures, bonding in solutions and the thermodynamics of spin systems and heat exchange between spin reservoirs (Leppelmeier, et al., 1966). Another method for cycling the magnetic field was developed by Kimmich in the late 1960s in Noack's lab in Germany (Kimmich, 1980). This method used electronic variation of current flowing through an electromagnetic coil to vary the magnet field. This technique is called "Fast Field-Cycling (FFC) NMR relaxometry" because the time taken to switch between magnetic fields is lower than the T1 relaxation time of most samples.

The 1980s saw the birth and rapid growth of MRI as an important imaging technique, allowing highly detailed images of soft tissue. The contrast in these images was predominantly based on T1 relaxation times of tissues, which could be manipulated or enhanced using paramagnetic contrast agents injected into the body. As a consequence it became more important to understand the relaxation mechanism of tissues, especially relating to the effect of paramagnetic ions in biological samples. FFC-NMR relaxometry techniques were used to study relaxation mechanisms in organic systems and could assist in the development of contrast agents (Aime, et al., 2002).

2.2 NMR Relaxometry systems

A number of different systems have been designed for NMR relaxometry applications. These include both shuttling devices and electronic switching devices. Some systems have been designed specifically for NMR relaxometry while others have been adapted from experimental MRI scanners.

In the 1996 an Italian company 'Stelar S. R. L.' became the world's first commercial producer of FFC-NMR instruments The Stelar relaxometer uses the electronic field switching technique for FFC-NMR relaxometry, which allows rapid changes of current through the electromagnetic coil and hence faster field induction times. This enables the system to measure T1 relaxation times of less than a millisecond (Ferrante, et al., 2004). The creation of the Stelar commercial "SPINMASTER" Relaxometer coincided with high interest in Field-cycling relaxometry and the creation in 1998 of a bi-annual international conference on FFC-NMR Relaxometry, all of which helped Stelar Relaxometers to achieved both commercial and scientific success allowing accurate and reproducible T1 dispersion curve measurements between different research centres. In this project, T1 dispersion curve acquisition was carried out using both a commercial FFC-NMR relaxometer "SMARtracer" from 'Stelar S.r.l.' capable of scanning from 0 to 10 MHz and also using an experimental whole body FFC-MRI scanner capable of scanning from 0 to 4 MHz. The whole body system will be described in detail in chapter 5, but here we will describe the components of a designated FFC-NMR relaxometer.

2.3 FFC-NMR Components

The most important components of an FFC-NMR Relaxometer are shown in Figure 2.1 and include the following: the electromagnet, the magnet power supply, the cooling system, the detection probe, and the control console.

Figure 2.1: Block diagram of Stelar FFC NMR Relaxometer.

2.3.1 Magnet:

Magnets in MRI are designed with the focus on the permanent magnetic field strength B. Field-cycling electromagnets however must be designed in a way that takes into account the specific requirements of fast field-cycling. This includes the following:

1. Provide a stable magnet field with good homogeneity at a range of different values up to Bmax (and including the polarization field Bp, the relaxation field Br and the acquisition field Ba) (Ferrante, et al., 2004; Blanz, et al., 1993).

2. To keep the slewing rate (i.e. the maximum field variation rate S = (dB/dt)max) as high as possible (Ferrante, et al., 2004).

The maximum field of an electromagnetic is given by equation 2.1


Where is the magnetic permeability of the material and H is the magnetic intensity which is dependent on the electric current (I) as well as other properties of the electromagnet).

High magnetic permeability of a material also means high inductance (L). However in order to have a high slewing rate, the magnet inductance L must be kept low. For an FFC-NMR electromagnet a compromise must be reached between having higher Bmax or having faster dB/dt. In general high fields are not considered an absolute necessity for FFC-NMR relaxometer as long as the field can provide enough signal from samples. The electromagnetic design which seems most suitable for FFC-NMR relaxometry is that of an air-core solenoids composed of one or more coaxial wires (Ferrante, et al., 2004). In which case equation 2.1 becomes equation 2.2


Wher n is the number of turns, l is the length of the solenoid, r is the radius and I is the current.

Figure 2.2 Cross section of a solenoid magnet

This design allows maximum field values Bmax to be reached with fast slewing rates suitable for relaxometry purposes. For a real coil of the type shown in Figure 2.2 , the magnetic field B can also be expressed with as equation 2.3


Where P is the electrical power applied to the magnet, f is the packing factor, which expresses the ratio between the total conducting volume and the total magnet volume. G is the Fabry factor which depends upon the geometry of the magnet (for example, in the case represented by Figure 4, G depends only on the ratios r1/r0 and l/r0 ). The coefficient ?0 defines the resistivity of the solenoid conductor. Decreasing the resistivity decreases the power required to generate a given field, hence, the quantitative advantage of using metals with the lowest possible resistivity. The solenoid bore r0 also affects the generated field inductance B. Unfortunately for most solenoid coils the homogeneity at their centre is usually insufficient for NMR relaxometry. The homogeneity can be improved using suitable coil winding configuration. In fact an algorithm to determine the most suitable electromagnet configuration was developed by Schweibert and Noack which used different layers of a conducting material, each with helical grooves etched into them whose pattern can be determined using the Schweibert-Noack algorithm (Schweikert, et al., 1988)

Most electromagnets are built from ferromagnetic material in order to maximize the field strength, however ferromagnetic electromagnets have high inductance values (~1-10 Henry) resulting in low slewing rates. When the physical and electrical characteristics of different materials are considered as shown in table 2.1 silver shows the best characteristics. The nearest (and cheaper) alternative is oxygen free (OF) copper.

Resistivity ? Temperature coefficient a Thermal conductivity s Mechanical cutting

Copper OF 1.78 x 10-8 0.0068 383 Very difficult

Silver 1.58 x 10-8 0.0061 419 Difficult

Table 2.1: Resistivity is in O.m, temperature coefficient is in K-1, and thermal conductivity is in W.m-1.K-1.

From equation 2.3 it is clear that the low resistivity of silver reduces the electrical power needed to produce a given field, it also reduces the slewing rate by lowering the time constant R/L of the magnet. Furthermore its lower temperature coefficient and higher thermal conductivity help to improve the final field stability.

2.3.2 Magnet power supply

The second most important component for FFC-NMR relaxometry is the power supply. The magnet current needs to be switched on and reach a maximum peak power in order to produce the required magnetic field, then when the relaxation field is reached it must be able to settle in a very short time (less than a millisecond) once the relaxation field is reached. The magnet current should be very stable once a field level is reached. This in particular refers to the detection field where a stability of 10-5 is needed (Kimmich, et al., 2004).


The theoretical minimum switching time is limited by the power supply voltage and the resistance R and inductance L of the magnet. In a basic circuit like that shown in Figure 10 with a fixed power supply voltage V, when the switch trips on, the current evolves according to equation 2.4


Figure 2.3: once the switch has been turned on, the voltage instantly jumps from 0 to V. The current however evolves according to equation 2. The starting slope of theI(t) curve shown by the dotted line corresponds to the maximum field-slewing rate given by V/L = (R/L)Imax.

An alternative FFC power supply was proposed by Redfield in (Redfield, et al., 1968) in which an energy storage circuit was used to overcome the delay caused by magnet inductance and reach the desired value of B in a shorter time while minimizing the required power. When a magnet is energised, a large amount of energy is stored in its magnetic field. Consequently when the magnet is switched off instead of wasting this energy, it is possible to store it as high voltages in a storage capacitor. This stored energy can then be used to help energise the magnet by connecting the storage capacitor to the charging circuit thus boosting the voltage. This results in much faster field switching with only a small increase in power.

Stelar developed this method in order to increase the magnetic field slew rate by making the current vary along suitable and well defined waveforms during the switching interval further decreasing the field switching times.

2.3.3 Cooling system

Fast field-cycling systems generally require that high voltages are passed through a resistive magnet. This in turn leads to a large dissipation of power as heat which must be removed by a suitable cooling system to prevent damage to the magnet. The cooling system designed by 'Stelar' is split into a primary and a secondary cooling circuit. The primary cooling circuit uses a commercially available cooling fluid (GaldenTM) which surrounds the electromagnet because unlike water Galden is electrically non-conductive and does not suffer from electrolysis when a voltage is applied across the magnet. Galden is also chemically inert and non-toxic. Heat from the magnet and the power supply is transferred to the primary cooling circuit which then exchanges heat with the secondary cooling circuit via a high performance counter current heat exchanger. The secondary cooling circuit consists of tap water as it does not come into contact with the electromagnet or other electrolysis inducing components.

2.3.4 Signal detection probe

The detection probe used in an FFC NMR system is essentially the same as a probe used with any other NMR instrument. However a probe using the Helmholtz coil geometry has the design advantage of fitting easily into the electromagnet thus allowing standard 10 mm NMR sample tubs to be easily inserted into the coil from above as well as being tunable and allowing a wide range of temperature control.

2.4 Data Acquisition

In this section some of the most common pulse sequences can be used to obtain T1 values from a sample are described. There are a number of different methods for acquiring T1, however each method is essentially based on observing how the bulk magnetisation of a sample changes with time following an RF pulse. Equation 1.4 can then be used to determine the rate of change (and hence T1) of the sample.

2.4.1 Multiple point methods

Most commercial relaxometers including those from 'Stelar' use a multiple point best fit method for determining T1 of a sample. The three pulse sequences most commonly used to determine the T1 relaxation time of a sample are non-polarised, pre-polarised, and inversion recovery pulse sequences as shown in Figure 2.8 a, b, and c below.




Figure 2.4: Pulse sequences for acquiring T1 data a: Non-polarised, b) Pre-polarised, c) Inversion Recovery.

In fact these three pulse sequences are quite similar. In each case the sample undergoes a preparation phase, a relaxation phase and a detection phase.

The non-polarised pulse sequence is used in cases where the evolution field strength is relatively high (usually ~ 60 mT/2 MHz), which means that there is sufficient signal from the sample magnetisation during the evolution phase to be able to determine T1 accurately. During the preparation field of a non-polarised pulse sequence the longitudinal magnetisation of the sample is nulled by reducing the magnetic field to zero for a preparation time tprep. The magnetic field is then switched rapidly (in a time period tramp) to the evolution field strength (B0E) and the sample magnetisation is allowed to evolve from zero towards its equilibrium magnetisation at that field strength for a variable time period tevol. The magnetic field is then switched rapidly (again in a time period tramp) to the detection field strength (B0D) and allowed to stabilise for a short time period (tdelay) before a 90 degree RF pulse is applied in order to detected the signal {{26 Kimmich, Rainer 2004; }}.

The pre-polarised pulse sequence is usually used when the evolution field strength is very low in order to have higher sample magnetisation during the pulse sequence which allows accurate determination of T1 . During the preparation field the magnetic field is switched to preparation field strength B0P for a time tpol in order to increase the magnetisation. The magnetic field is then switched rapidly to the evolution field strength (B0E) and the sample magnetisation is then allowed to evolve for a variable time period tevol. The magnetic field is then switched rapidly to the detection field strength (Bd) allowed to stabilise for a time period (tdelay) and a 90 degree RF pulse is applied in order to detected the signal {{26 Kimmich, Rainer 2004; }}.

The inversion recovery (IR) pulse sequence is the same as the pre-polarised pulse sequence except following the polarisation period and prior to field-cycling to the evolution field strength an inversion RF pulse is applied which inverts the sample magnetisation.

Each of the above pulse sequences are then repeated with step changes in the evolution time (t). The magnetisation varies with time as described by equation 1.4, and this equation can be used to produce a best fit magnetisation curve for the experimental data which determines the most probable value of T1 at that magnetic field strength. The evolution field strength is then changed and the process is repeated at the new field.

2.4.2 Data Analysis

For each pulse sequence (NP PP or IR) a 90 degree pulse is used to obtain a free induction decay (FID) signal as shown in Figure 2.5 a. The average FID signal is proportional to the sample magnetisation M, and behaves similar to equation 1.4 however as the magnetic field is changed during the pulse sequence the equation can be given by the following

S(t) = S0 + S8[1-exp(-t/T1)] 2.3

where S(t) is the signal at time t, S0 is the signal for t = 0 (i.e. prior to field cycling ), and S8 is the signal for t = 8 (when the magnetization reaches equilibrium at the evolution field). The magnetisation curves for different field-cycling pulse sequences are shown in Figure 2.5 b, c and d.

a) b)

c) d)

Figure 2.5: a) shows a single FID after a 90 degree RF pulse following magnetisation evolution over a time period t at a specified evolution field. b) Shows a series of FIDs for 12 different evolution times during a non-polarised pulse sequence. The average value of each FID is shown as a point through which a best fit curve (straight line) is plotted. This best fit curve gives an accurate estimation of T1. c) Shows the magnetisation curve for an inversion recovery pulse sequence while d) shows the magnetisation curve for a pre-polarised pulse sequence.

Equation 2.3 can be used to produce a least-squares fit function Q(T1) which gives the quadratic deviation between the experimental curve and a theoretical slope Y(t)th using different values of T1 to calculate Y(t)th. The value of T1 which gives the minimum deviation between theoretical and experimental data is the best estimate for the T1 value of the sample.

One issue of concern regarding the evolution of magnetisation is the field switching issue. Following the evolution time period, the field is switched back to the acquisition field and a 90 degree pulse is used to acquire a signal. Before the 90 degree pulse is applied the sample magnetisation is first exposed to a varying field during the ramp times, followed by a brief delay allowing the magnet to stabilise before the RF pulse is applied. During this time the magnetisation continues to evolve meaning that the final magnetisation and hence the detected signal is not what it would have been directly following the evolution time period. Figure 2.5 shows a comparison between the theoretical magnetisation and experimental magnetisation evolution with time for both non-polarised and pre-polarised pulse sequences.

Figure 2.6 Comparison of theoretical magnetisation and experimental magnetisation evolution. Thin straight line shows theoretical magnetisation evolution (mth(0)- mth8 ) with time for a non-polarised pulse sequence ignoring effects from the ramp times and the delay times while the thick straight line shows experimental magnetisation (mexp(0) - mexp8) evolution with time. Thin dotted line shows theoretical magnetisation evolution (Mth(0)- Mth8 ) with time for a pre-polarised pulse sequence ignoring effects from the ramp times and the delay times while the thick dotted line shows experimental magnetisation (Mexp(0) - Mexp8) evolution with time

In the case of the 'Stelar' relaxometer the ramp times and delay times are very short (~ 3 ms), hence the resulting effects on magnetisation are very small. This means that the relaxation rates are the same for both experimental and theoretical magnetisation curves provided that the ramp and delay times are held constant for different evolution time values (Ferrante, et al., 2004). For other systems capable of measuring T1 such as the 59 mT whole body MRI scanner the ramp times and delay times are much longer, and the effects on magnetisation need to be included in calculations in order to accurately determine T1 values. These calculations will dealt with in more detail in Chapter 5 on the whole body system.

2.4.3 Factors of error

Error in the T1 calculations can be caused by a number of issues. These include low signal to noise ratio which is undoubtedly worse at very low fields (though Pre-polarisation helps to increase signal at low field). A higher number of evolution times helps to give a better evaluation of the magnetisation curve which allows a better estimation of T1, as well as larger number of averages for each FID. For pre-polarised and non-polarised pulse sequences the variation of magnetisation between preparation time and evolution time is also a contributing factor to the error. Thus to reduce the error longer acquisition times are needed. For faster NMRD profile acquisitions the number of averages per FID can be reduced to 1 and the number of evolution times per T1 value can also be reduced at a cost of loss in accuracy.

2.4.4 Two point acquisition

T1 estimates can even be made use only two point acquisitions as has been shown on the 59 mT whole body FFC-MRI system. This two point acquisition switched between a saturation recovery (i.e. a simple 90 degree) RF pulse and an inversion recovery pulse which inverts the magnetisation and allows it to evolve for set evolution time before applying a 90 degree detection pulse. The saturation pulse gave a value for M0 while the inversion recovery pulse gave a value for M(t) at some evolution time following the inversion pulse. This data can then be plotted into a modified version of equation 1.4 which takes into account the ramp times needed to switch between fields. This pulse sequence and the equations for calculating T1 are discussed in greater detail in chapter 5.