Last updated: February 22, 2019
Topic: ArtDesign
Sample donated:

Field-Cycling NMR relaxometry is a technique for geting T1 scattering curves ( a secret plan of T1 ( or relaxation rate R1, where R1 = 1/T1 ) against magnetic field strength ) besides known as Nuclear Magnetic Relaxation Dispersion ( NMRD ) curves. FFC-NMR Relaxometry, has proven to be an priceless tool in relation to this undertaking, as it allows rapid and accurate finding of the T1 scattering curves of different contrast agents. This information can be used to choose the magnetic field strengths at which to image in order to optimize contrast. This chapter gives an penetration into the methods used to look into the T1 clip invariable of samples. First a brief history is given of the different instruments used for relaxometry. This is followed by a more elaborate description of the commercial relaxometer used in this undertaking, along with the methods in which relaxometry informations is acquired.

2.1 History:

The really first NMR experiments carried out ( individually ) 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 place built RF transmitter/detector circuits in magnetic Fieldss. The magnetization behavior was observed following an RF pulsation and the T1 values of different samples could be measured utilizing equation 1.4. It was merely a few old ages subsequently that field cycling techniques were used to find T1 relaxation rates of proton magnetization precessing in the Earth ‘s magnetic field ( Packard, et al. , 1954 ) . The first field-cycling technique involved physically shuttling the sample between countries with different field strengths ( Ramsey, et al. , 1951 ; Packard, et al. , 1954 ) . From these initial relaxometry experiments information sing 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 clip devouring necessitating up to 250 MS to travel samples between Fieldss ( Kimmich, et al. , 2004 ; Stork, et al. , 2008 ) .

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

As the technique developed so excessively did the scope of applications and FC-NMR became an of import tool for analyzing molecular constructions, adhering 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 sixtiess in Noack ‘s lab in Germany ( Kimmich, 1980 ) . This method used electronic fluctuation of current fluxing through an electromagnetic spiral to change the magnet field. This technique is called “ Fast Field-Cycling ( FFC ) NMR relaxometry ” because the clip taken to exchange between magnetic Fieldss is lower than the T1 relaxation clip of most samples.

The 1980s saw the birth and rapid growing of MRI as an of import imagination technique, leting extremely elaborate images of soft tissue. The contrast in these images was preponderantly based on T1 relaxation times of tissues, which could be manipulated or enhanced utilizing paramagnetic contrast agents injected into the organic structure. As a effect it became more of import to understand the relaxation mechanism of tissues, particularly associating to the consequence of paramagnetic ions in biological samples. FFC-NMR relaxometry techniques were used to analyze relaxation mechanisms in organic systems and could help in the development of contrast agents ( Aime, et al. , 2002 ) .

2.2 NMR Relaxometry systems

A figure of different systems have been designed for NMR relaxometry applications. These include both shuttling devices and electronic shift 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 universe ‘s first commercial manufacturer of FFC-NMR instruments The Stelar relaxometer uses the electronic field exchanging technique for FFC-NMR relaxometry, which allows rapid alterations of current through the electromagnetic spiral and therefore faster field initiation times. This enables the system to mensurate T1 relaxation times of less than a msec ( Ferrante, et al. , 2004 ) . The creative activity of the Stelar commercial “ SPINMASTER ” Relaxometer coincided with high involvement in Field-cycling relaxometry and the creative activity in 1998 of a bi-annual international conference on FFC-NMR Relaxometry, all of which helped Stelar Relaxometers to accomplish both commercial and scientific success leting accurate and consistent T1 scattering curve measurings between different research Centres. In this undertaking, T1 scattering curve acquisition was carried out utilizing both a commercial FFC-NMR relaxometer “ SMARtracer ” from ‘Stelar S.r.l. ‘ capable of scanning from 0 to 10 MHz and besides utilizing an experimental whole organic structure FFC-MRI scanner capable of scanning from 0 to 4 MHz. The whole organic structure system will be described in item in chapter 5, but here we will depict the constituents of a designated FFC-NMR relaxometer.

2.3 FFC-NMR Components

The most of import constituents of an FFC-NMR Relaxometer are shown in Figure 2.1 and include the undermentioned: the electromagnet, the magnet power supply, the chilling system, the sensing investigation, 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 focal point on the lasting magnetic field strength B. Field-cycling electromagnets nevertheless must be designed in a manner that takes into history the specific demands of fast field-cycling. This includes the followers:

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

2. To maintain the slewing rate ( i.e. the maximal field fluctuation rate S = ( dB/dt ) soap ) every bit high as possible ( Ferrante, et al. , 2004 ) .

The maximal field of an electromagnetic is given by equation 2.1

( 2.1 )

Where is the magnetic permeableness of the stuff and H is the magnetic strength which is dependent on the electric current ( I ) every bit good as other belongingss of the electromagnet ) .

High magnetic permeableness of a stuff besides means high induction ( L ) . However in order to hold a high slewing rate, the magnet induction L must be kept low. For an FFC-NMR electromagnet a via media must be reached between holding higher Bmax or holding faster dB/dt. In general high Fieldss are non considered an absolute necessity for FFC-NMR relaxometer every bit long as the field can supply adequate signal from samples. The electromagnetic design which seems most suited for FFC-NMR relaxometry is that of an air-core solenoids composed of one or more coaxal wires ( Ferrante, et al. , 2004 ) . In which instance equation 2.1 becomes equation 2.2

( 2.2 )

Wher N is the figure of bends, cubic decimeter is the length of the solenoid, R is the radius and I is the current.

Figure 2.2 Cross subdivision of a solenoid magnet

This design allows maximal field values Bmax to be reached with fast swerving rates suited for relaxometry intents. For a existent spiral of the type shown in Figure 2.2, the magnetic field B can besides be expressed with as equation 2.3

( 2.3 )

Where P is the electrical power applied to the magnet, degree Fahrenheit is the packing factor, which expresses the ratio between the entire conducting volume and the entire magnet volume. G is the Fabry factor which depends upon the geometry of the magnet ( for illustration, in the instance represented by Figure 4, G depends merely on the ratios r1/r0 and l/r0 ) . The coefficient? 0 defines the electric resistance of the solenoid music director. Decreasing the electric resistance decreases the power required to bring forth a given field, therefore, the quantitative advantage of utilizing metals with the lowest possible electric resistance. The solenoid dullard r0 besides affects the generated field induction B. Unfortunately for most solenoid coils the homogeneousness at their Centre is normally deficient for NMR relaxometry. The homogeneousness can be improved utilizing suited spiral weaving constellation. In fact an algorithm to find the most suited electromagnet constellation was developed by Schweibert and Noack which used different beds of a carry oning stuff, each with coiling channels etched into them whose form can be determined utilizing the Schweibert-Noack algorithm ( Schweikert, et al. , 1988 )

Most electromagnets are built from ferromagnetic stuff in order to maximise the field strength, nevertheless ferromagnetic electromagnets have high induction values ( ~1-10 Henry ) ensuing in low slewing rates. When the physical and electrical features of different stuffs are considered as shown in table 2.1 Ag shows the best features. The nearest ( and cheaper ) option is oxygen free ( OF ) Cu.

Resistivity? Temperature coefficient a Thermal conduction s Mechanical cutting

Copper OF 1.78 ten 10-8 0.0068 383 Very hard

Silver 1.58 ten 10-8 0.0061 419 Difficult

Table 2.1: Electric resistance is in O.m, temperature coefficient is in K-1, and thermic conduction is in W.m-1.K-1.

From equation 2.3 it is clear that the low electric resistance of Ag reduces the electrical power needed to bring forth a given field, it besides reduces the swerving rate by take downing the clip changeless R/L of the magnet. Furthermore its lower temperature coefficient and higher thermic conduction aid to better the concluding field stableness.

2.3.2 Magnet power supply

The 2nd most of import constituent for FFC-NMR relaxometry is the power supply. The magnet current needs to be switched on and make a maximal peak power in order to bring forth the needed magnetic field, so when the relaxation field is reached it must be able to settle in a really short clip ( less than a msec ) one time the relaxation field is reached. The magnet current should be really stable one time a field degree is reached. This in peculiar refers to the sensing field where a stableness of 10-5 is needed ( Kimmich, et al. , 2004 ) .

.

The theoretical lower limit shift clip is limited by the power supply electromotive force and the opposition R and induction L of the magnet. In a basic circuit like that shown in Figure 10 with a fixed power supply electromotive force V, when the switch trips on, the current evolves harmonizing to equation 2.4

( 2.4 )

Figure 2.3: one time the switch has been turned on, the electromotive force immediately jumps from 0 to V. The current nevertheless evolves harmonizing to equation 2. The get downing incline of theI ( T ) curve shown by the flecked line corresponds to the maximal field-slewing rate given by V/L = ( R/L ) Imax.

An alternate FFC power supply was proposed by Redfield in ( Redfield, et al. , 1968 ) in which an energy storage circuit was used to get the better of the hold caused by magnet induction and make the coveted value of B in a shorter clip while minimising the needed power. When a magnet is energised, a big sum of energy is stored in its magnetic field. Consequently when the magnet is switched off alternatively of blowing this energy, it is possible to hive away it every bit high electromotive forces in a storage capacitance. This stored energy can so be used to assist excite the magnet by linking the storage capacitance to the bear downing circuit therefore hiking the electromotive force. This consequences in much faster field exchanging with merely a little addition in power.

Stelar developed this method in order to increase the magnetic field batch rate by doing the current vary along suited and good defined wave forms during the exchanging interval further diminishing the field exchanging times.

2.3.3 Cooling system

Fast field-cycling systems by and large require that high electromotive forces are passed through a resistive magnet. This in bend leads to a big dissipation of power as heat which must be removed by a suited chilling system to forestall harm to the magnet. The chilling system designed by ‘Stelar ‘ is split into a primary and a secondary chilling circuit. The primary chilling circuit uses a commercially available chilling fluid ( GaldenTM ) which surrounds the electromagnet because unlike H2O Galden is electrically non-conductive and does non endure from electrolysis when a electromotive force is applied across the magnet. Galden is besides chemically inert and non-toxic. Heat from the magnet and the power supply is transferred to the primary chilling circuit which so exchanges heat with the secondary chilling circuit via a high public presentation counter current heat money changer. The secondary chilling circuit consists of tap H2O as it does non come into contact with the electromagnet or other electrolysis bring oning constituents.

2.3.4 Signal sensing investigation

The sensing investigation used in an FFC NMR system is basically the same as a investigation used with any other NMR instrument. However a investigation utilizing the Helmholtz spiral geometry has the design advantage of suiting easy into the electromagnet therefore leting standard 10 millimeter NMR sample baths to be easy inserted into the spiral from above every bit good as being tunable and leting a broad scope of temperature control.

2.4 Data Acquisition

In this subdivision some of the most common pulse sequences can be used to obtain T1 values from a sample are described. There are a figure of different methods for geting T1, nevertheless each method is basically based on detecting how the majority magnetization of a sample alterations with clip following an RF pulsation. Equation 1.4 can so be used to find the rate of alteration ( and therefore T1 ) of the sample.

2.4.1 Multiple point methods

Most commercial relaxometers including those from ‘Stelar ‘ usage a multiple point best tantrum method for finding T1 of a sample. The three pulse sequences most normally used to find the T1 relaxation clip of a sample are non-polarised, pre-polarised, and inversion recovery pulse sequences as shown in Figure 2.8 a, B, and c below.

a )

B )

degree Celsiuss )

Figure 2.4: Pulse sequences for geting T1 data a: Non-polarised, B ) Pre-polarised, degree Celsius ) Inversion Recovery.

In fact these three pulsation sequences are rather similar. In each instance the sample undergoes a readying stage, a relaxation stage and a sensing stage.

The non-polarised pulsation sequence is used in instances where the development field strength is comparatively high ( normally ~ 60 mT/2 MHz ) , which means that there is sufficient signal from the sample magnetization during the development stage to be able to find T1 accurately. During the readying field of a non-polarised pulsation sequence the longitudinal magnetization of the sample is nulled by cut downing the magnetic field to zero for a readying clip tprep. The magnetic field is so switched quickly ( in a clip period hobo ) to the development field strength ( B0E ) and the sample magnetization is allowed to germinate from zero towards its equilibrium magnetization at that field strength for a variable clip period tevol. The magnetic field is so switched quickly ( once more in a clip period hobo ) to the sensing field strength ( B0D ) and allowed to brace for a short clip period ( tdelay ) before a 90 grade RF pulsation is applied in order to observe the signal { { 26 Kimmich, Rainer 2004 ; } } .

The pre-polarised pulsation sequence is normally used when the development field strength is really low in order to hold higher sample magnetization during the pulsation sequence which allows accurate finding of T1. During the readying field the magnetic field is switched to preparation field strength B0P for a clip tpol in order to increase the magnetization. The magnetic field is so switched quickly to the development field strength ( B0E ) and the sample magnetization is so allowed to germinate for a variable clip period tevol. The magnetic field is so switched quickly to the sensing field strength ( Bd ) allowed to brace for a clip period ( tdelay ) and a 90 grade RF pulsation is applied in order to observe the signal { { 26 Kimmich, Rainer 2004 ; } } .

The inversion recovery ( IR ) pulsation sequence is the same as the pre-polarised pulse sequence except following the polarization period and anterior to field-cycling to the development field strength an inversion RF pulsation is applied which inverts the sample magnetization.

Each of the above pulsation sequences are so repeated with measure alterations in the development clip ( T ) . The magnetization varies with clip as described by equation 1.4, and this equation can be used to bring forth a best fit magnetization curve for the experimental informations which determines the most likely value of T1 at that magnetic field strength. The development field strength is so changed and the procedure is repeated at the new field.

2.4.2 Data Analysis

For each pulsation sequence ( NP PP or IR ) a 90 grade pulsation is used to obtain a free initiation decay ( FID ) signal as shown in Figure 2.5 a. The mean FID signal is relative to the sample magnetization M, and behaves similar to equation 1.4 nevertheless as the magnetic field is changed during the pulse sequence the equation can be given by the followers

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

where S ( T ) is the signal at clip T, S0 is the signal for T = 0 ( i.e. anterior to field cycling ) , and S8 is the signal for T = 8 ( when the magnetisation reaches equilibrium at the development field ) . The magnetization curves for different field-cycling pulsation sequences are shown in Figure 2.5 B, degree Celsius and vitamin D.

a ) B )

degree Celsius ) vitamin D )

Figure 2.5: a ) shows a individual FID after a 90 grade RF pulsation following magnetization development over a clip period T at a specified development field. B ) Shows a series of FIDs for 12 different development times during a non-polarised pulsation sequence. The mean value of each FID is shown as a point through which a best tantrum curve ( consecutive line ) is plotted. This best fit curve gives an accurate appraisal of T1. degree Celsius ) Shows the magnetization curve for an inversion recovery pulse sequence while vitamin D ) shows the magnetization curve for a pre-polarised pulsation sequence.

Equation 2.3 can be used to bring forth a least-squares tantrum map Q ( T1 ) which gives the quadratic divergence between the experimental curve and a theoretical incline Y ( T ) Thursday utilizing different values of T1 to cipher Y ( T ) Thursday. The value of T1 which gives the minimal divergence between theoretical and experimental information is the best estimation for the T1 value of the sample.

One issue of concern sing the development of magnetization is the field exchanging issue. Following the development clip period, the field is switched back to the acquisition field and a 90 grade pulsation is used to get a signal. Before the 90 grade pulsation is applied the sample magnetization is foremost exposed to a variable field during the incline times, followed by a brief hold leting the magnet to brace before the RF pulsation is applied. During this clip the magnetization continues to germinate significance that the concluding magnetization and therefore the detected signal is non what it would hold been straight following the development clip period. Figure 2.5 shows a comparing between the theoretical magnetization and experimental magnetization development with clip for both non-polarised and pre-polarised pulsation sequences.

Figure 2.6 Comparison of theoretical magnetization and experimental magnetization development. Thin straight line shows theoretical magnetization development ( mth ( 0 ) – mth8 ) with clip for a non-polarised pulsation sequence disregarding effects from the incline times and the hold times while the thick heterosexual line shows experimental magnetization ( mexp ( 0 ) – mexp8 ) development with clip. Thin dotted line shows theoretical magnetization development ( Mth ( 0 ) – Mth8 ) with clip for a pre-polarised pulsation sequence disregarding effects from the incline times and the hold times while the midst dotted line shows experimental magnetization ( Mexp ( 0 ) – Mexp8 ) development with clip

In the instance of the ‘Stelar ‘ relaxometer the incline times and hold times are really short ( ~ 3 MS ) , therefore the resulting effects on magnetization are really little. This means that the relaxation rates are the same for both experimental and theoretical magnetization curves provided that the incline and hold times are held changeless for different development clip values ( Ferrante, et al. , 2004 ) . For other systems capable of mensurating T1 such as the 59 mT whole organic structure MRI scanner the incline times and hold times are much longer, and the effects on magnetization demand to be included in computations in order to accurately find T1 values. These computations will cover with in more item in Chapter 5 on the whole organic structure system.

2.4.3 Factors of mistake

Mistake in the T1 computations can be caused by a figure of issues. These include low signal to resound ratio which is undoubtedly worse at really low Fieldss ( though Pre-polarisation helps to increase signal at low field ) . A higher figure of development times helps to give a better rating of the magnetization curve which allows a better appraisal of T1, every bit good as larger figure of norms for each FID. For pre-polarised and non-polarised pulsation sequences the fluctuation of magnetization between readying clip and development clip is besides a lending factor to the mistake. Therefore to cut down the mistake longer acquisition times are needed. For faster NMRD profile acquisitions the figure of norms per FID can be reduced to 1 and the figure of development times per T1 value can besides be reduced at a cost of loss in truth.

2.4.4 Two point acquisition

T1 estimations can even be made use merely two point acquisitions as has been shown on the 59 mT whole organic structure FFC-MRI system. This two point acquisition switched between a impregnation recovery ( i.e. a simple 90 grade ) RF pulsation and an inversion recovery pulsation which inverts the magnetization and allows it to germinate for set development clip before using a 90 degree sensing pulsation. The impregnation pulse gave a value for M0 while the inversion recovery pulse gave a value for M ( T ) at some development clip following the inversion pulsation. This information can so be plotted into a modified version of equation 1.4 which takes into history the incline times needed to exchange between Fieldss. This pulse sequence and the equations for ciphering T1 are discussed in greater item in chapter 5.