HY Ιατρική Απεικόνιση. Διδάσκων: Kώστας Μαριάς

Transcription

1 HY Ιατρική Απεικόνιση Διδάσκων: Kώστας Μαριάς

2 11. MRI Τ1,Τ2, PD and physiological parameter imaging

3 Summary and Clarifications Resonance is referred to as the property of an atom to absorb energy only at the Larmor frequency. This is the basis of MR!! An atom will only absorb external energy if that energy is delivered at precisely it s resonant frequency. The energy must also be delivered at 90 to the net magnetic vector (NMV) and main magnetic field (B 0 ). Otherwise, no energy will be absorbed, resonance will not have occurred and an image cannot be created. As resonance occurs and the NMV moves out of alignment with the B 0 to a pre-specified angle. The deflection of the magnetization or total angle created after the end of the RF pulse is referred to as the flip angle.

4 Summary and Clarifications The stronger the RF energy applied to the protons, the greater the angle of deflection for the magnetization. The two most common flip angles in MR are 90 and 180. A 90 pulse will flip the magnetization into the x-y plane (Mxy). A 180 pulse will flip the magnetization through the x-y plane and into the opposite direction of B 0. Paul Lauterbur, implemented the concept of tri-plane gradients used for exciting selective areas of the body (Gx, Gy, and Gz.). Based on these concepts each plane is scanned in the k-space and then the image is produced via the inverse FT.

5 Summary and Clarifications With the net magnetization in the transverse plane (created with a 90 flip angle), and a receiver coil or antenna in the transverse plane, a voltage is induced within the receiver coil. This oscillating signal voltage over time is the MR signal. The magnitude of the signal is dependent on the magnetization present in the transverse plane. At the termination of the RF, the freely precessing protons in the transverse plane (Mxy) give up energy (RF) in order to try to realign with B 0. As the transverse magnetization starts to decay due to the loss of phase coherence, the protons eventually realign with B 0.

6 Measuring the MR Signal z RF signal from precessing protons Β 0 y x RF antenna

7 Summary and Clarifications After the external RF signal is turned off, two phenomenons simultaneously occur. Longitudinal magnetization gradually increases and is called T1 recovery. Transverse magnetization gradually decreases and is called T2 decay In the presence of an external magnetic field, the atoms align either with or opposed to the main magnetic field; the parallel and antiparallel protons cancel each other out, leaving a relatively small number of protons aligned with the main magnetic field. As an RF signal is applied at the Larmor frequency, the individual protons resonate, or absorb the applied energy, and precess in phase.

8 Summary and Clarifications Depending on the strength of the applied energy, the protons will flip into the x-y plane (transverse magnetization), or exactly the opposite direction of the main magnetic field. The transverse magnetization induces a voltage in an antenna or receiver coil which will be eventually become the MR signal. As the RF is turned off, the protons dephase and lose their coherence as they try to realign with B 0. Two phenomena occur simultaneously. Transverse magnetization decreases (T2 decay), while longitudinal magnetization increases (T1 recovery).

9 Summary and Clarifications Longitudinal relaxation is the return of longitudinal magnetization to equilibrium (B 0 ) and is termed T1 recovery. Transverse relaxation is the return of transverse magnetization to equilibrium and is termed T2 decay. the NMV gives up its absorbed RF energy while trying to return to B 0 the process of relaxation occurs. As relaxation is occurring, magnetization is recovering in the longitudinal plane while decaying in the transverse plane. Longitudinal and transverse magnetization occur at simultaneously but are two completely different processes.

10 Summary and Clarifications T1 recovery is the time it takes for 63% of the longitudinal magnetization to "regrow" or recover in the tissue. The rate of T2 decay is also expressed as a time constant. T2 decay occurs when the transverse magnetization has decreased to 37% of its initial value. Longitudinal relaxation is a regrowth or an increase in value, whereas transverse relaxation is a decrease or decay. Although these two processes occur together, T2 decay almost always occurs more rapidly than the regrowth of longitudinal magnetization.

11 Summary and Clarifications TR and TE are parameters controlled by the operator and are usually measured in milliseconds. TR stands for repetition time, or the elapsed time between successive RF excitation pulses. TE stands for echo delay time, or the time interval between the RF pulse and the measurement of the first echo. The T1 constants indicate how quickly the spinning nuclei will emit their absorbed RF into the surrounding tissue.

12 Summary and Clarifications Fat Versus Water Due to the slow molecular motion of fat nuclei, longitudinal relaxation occurs rather rapidly and longitudinal magnetization is regained quickly. The net magnetic vector realigns with B 0 leading to a short T1 time for fat. Water is not as efficient as fat in T1 recovery due to the high mobility of the water molecules. Water nuclei do not give up their energy to the lattice (surrounding tissue) as quickly as fat, and therefore take longer to regain longitudinal magnetization resulting in a long T1 time. As we know, T2 decay is dependent on the interaction of nuclei and the exchanging of energy with near by nuclei. Fat has a very efficient energy exchange and therefore has a relatively short T2. Water is less efficient than fat in the exchange of energy, and therefore has a long T2.

13 Summary and Clarifications T1, T2 and Proton Density Contrast Fat has a shorter T1 time than water, therefore the fat vector will realign more quickly with the main magnetic field. Fat has a larger longitudinal component prior to an RF pulse, and it has a larger transverse component after an RF pulse. Due to the larger longitudinal and transverse magnetization, fat has a higher signal and will appear bright on a T1 contrast MR image. Conversely, water appears dark on a T1 contrast image. Images created with TR's and TE's to enhance T1 contrast are referred to as T1-weighted images.

14 Summary and Clarifications The previously learned concepts of transverse magnetization apply for T2 contrast. Fat has a shorter T2 time than water and relaxes or decays more readily than water. Since the amount of transverse magnetization in fat is small, fat generates very little signal on a T2 contrast image and appears dark. Water has a very high T2 constant, therefore has very high T2 signal and thus appears bright on a T2 contrast image. Images created with TR's and TE's to enhance T2 contrast are referred to as T2-weighted images.

15 Summary and Clarifications Proton density contrast is a quantitative summary of the number of protons per unit tissue. The higher the number of protons in a given unit of tissue, the greater the transverse component of magnetization, and the brighter the signal on the proton density contrast image. Conversely the lower the number of protons in a given unit of tissue, the less the transverse magnetization and the darker the signal on the proton density image.

16 Several t values are used in repeated runs of the Inversion Recovery sequence, 180- tau-90-acq, so that enough values are acquired, to be later fitted to the function: T1,T2 measurement d e liz m a o r )n (t M M(z) afte r inve rs ion, T1=1.5s t (s) Mz() t = Mz, eq 1 2exp t T 1

17 z T1,T2 measurement The pulse sequence: z M eq y y x z x z t M(t) y 90 0 y x x M(0)=-M eq Acquisition

18 Relating Signal to Contrast Agent Concentration MRI is a clinically useful imaging modality but its diagnostic utility is dramatically enhanced by using certain techniques to improve contrast relaxation characteristics of the magnetisation. Changes in both T1 (spin-lattice relaxation) and T2 (spin-spin relaxation) can be used to attain different sorts of useful clinical images, here we focus on T1. Spin-lattice relaxation describes the rate of recovery of the z- component of magnetisation toward equilibrium after it has been pulsed by an RF signal. The recovery is given by: M z ( t) = t / T 0 (1 e ) + M z (0) 1 t / where M(0) is the equilibrium magnetisation. M e T 1

19 Relating Signal to Contrast Agent Concentration Changes in the T1 constant can be used to produce enhanced image contrast by exciting all magnetisation and the imaging again before recovery has been achieved. This is illustrated in the next Figure where an initial π/2 RF pulse destroys all longitudinal magnetisation. The two curves show the recovery rate of two different T1 tissues: The short T1- value recovers faster and produces more signal. Magnetisation Short T1 T1 contrast The result is what is known as a T1-weighted image. Long T1 Time

20 Relating Signal to Contrast Agent Concentration To further enhance image clarity, particularly for pathological regions, contrast agents based on various kinds of paramagnetic (Gd) and ferromagnetic (ferrous oxide) compounds are used. In simple terms, contrast agents are injected into the blood stream and when absorbed into tissues (via pharmacokinetic mechanisms), these imaging agents affect the T1 characteristics of diseased tissue, resulting in increased visible signal in regions that may be of concern to the radiologist.

21 Relating Signal to Contrast Agent Concentration Dynamic contrast-enhanced magnetic resonance imaging (CE-MRI) is commonly used for breast cancer imaging; in particular for younger women, and for those cases that have an inconclusive diagnosis based on x-ray mammography. A conventional CE-MRI study involves intravenous injection of a contrast agent (typically gadopentetate dimeglumine) immediately prior to acquiring a series of T1-weighted MRI volumes with a temporal resolution currently around a minute. The presence of contrast agent within an imaging voxel results in an increased signal that can be observed over the time course of the experiment. Study of such signal-time curves enables identification of different tissue types due to their differential contrast uptake properties as illustrated in the next Figure.

22 Relating Signal to Contrast Agent Concentration Typical signal enhancement uptake curves, illustrating the differences in enhancement over time for malignant, benign, parenchymal and fatty tissues.

23 Relating Signal to Contrast Agent Concentration Typically, cancerous tissue shows a high and fast uptake due to a proliferation of leaky angiogenic microvessels, while normal and fatty tissues show little or slow uptake. The uptake curves have often been fitted using a pharmacokinetic model to give a physiologically relevant parameterisation of the curve. Study of these curves/parameters has been used clinically to identify and characterise tumours into malignant or benign classes, although the success has been variable with generally very good sensitivity (> 95 %) but often very variable specificity.

24 Relating Signal to Contrast Agent Concentration There are a number of reasons for the poor specificity of conventional signal enhancement based studies, relating to the underlying assumptions made in the signal and pharmacokinetic modelling. Pharmacokinetic modelling using signal enhancement uptake curves was initially based on the erroneous assumption that the enhancement is linearly proportional to the contrast agent concentration. It will be shown later that this relationship is both non-linear and highly dependent on the intrinsic tissue T1 value. This approach aims to develop a framework for extracting and visualising physiological information from the CE-MRI data.

25 Relating Signal to Contrast Agent Concentration In order that the measured magnetic resonance (MR) signal S can be related to the contrast agent concentration, an appropriate signal model is required. In the case of a gradient echo MR pulse sequence, this takes the form: * 1 exp S = gρ exp( TE / T ) sin α 2 1 cosα exp ( TR / T ) 1 ( TR / T ) 1 where S is the measured signal, g the scanner system gain, ρ the proton density, ΤΕ the echo time, TR the repetition time, α the flip * angle and Τ 1 and T 2 are the longitudinal and transverse relaxation times, respectively.

26 Relating Signal to Contrast Agent Concentration The effect of a contrast agent (such as gadopentetate dimeglumine) is to alter and in the above expression, such that 1 T 1 1 T + R1C t = = + * * 2 t 10 T2 T R C where R 1 and R 2 are the tissue relaxation rates for the contrast agent, * C t is the contrast agent concentration at time t and T 10 and T 20 are the longitudinal and transverse relaxation times before administration of contrast agent (i.e. at t = 0) Substituting to the previous equation expression for the MR signal as a function of contrast agent concentration S ( C ) t 1 exp = k sinα 1 cosα exp ( TR / T ) 10 R1C ttr ( TR / T R C TR) 10 1 t where k = gρ exp * ( TE / T R C TE) 20 2 t

27 Relating Signal to Contrast Agent Concentration ( ) An expression for the signal enhancement E C t then follows E ( C ) t = S ( Ct ) ( 0) S 1 = exp ( R C TE) 1 exp 1 exp ( P Q) cosα( exp( P) exp( 2P Q) ) ( P) cosα( exp( P Q) exp( 2P Q) ) 2 t 1 where P = TR / T 10 and Q = R C 1 This expression enables the relationship between signal enhancement and contrast agent concentration to be observed for different combinations of pulse sequence parameters and with different MR tissue properties. A necessary pre-requisite for obtaining the contrast agent concentration from MR signal enhancement data is that the intrinsic pre-contrast longitudinal relaxation time T 10 must be known at each voxel. Several methods have been proposed for measuring T10 in breast imaging, including those based on inversion recovery protocols and those using gradient echo sequences acquired with either variable flip angle or. t TR

28 Relating Signal to Contrast Agent Concentration Next Figure illustrates the relationship between signal enhancement E and contrast agent concentration C t plotted for different values of pre-contrast for a typical set of pulse sequence parameters (TE/TR= 4.2 / 8.9 ms, α=10 ο ).

29 Relating Signal to Contrast Agent Concentration T 10 The values of are selected to be representative of those found in a typical breast acquisition. It is clear from this figure that the relationship between signal enhancement and contrast agent concentration is non-linear and shows an extremely high dependency on the intrinsic pre-contrast tissue relaxation parameter T 10. These properties mean that subsequent pharmacokinetic modeling based on signal enhancement data will be erroneous and in order to calculate the contrast agent concentration correctly, the signal model must be used along with an appropriate measurement of T 10.

30 Pharmacokinetic Modeling Pharmacokinetic models enable physiological information on volume and exchange rate mechanisms to be gained from analysis of the dynamic MR data. These models have been developed to describe the time varying distribution of contrast agent in different compartments of the body. The two-compartment model is illustrated in next Figure and was originally proposed by Brix et al., with a full derivation later being given by Hayton et al. This model consists of a central compartment corresponding to the blood plasma pool (contrast agent concentration C p (t)), which is able to exchange, via rate constants k pe and k ep, with the extravascular extracellular space EES (concentration C e (t)).

31 Pharmacokinetic Modeling Schematic illustration of the two-compartment pharmacokinetic model. Contrast agent is injected into the blood plasma compartment and excreted to the kidneys as determined by rate constant k out. Exchange also takes place between the blood plasma and extravascular extracellular space compartments governed by the rate constants k pe and k ep as indicated in the above diagram.

32 Pharmacokinetic Modeling The initial concentration in the blood plasma is determined by the administered contrast agent dose and is depleted by loss of contrast agent to the kidney governed by the rate parameter k out. The concentration-time curves observed in dynamic MR imaging are assumed to result from changes in contrast agent concentration in the EES C e (t) corresponding to contrast uptake by the lesion EES from the plasma. The solution of the pharmacokinetic model is therefore found to describe C e (t) in terms of the various rate and volume parameters of the model. The equations describing the concentration of contrast agent in each compartment as a function of time can be constructed by considering conservation of mass within the model. The solution is

33 Pharmacokinetic Modeling C e (t) describes the concentration-time curve obtained from dynamic MR data and the parameters A, a and b can be found by using a non-linear fitting routine (e.g. Levenberg- Marquardt or Simplex-minimisation). While these parameters are extremely useful for characterising the contrast uptake curves, their relationship to the physiological rate and volume parameters is less obvious, as can be seen from these equations. Nevertheless, these parameters have been used effectively for characterising different tumour types in clinical practice. More sophisticated methods are being developed for estimating physiological parameters from MR signals.

34 Μαγνητική Τομογραφία Ανακατασκευή τομής του εγκεφάλου με τη μέθοδο υπολογιστικής τομογραφίας μέσω δέσμης ακτινών Χ (αριστερά) και με τη μέθοδο πυρηνικού μαγνητικού συντονισμού (δεξιά).

35 Μαγνητική Τομογραφία Τ 1 Τ 2

36 FIN