CA1322220C - In-vivo method for determining and imaging temperature of an object/subject from diffusion coefficients obtained by nuclear magnetic resonance - Google Patents

Abstract

Abstract of the Disclosure A method of determining and imaging the temper-ature or the temperature change of an object (human, animal, liquid or solid) by nuclear magnetic resonance of molecular diffusion coefficients is disclosed which includes placing the object in a magnetic field Bo at a temperature To, subjecting the object to a first series of magnetic resonance imaging sequences to obtain first numerical values or images of molecular diffusion coefficients Do for individual points of the object or of a limited volume thereof, changing the temperature to a temperature T of a part of the object measured in step (b), or waiting for a spontaneous change to said temper-ature, subjecting the object to a second series of mag-netic resonance imaging sequences to obtain second numerical values or images of molecular diffusion coefficients D for individual points of the object or of a limited volume thereof, comparing point-by point the values of the diffusion coefficients Do allocated for the first series of diffusion images obtained in step (b) with the values of the diffusion coefficients D obtained in the second series of diffusion images in step (d) to determine and to generate a third series of values or images representing temperature changes dT between steps (b) and (d) for each individual point i of the object or of a limited volume thereof from the formula dTi = (kTo2/E) Log (D/Do)i wherein k is Boltzman's constant (1.38 10-23 J/K) and E
is the activation energy (?0.2 eV at 20°C), provided dT
<<To and E constant, repeating steps (c) to (e) continu-ously for different points of the object so that tempera-ture changes dTi can be monitored continuously, determining the absolute temperature To for individual points of the entire object or a limited volume thereof so that by repeating steps (b) to (f) the absolute temperature T can be determined and imaged continuously in each point of the object or of a limited volume thereof from the formula T = To + dTi wherein dT is determined and imaged in step (e). Because of the non-invasive, non-destructive and non-ionizing properties of nuclear magnetic resonance the present invention may be employed in an object or an animal con-tinuously.

Description

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IN-VIVO METHOD FOR DETERMINING AND IMA~ING TEMPER~TURE
OF AN OBJECT/SUBJECT FROM DIFFUSION COEFFICIENTS
OBTAINED BY NUCLEAR MAGNETIC RESONANCE
Backqrou~ 5b~[~
5The application of nuclear magnetic resonance (NMR) to the study and imaging of intact biological systems is relatively new. Like X-rays and ultrasound procedures, NMR is a non-invasi~ analytical technique which can be employed to examine living tissues. Unlike X-rays, however, NMR is a non-ionizing, non-destructive process that can be employed continuously to a host.
Furkher, N~R imaging is cap~ble of providing anatomical information comparable ko that supplied by X-ray CAT
scans in any orientation without patient discomfort. On the other hand, the quality of projections or images reconstructed from currenkly known NMR techniqu~s either rival or transcend those observed with ulkrasound pro-ceduxes. Thus NMR has the potential to be one of the most versatile and useful diagnosing tools ever used in biological and medical communities today.
NMR occurs when nuclei with magne*ic moments are subjected to a magnetic field. If electromagnetic radiation in the radio-frequency region of the spec~rum is subsequently applied, the magnetized nuclei emit a detectable signal having a frequency similar to the one applied.
Many nuclei have intrinsic magnetism resulking from the angular momentum, or spin, of such nuclei.
Resembling a b~r magnet, the spin property generates a magnetic dipole, or magnetic moment, around such nuclei. Thus, when two external fields are applied to an object the strong magnetic field causes the dipoles for such nucle.i, e.g., nuclei with spin designated 1/1, to align either parallel ox anti-parallel with said magne~ic field. Of the two orientations, the parallel alignmenk xequires the nuclei ko store less energy and hence is the more stable or preferred orientation. The second applied field comprises radio-frequency waves of a prPcise frequency or quantum of electromagnetic radiation. These ~' ~22~

waves cause such nuclei to mutate or flip into a less stable orientation. The second applied field comprises radio-frequency waves of a precise frequency or quantum of electromagnetic radiation. These waves cause such nuclei to mutate or flip into a less stable orienta-tion. In an attempt to re-e~tablish the prefe~r~d parallel or stable orientation, the excited nuclei will emit electromagnetic radio waves at a frequency nominally proportional to the magnitude of the strong field, but specifically characteristic of thPir chemical environ-ment.
NMR technology therefore detects radio-frequency signals emitted from nuclei as a result of a process undergone by the nuclei when exposed to at least two externally applied fields. If a third magnetic field ln the form of a gradient is applied, nuclei with the same magnetogyric constant will mut~te at differenk fre-quencies, i.e., Laxmor frequencies, depending upon the location within the object. Thus, similar nuclei in an object can be detected discriminately for a partisular region in said object according to their Larmor frequency corresponding to a particular magnetic field strength along the applied magnetic gradient, as demonstrated by the following equation:
fo y H~
wherein fO is the Larmor frequency, y is the magnetogyric constant, and Ho is the applied magnetic field.
Several factors, however, limit the usefulness of NMR applications in vivo. In general, NMR is an insensitive radiologic modality requiring significant amount~ of nuclei with magnetic moments to be present in an object. Consequently, not all nuclei in vivo are present in sufficient quantities to be detected by present NMR techniques. Further, not all nuclei found in vivo have magnetic moments. Some of the more common isotopes that do not have magnetic moments which are found in vivo include 12C~ 160 and 32S.

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Thus, current NMR applications in vivo are restricted to those nuclei that have magne~ic moments and are sufficiently abundant to overcome the insen~itivity of pre~ent NMR techniques. For ~he most part, in vivo NMR applications almost invariably concern themselves with imaging or detecting the water dis~ribu~ion within a region of interest derived from the detection of proton resonance. Other nuclei not only have lower intrinsic NMR sensitivities but are also less abundant in bio-logical material. Consideration hai been given, however,to the use of other nuclei such as 31p which represents the ne~t best choice for NMR in ViV5 applications due to its natural and abundant occurrence in biological fluids. For example, 31p NMR has been found to provide an indirect means for determining intracellular pH and Mg+~ concentration simply by measuring the chemical shift of the inorganic phosphate resonance in vivo and deter-mining from a standard titration curve the pH or Mg++
concentration to which the chemical shift corresponds.
~Gadian, D.G., Nuclear Magnetic Resonance and its Applications to Livin~ Systems, First Ed. Oxford Clarendon Press~ pp. 23-42 (1982~; Moon, ~.B. and Richards, J.H., De~ermination of Intracellular pH by 31p Magnetic Resonance. J. Biological Chemis~ry 218(20:7276-7278 (Oct. 25, 1973)). In addition, 23Na has been used to image a heart perfused with a medium containing 145 m~
sodium in vivo. Difficulties with these nuclei arise because of inherent sensitivity losses due ~o the lower resonant frequencies of these nuclei (Moon, R.B. and Richards, J.H., Determination of Intracellular pH by 31p Magnetic Resonance, J. Biol. Chem. 218(20):7276-7278 (Oct. ~5, lg73).
Another stable element which is uniquely suited for NMR imaging is F because its intrinsic sensitivity practically commensurates with that of protons t i~ has a ; spin of 1/2 so as to give relatively uncomplica~ed, well resolved spectra, its natural isotopic abundance is 100 ~3~222~

percent, it gives large chemical shifts, and its mag-netogyric constant is similar to that of protons.
Accordingly, the same equipment used for proton NMR can be used in vivo. ~owever, F NMR applica-tions are not used due to the practical non-existence in hiological materials of fluorine obsex~able by NMR methods normally employed in studying biological systems. However, nuclear medicine proceduras using a 19F positxon emitter are well documented and include, for example, bone scanning, brain metabolism and infarct in~e~tigations using fluorodeoxyglucose, and myocardial blood flow and metabolism. Suggestions have been presented involving the study of vascular system disorder~ with F imaging (Holland, G. M. et al, 19F Magnetic Reson. Imaging, J.
Magnetic Resonance 28:133-136 (1977)) and the localiza-tion/kinetics of fluorocarbon following liquid breath-ing. Further, in ~itro canine studies investigating the feasibility of fluorine as an agent for NM~ imaging of myocardial infarction have also been performed (Thomas, S.R. et al, Nuclear Magnetic Resonance Imaging Techniques Developed Modestly Within a University Medical Center Environment: What Can the Small System Contribute at this Point?, Magnetic Resonance Imaging 1(1)~ 21 (1981)).
Studies directed to con~ormational equilibria and equilihration by NMR spectroscopy have been con-ducted, par~icularly with cyclohexane and ~luorocyclo-hexane rings. In such application~, the po~ition of the equilibria between conformational isomers and mea ure ments of rates of equilibration of ~uch isomers as a function of temperature have been determined. The studies, however, were dependent upon the implementation of known tempsratures to determine the equilibria and equilibrium rates (Roberts, J.D., Studies of Conformational Equilibria and Equilibration by Nuclear Magnetic Resonance Spectroscopy, Chem. in Britain, 2:529-535 (1966); Homer, J. and Thomas, L.F.: Nuclear Magnetic i ,~

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Resonance Spectra o Cyclic Fluorocarbons. Trans.
Faraday Soc. 59:2431-~443 (19h3)). It has further been illustrat~d that 13C may be employed as a kin~tic ther-mometer in a laboratory environment. This pa.r~icular application requires the examina~ion sys~em to contain a~
least two chemically exchanging si~es which correspond to one exchange process and an independent means of det~r-mining the kinetic parameters describing the exchange process in order for 13C ~o ser~e as 2 kinetic ther-mometer. Such application, however, is limited ko de~er-mining temperature at coalescence and is, thus, operable a~ only one temperature for each independent exchange process as opposed to over a continuous range. The method is further employed as a calibration technique and its accuracy is inherently unreliable to be of practical significance (Sternhell, S. Kinetic 13C NMR Thermometer, Texas A&M U. NMR Newsletter. 285:21-23 ~June 198~)).
Unfortunately, NMR studies based on 19F or 13C require infusion in the body of molecules containing these atoms due to their very low abundance in vivo.
Temperature has been measured by means of ~he NMR spectrum of liquid samples for the purpose of cali~
brating the temperature control appara~us of an NMR spec~
trometer. Many features of the NMR spec~rum, for instance chemical shifts, of~en show weak temperatur dependence, and could be used to determine temperature (Bornais, Jr. and Browstein, S., A Low-Temperature Thermometer for 1H, 19F and 13C, J Magnet. Reson.
29:207-211 (1978)3. The peak s~paration and spin-spin coupling in the proton NMR spectrum of a liquid test sample changed by 1.75 Hz and 0.07 Hz, respectively, when the temperature was varied by 10.5C. In objects, such as animals, were the best obtainable spectral resolution could be 10 to 50 Hz or largerl and it is desired to measure temperatures to an accuracy of 1C or 2C or better, such as means of temperature measurement is inap-plicable.

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As to temperature in an animal, it is well known that abno~mal fluctuations in temperature such as increases may reflect infection or hyperthermia, while decrea~es may represent ischemia hypothermia. Thus, it is useful to m~asure temperature in an animal accurately, inexpensively and reliably. Furthermore, induced hyper-thermia can also be used as an adjunctive cancer treat-ment.
In the past, temperature measurements have generally consisted of invasive and cumbersome techniques that often result in les~ than reliable measurements.
Examples of such techniques comprise invading needles, electrical wires, cables, or instruments that must be inserted into a region of interest. Such penetrating procedures possess unfortunately the potential to cause chemical and biological contamination to the host. Thus, proper preparation and sterilization procedures are required to prevent transmittal and corrosive contamina-tion when the instruments to detect temperature are reused. Another disadvantage inherent to the conven-tional techniques concerns the discomfort and incon-venience experienced from communication wi~h penetrating probes. As to highly delicate structures, the temper-ature may be obtained but not without sacrifice to the integrity of the structure. Generally, the structure may be damaged, repositioned or its dimen~ions changed.
Short circuiting of the employed instruments may add additional expenses and time to the procedure. The instrument itself when exposed to physical and chemical extremes may interfere with its relia~ility. Moreover, conventional techniques are unable to measure a continu-ous temperature field in an object or animal and, thus, the invasive and cumbersome procedure must be duplicated for each time or at each point in space a temperature measurement is desired, or employ simul~aneously a large number of temperature sensors.
Non-invasive and non-destructive temperature - - ' .

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imaging in biological systems may be useful in many dis-ciplines. One important application is clinical hyper-thermia (HT) which is being used as an adjunctive cancer treatment (Hahn, G.M., supra) ~lthough very promising results have been obtained, the effectiYeness and safety of deep-sea~ed HT treatment has been limited, mainly due to a lack of temperature control (Gibbs, F.A., Hyper-thermic Oncology, eds. Taylor and Frances, Phila, pp 2155-167 (1984)). Indeed, the effectiveness of a HT
treatment depends upon the minimum temperature reached in the tumor (greater than 42C) while safety considerations limit the maximum temperature that can be reached in normal healthy tissues (less than 42C) lHahn, G.M., Hyperthermia in Cancer, Planum Press (New York, 1982)).
The temperakure must be, therefore, monitored throughout the entire heated region with at least one cm spacial resolution and 1C sensitivity lHahn, G.M., supra).
A method to conduct non-invasive temperature monitoring by magnetic resonance imaging (MRI) ~as recently proposed which employs T1 temperature dependency (Parker D . L ., Smith, V., Shelton, P., Med. Phys. 10:321 (1~83); Dickinson, R.J., Hall, A.S., Hinde, A.J., Young, I.R., J. Comput. Assist. Tomogr. 10:468 (1986); U.S.
Patent 4,558,279 to Ackerman e~ al). MRI, a non-invasive and non-ionizing im~ging me~hod (Lauterbur, P.C. (1975) Nature 18,69-83) has the advantage of producin~
anatomical images of any part of the body in any orien tation with high resolution. Contrast in MRI is defined by parameters mainly related to certain physical proper~
ties of water molecules. Temperature sensitivi~y of one of these parameters, namely, the spin-lattice relaxation time or T1 has been demonstrated in-vitro for different ; biological systems thereby suggesting the thermal imaging potentiality of MRI (Lewa, C.J., Majeska, Z., Bull.
Cancer (Paris) 67:525-530 (1980) Parker, D.L., supra;
Dickinson, R.J., supra). However, in general, precise Tl MRI measurements are difficult and the accuracy for ~ S~2222~

temperature determination is limited. In most cases the accuxacy is no-t greater than 2C/cm/5min acquisition time. (Parker D.L., Smith V. and Sheton P., supra;
Dickinson R.J., Hall ~.S., Hinde AoJ~ / and Young I.R. r supra; U.S. Patent 4,558,279).
Unfortunately, there are large variations in T1 between different tissues and for the same tissue between different subjects. This has been ascribed to the mul~i-factorial nature of Tl (Bottomley, P.A., Foster, T.H., Argensinger, R.E., Pfeifer, L.M., Med. Phys II: 425-448 (1984). The applicability of this technique seems there-fore to be limited because a relative change of at least 1~ in T1 is needed to detect a 1C change in temperature (Cetas, E.C., supra) and Tl measurements using MRI are difficult due ~o its sensitivity to envixonmPnt (Young, I.R., Bryant, D.J. and Payne, J.A. Magn Res. Med. 2:355-389 (1985)- U.S. patents 4,319,190, 4,558,279 and 4,361,807 also disclose methods of imaging chemical shifts in a body. However, these methods wera not directly applied to the indirect measurement of tempera-tur0s in vi~o. The use of chemical-shift resolved MRI
has also been experimentally proposed but has severe limitations (Hall, L.D., Reson~ 65-501-505 (1983)).
Furthermore, all these techniques have failed for temper-ature monitoring in vivo, so that NMR was not considered ; as a likely temperature imaging method.
A variety of msthods are available in the prior art for measuring the diffusion constant of the regents of a medium. One is that described by George et al "Translation on Molecular Self-Diffusion in Magnetic Resonance Imaging- Effects and Applications", in ~iomedical Magnetic Resonance, published by Radiology Research and Education Foundation, San Francisco 1984.
This method describes the measurement of the diffusion constant by comparing the relative effect of the diffu-sion of the studied medium and on a standard substance during different magnetic excitation sequences. This - ~ .

~3?,~220 g method relies on increasing the intensity of a section selection gradient which modifies the thic~ness of the iatudied section. Thu3, this method can only be applied to objects which are finer than the finest section thick-ness obtained by the sequences used and practically of nouse in animal or human sub~ects. The sensitivity of this method to diffusion is also rela~ively limited.
Another method which lends itself to the mea-surement of temperatures in living tissues, including animals and humans, utilizes relatively long echo times and effective gradients as a resul~ o their intensity and posi~ion. In addition the exact determination of diffusion coefficients is obtained without a standard substance by basing the calculations on acquii-aition parameters. This method is described in a patent appli-cation entitled "Process for Imaging by Nuclear Magnetic Resonance" flled by Breton, E.A., LeBihan, D. and LeRoux, P. in France on June 27, 1985 (FR 8S 09824 - Patent

2,584,188), and in the U~S. on December 24, 1986 under Serial No. 06/946,034, -U.SO patent No. 4,780,674.
The patent applications describe basic sequences using Spin-Echoes to measure and image dif~usion. Effects o~
blood microcirculation can be eliminated by using longer and/or more powerful field gradient pulses.
An additional method is described in French patent ; 2,604,524 entitled l'Method of Imaging Nuclear Magnetic Resonance" by Breton, E.A., and LeBihan, later filed in the EP0 on September 21, 19~7, in Japan on September 25, 1987 and in the U.S. on September 23, 1987 USP 4,809,701.
These patent applications describe improvements in diffusion measurements and images which can be obtained when NMR excitation sequences and recording of NMR signals by synchronization with heart beats in living tissues.
Diffusion measure-~i, .
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ments and images can be obtained quickly by using Steady-State Free Precession NMR. Yet another method is described in a patent application entitled "Precede and Imagerie des Movements ~ntravoxels par ~MN dans in Corps"
filed in France by Lebihan D. on October 13, 1987 and has a Serial No. 87 1409B, (French Patent No. 2,621,693), which is related to the publication Lebihan, D., "Intravoxel Incoherent Motion Imaging Using Steady-5tate Free Precession", Magnetic Resonance in Medicine 7:346 (1988). This is a method for the fast imaging of diffusion by using steady State Free Precession NMR.
In view of the foregoing description of th0 limitations posed by prior art NMR temperature measuring techniques there is a clear need in the art, with par-ticularly imminent application to cancer treatments, or an improved method of de~ermining in vivo the temperature coefficient and obtaining temperature imagss which is safe, non-invasive and can provide the sensitivity and reliability required of such measurements.
Summary of the Invention This invention relates to a novel and improved method of de~ermining and imaging the temperature or ~he temperature change of an object (human, animal, liquid or solid) by nuclear magnetic resonance of molecular diffu-sion coefficients, said method comprising (a) placing the object in a magne~ic field Bo at a temperature To;
(b) subjecting the thus positioned object to a first series of magnetic resonance imaging sequences able to give first numerical values or images of molecular diffusion coefficients, namely Do for individual points of the object or of a limited volume thereof;
(c) maintaining the object or a part thereof utilized in step (b) to a temperature T, or waiting for a spontaneous change to a temperature T in said part;
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(d) subjecting the thu positioned object to a second series of magnetic resonance imaging sequences to obtain second numerical values or images of molecular difusion coefficients, namely D, for individual points of the object or of a limited volume thereof;
(e) comparing point-by-point the values of the diffusion coefficients Do allocated for the first series of diffusion images obtained in step (b) with the values of the difusion coefficients D obtained in the second ]0 series of diffusion images in step (d) in order to determine and to generate a third series of images representing temperature changes dT between steps (b) and ~d) for individual pint i of the object or of a limited volume of the object from the formula dTi = (kTo/E3 Log (D/Do)i wherein k is Boltzman's constant (1.38 10 ~3 J/K) and E
is the activation energy (~0.2 eV at 20C~, provided dT
<< To and E ~ constant, (f) repeating steps (c) to (e) continuously for different points of the object so that temperature changes dTi a~ be monitored continuously, (g) determining the absolute temperature To for individual points of the entire obje~t or of a limited volume thereof so that by repeating steps (b~ to (f) the absolute temperature T can be determined and imaged continuously in each point of the object or of a limited volume of the object from the formula T = To + dTi wherein dT is determined and imaged in step (e).
The present method may b~ utilizPd to determine the temperature of a subject also receiving, e.g., cancer therapy, or other treatments where the temperature of the body or of a particular portion of the body is bound to be varied. The method of this invention is highly sensi-tive to changes in temperature, accurate, non-invasive and provides a sensitivity for the measurement of temper-ature which is greater than 2% in the resolu~ion of the :L32222~

temperature images better than 0.5C.
A mor~ complete apprecia~ion of the invention and many of the attendant advantages thereof will b~
readily perceived as the same becomes better unders~ood by reference ~o the following de~tailed d~scription when considered in connec~ion with the accompanying figure.
Brief Description of the Drawinq The sole figure in this patent show~ the relative varia~ion of the diffusion coefficient as a function of temperatuxe change. T is 36.7C and Do is 2.31 X 10-3 mm2/s.
Other objects, advantages and features of the present invention will become apparent to those skilled in the a.rt from the following discussion.
Detalled Description of the Preferred Embodiments The present invention arose from a desire to improve an prior methods for the determination of body temperature, particularly associated with hypertharmia (HT) which is used as an adjunctive cancer treatment. In gene.ral, the effectiveness of HT ~reatments depend upon reaching a minimum temperature in a tumor, e.g., mostly greatex than 42C, while for all practical purposes temperatures greater than 42C are not really permis3able in normal healthy tissues. Ther~fore, the temperaturas applied during treatment must be thoroughly and acc~rate-ly monitored throughout the application of a treatment in the heated areas of the body within at least 1 cm spacial resolution and 1C sensitivity. This degree of sensi-tivity and accuracy has not been attained by prior non-invasive methods currently available.
The inventors discovered th t by usingmolecular diffusion measurable by nuclear magnetic resonance (NNR) techniques they could measure and imag~
body temperature. A relationsh.ip betwean the diffusion coefficients and temperature known in the art is u~ilized .: as applied to the measurement of body kemperature. In addition, this invention also incorporates available .-'~ .

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methods for quantita~ive diffusion imaging using MRI
(LeBihan D.~ Breton E., L~llemand D, Grenier P., Cabanis E. and Laval-Jeantet M., supra; Taylor D.G. and Bushell M.C., Phy~. Med. Biol. 30:345 (1985)); LeBihan, D., sreton~ E. (1985) C.R. Acad. Scr supra; LeBihan, D., Breton, E., Lallemand, D., Grenier, P., Cabanis, E., Laval Jeantet, M., Radiology 1986, supra; LeBihan, D., Magn. Reson. Med., 198~, supra; Taylor, D.G., Bushell, M.C. (1985) Phys. Med. Biol. 30,345-349; Merkolt, K.D., Manicke, W., Frahm, J., J.Maqn. Reson (1985).
The present method is based on the following theoretica! considerations.
The following temperature dependence of the translational self-diffusion coefficient D and viscosity are established on the basis of the Stokes-Einstein rela-tionship (Simpson, J.H. and Carr H.Y., Phys. Rev.111:1401 (195~)).
Dd ~ exp ~-E/kT) (1) wherein k is Boltzman's constant (1.38 123 J/K~ and E
is the activation energy No. 2eV at 20C, Simpson et al, supra).
Thus, it can be stated that when an object is subjected to changing temperatures, these temperature changes induce chang~s in the diffusion coefficient which can be calculated from differentiating the equation (1) abo~e as long as the variations of E with T are small, as follows:
dD/D = (E/kT)dT/T (2) As can be seen from equation (2) above temper-ature changes may be detected from diffusion coefficien~
measurements. This permits the application of magnetic resonance technology of the measuremen~ of diffusion coefficients to the ~emperature of the object su~jected to the magnetic field.
A map of temperature changes (T-T )xy can thus be obtained by ~he method of the invention from two diffusion images Dx y and Do x,y. The first image is ,, .

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obtained before heating (Tor Do) and the second is obtained during heating at a temperature T (T,D). The two sets of data can be correlated as follows.
(T-To)x y = (kTo/E) Log (D/DO3xy (3) provided khat T-To< To in ~hat E~~constant.
Diffusion coefficients of hydrogen nucl~i in water can be measured and imaged using MRI for instance, (LeBihan, D., Breton, E., C.R. Acad, supra; (LeBihan, D~, Breton, E., C.R. Acad. Sc (Paris;) 301, 1109-1112 ~1985) LeBihan, D. Breton, E. Lallemand, D., Cabanis, E~, Laval-Jeantet supra)). The effect of molecular diffusion in the presence of a magnetic field gradien~ on MR spin-echo signals was described long ago (Hahn, EoL~ r Phys. Rev.
80:580 (1950). Diffusion produces a pure amplitude attenuation of the MR signal due to the loss of phase coherence between processing spins produced by their random walk through the gradient~ Thi~ amplitude attenuation A depends only on the diffusion coefficient D
and the gradient so ~hat A = exp ( -b.D) (4) ~ where b is a gradient factor which can be calculated from - gradient characteristics (strength and dura~ion) (LeBihan, D., Breton, E.A., C.R. Acad Sc, (19853 supra;
LeBihan, D. Breton, E., Lallamand, D., Grenier, P., Cabanis, E., Laval-Jeantet, M., supra; Hahn, E.L., supra;
Carr, Y.Y. and Purcell E.M. supra; Stejskal, E. Tanner J.E., J. Chem. Phys 42:288 (1965)).
Stejskal and Tanner, supra, introduced a diffusion measurement method that used pulsed magnetic field gradients, thereby improving the sensitivity of the measurements and allowing smaller values of diffusion coefficients to be determined. More recently, these concepts were extended to MRI (LeBihan, D., Breton, E., ; Lallemand, D., Grenier, P., Cabanis, E. and Laval~
J~antet, M. supra) and applied to a diffusion mapping method based on two MR images differently sensitized to diffusion by the presence of specially designed gradient .
. -~3~2~0 _ 15 -pulses (LeBihan, D., Breton, E., Lallemand, D., Grenier, P., Cabanis/ E. and Laval~Jeante~, M, supra; LeBihan, A.
and Breton, E. Under these conditions, the difusion image is derived from Dx y-Log(A2x,yJA1x,y)/(bl b2) ( ~
where bl and b2 are the calculated gradient factors in both images, and ~2/A1 i~ the amplitude attenuation ratio equal to the signal amplitude ratio of both images because both ima~es are identical with respect to all the o~her MRI parameters.
The method of the invention has been testad a~
different temperatures which are permissi~e to the human body. One such test is provlded in the example hexe-below. These tests demonstrate the ability of ~RI to measure temperature changes using molecular diffusion imaging.
The sensitivity of the present method for temperature determination using diffusion i5 at least twice that of available prior art procedures using Tl (Parker~ D.L., Smith, VOI Shelton, P.; supra; Dickinson, R.J., Hall, A.S., Hind, A.J., Young, I.R., supra;
Bottomley, P.A., Forster, T.H. Argersinger, R.E. and Pfeifer, supra; U.S. Patent 4,558,279.
Thîs increased sensitivity may be ascribed to the basic relationship betwe~n diffusion, Tll and temperature. Tl relaxation depends in part on diffusional processes. However, in biological tissues, the diffusion term that predominates in T1 is rotational diffusional which is 1.5 times less sensitive to temper~
ature than translation diffusion (Abrogam, A., Principle Nuclear Magnetism (Oxford U. Prass., London) (1961).
Further~ore, thexe are other contributions to T1 so that its temperature dependence may not be simple (Abrogam, E.O., supra).
In addition, T1 de~erminations using MRI are of~en inaccurate because of difficulties in obtaining homogenous MR radiofre~uency fields through the imaged .'~

,, 222~0 slice (Young, I.R., Bryant, D.J. and Payne, J.A., Magn.
Reson. Med. 2:355-389 (1985). These difficulties dis-appear when using the present diffusion imaging method because it uses two MR imaging sequences identîcal as far a~ the radiofrequency field is concerned LeBihan, D., Breton, E.D, (1~35) supra; (LeBihan, D., Breton r E . ~
Lallemand, D., ~renier, P., Cabanis, E. and Laval-Jean~et, M. supra; LeBihan, D. and Breton, E., supra) Under these conditions, the signal imperfections will cancel each other.
This me~hod can be applied in-vitro and in-vivo for instance during clinical hyperthermia treatments.
Moreover, the relationship of equation (3) between T and D applies to biological tissues as well as the material of the sample in biological tissues. Measured diffusion ; coefficien s can be affected by restricted diffusion phenomena related to compartmental effects on water mobility (Stejskal, E.D., J. Chem Phys. 43:3597 (1965~.
Moreover, the non-Brownian character of restricted dif-fusion may affect its relation with temperature. How-ever, res~ricted diffusion effects are limi~ed if neces-sary by shortening the diffusion measurement times (echo time TE).
Furthermore, the use of Eq. (3) for temperature measurement assumes the previous determination of ~he acti~ation energy ~ in biological tissues, that there is a smaller variation in E between the same ti~sue in dif-ferent subjects, and that there are substantially no hysteresis effects when the temperature increases up to 42C and then decreases back to 37C contrary to what was found for the temperature dependence of T1 (Lewa, C.J., Majeska, Z., Bull Cancer (Paris) 67:515-530 (1980)).
In vivo diffusion coefficients should be measured with extreme care. These measurements may b~
affected by other intravoxel incoherent motions of water present in biological tissues as well known in the art (LeBihan, D., Breton, E., Lallemand, D., Grenier, P., ~,~
:

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Cabanis, E. and Laval-Jean~et, M., supra). In par~icu-lar, the separation of the contributions of diffu~ion from that of blood microcirculation must be achieved using a known appropriate algorithm (LeBihan, D., Breton, E., Lallemand, D., Aubin, M.L., Vignaud, J. and Laval-J~antet, M., Radiology 186:497 (1988~. On the other hand perfusion imaging may be very useful in hyperthermia studies, blood circulation having an important role in thermal clearance (Hahn, G.M., Physi.cs and Technology of Hyperthexmia pp. 441-447, Martinus Nijhoff Publishers, Boston). However, other NM~ me~hods able to generate diffusion images can be used for temperature imaging, for instance, methods using stimulaked echoes (Merboldt, K.D., Manicke, W., Maase, A.J., Magn~ Reson 64-81 (1985) or methods using Steady-State Free Precession (LeBihan, D.) Magnetic Resonance in Meidcine 7, 346-351, 1988).
More specifically, the method of the invention is a method of determining and imaging the temperature or the temperature change of an object (human, animal, liquid or solid) by nuclear magnetic resonance of molecular diffusion coeff.icients which comprises (a) placing the object in a magnetic field Bo at a temperature To;
(b) subjecting the thu positioned object to a first series of magnetic resonance imaging sequences to obtain first numerical valu~s or images of molecular diffusion coefficients Do for various points of the object or of a limited volume thereof;
(c) maintaining the object or part of the object including the points measured in step (b) at a temperature or waiting for a spontaneous change to said temperature T in said part of the object;
(d) subjecting the thus positioned object to a second series of magnetic resGnance imaging sequences to obtain values or images of molacular diffusion coefficients Di for the same points of the object or of a limited volume thereof measur~d in step (b);

, , ~

13~22~

(e) compar.ing point-by-poin~ the values of the diffusion coefficients Do allocated for the first series measured in s~ep (b) with the values of the diffusion coef-ficients Di obtained in the second series obtained in step (d) in order to determine and to generate a third series of images representing temperature changes dTi between steps (b) and (d) for each point of the object or of a limited volume of the object measured in steps (b) :: and (d) from the formula dTi = (kTo2/E) Log (D/Do)i wherein k is Boltzman's constant (1.38 10-23 J/K) and E
is the activation energy (~0.2 eV at 20C), provided dT
<c To and E ~ constant;
(f) repeating steps ~c) to (e) continuously so that temperature changes dTi can be monitored continuous-ly;
(g) determining the absolute temperature T o for each measured point of the object or of a limited volume of the object so that by repeating steps (b) to 20 (f) the absolute temperature Tl can be determined and : volume thereof from the formula Ti = Tio + dTiwhere dT is determined and imaged in scep le).
In a particularly useful embodiment of the method of the invention the magnetic field utilized is a constant magnetic field. Particulary suitable values for the magnetic field are about 0.2 T to lOT and more pre-ferably, 0.1 T to 2 T. However, othex values may also be utilized.
:~ 30 Suitable temperatures To to which the subject/ob~ect is exposed when practicing the present invention are (for water) from 0 to 100C, and more pre-; ferably 25 to 45C. The measuremen~s can be attained at ambient temperature as well.
In yet another particularly useful embodiment of the method, the series of magnetic reson~nce imaging sequences used to obtain measurements and images of '~' . . .

- 19 - ~322~2~
moleculax diffusion Call be Spin Echo seguences, Stimu-lated Echo sequence~ or Steady-State Free Precession sequences using gra~ient-recalled echoes.
The method using Spin-Echo~s is described in U.S.
Patent No. 4,780,674 filed on Dscember 24, 1985; and in LeBihan ~. and Breton E., supra; and in Lebihan D., Breton, E., Lallemand D., Grenier P., Cabanis E., Laval-Jeantet M., supra.
The method using Stimulated Echoes is described in Merboldt, K.D., Manicke W., Frahm J., J. Magn. Reson.
64:479-486 ~1985) The method using S~eady-State Free Precession i5 described in French Patent 2,621,693 filed on October 13, 1987. and in LeBihan, D., Magn.
Reson. Med., 7:346 (1988).

In a particular embodiment of the method of the invention, the calculation of the diffusion coefficients D and Do from Nuclear Magnetic Resonance sequences, as described for in the Spin Echo method, ~he StimulatPd Echo method and the Steady-State Free Precession method, can also be programmed and substituted direc~ly into the general formula for the tempera~ure shown as equation (3) ~o obtain the latter values directly and automatically~
In still another particular embodimenk of the method, the effects of blood microcirculation in living tissues can be eliminated and~or separat0d from the dif-fusion measurements using the 5pin-Echo method, the Stimulated Echo method or the Steady-State Free Pre-eSSiOTl method by using sequences with longer and/more powerful gradient pulses, described in U.S. Patent no. 4,780,674 filed on December 24, 1986 and French patent no. 2~621,693 filed on October 13, 1987 and in LeBihan, D., Breton, E., Lallemand, D., Aubin, M.L., Vignaud, J., Laval~Jeantet, M., supra, the 'r'~`'~

` 132222~

In Another particular em~odiment of the method, the efects of blood pulsations in diffusion measuremen~s and images are eliminated in living tissues bya synchronization of the NMR excitation sequences and recording of NMR signals with the heart beats of the living objects, as de~cribed in U.S. patent application serial No. 07/100,261, now Patent No. 4,809,701.
: In another embodiment of the m~thod, the diffu-sion and derived temperature measurements and images are obtained in any part of the object, in any orientation and one-, two-, three dimensions.
In a particularly useful embodiment of the invention, the method is conducted in a manner such tha~
steps ~b), (d) and (e) are conducted with the aid of a computer program. If the NNR appara~us is conn~cted to a computer and appropriate software is in placs the calc~
lations encompassed by the method may be conducted auto-matically and a plot of temperature vs. location in a three dimensional space may be produc~d automatically.
In another particularly u~eful embodLment of the method, the diffusion coefficients measuxements and images, and their deri~e~ tempexature measurements and ~: image~ can be obtained from other molecules than watex, although water i5 preferably used. The method can be applied ~o any molecule which can be studied by NM~. For instance, but non-limitatively, molecules containing hydrogen such as fat or lactates can be used. Similarly, compounds containing 31p, 23Na, 13C or 19F, among others, -; can be u~ed.
The method of the invention may be applied to the indirect determination of tempera~ure~ in objects and subjects such as animals, and more preferably humans.
The diffusion images obtained can translate into temper-ature maps with an accuracy of less than 1 cm and a , ~ .,.

'~ ;
,, .

:~3222~

temperature certainty greater than 0.5C. No prior art method has attained these values.
Having now generally described this invention, the same will be better understood by reference to a S specif7c example, which is included herein for purposes of illustration only and is not intended to be limiting of the invention or any embodiment therof, unless so specified.
Examples l~ Diffusion values and the corresponding temper-ature images are obtained on a 0.5 Tesla whole-body MRI
system (Thomson-CGR Magniscan S000)* working at 21 MHz.
The tests are conducted to validate equation (3) above r representing the mathematical basis of the method of the invention and to check the sensitivity of the present MRI
diffusion method for non-invasive in-vivo temperature measurements.
A phantom is designed to have MRI parameters close to those of biological tissues with respect to water content, relaxation times, and diffusion coeffi-cient. It consists of a polyacrylamide gel (7.5 wt%polyacrylamide) doped with S mM copper (II) sulfate con-tained in a cubic Plexiglas R box (10 cm x 10 cm x 10 cm). The phantom is placed within the central homo geneous radio frequency field of a 30 cm diameter imaging coil which is used as both NMR transmi~ter and receiver.
A temperature gradient of about 1Ctcm i5 induced between two opposite faces of the phantom in the direction of the main magnetic field. This thermal gra~
dient is produced by water streams at two different tem-peratures circulating in compartments placed at opposite faces of the phantom. The phantom and the water compart-ments are encased in a block of polystyrene which affords thermal insulation. The temperatures are monitored using coppex-constant thermocouples placed within catheters located along the direction of the induced thermal gradi-ent. The temperatures To and T are measured respectively *Trade-mark ~ .

1 3 2 2 2 2 ~ !
_ 22 -before and during heating every 5 mm along the thermal gradient.
Diffusion ima~es are obtained as previously described in LeBihan D., Breton, ~., Lallemand, D., Grenier, P., Cabanis, E., Laval-Jeantet, M., Radiology 62:401 (1986); LeBihan, D. and Breton, F., D.R. Acad~ Sc.
(paris) 301:1109 (1985), U.S. patent no. 4,780,674 filed on December 24, 1986 from two dif-ferent diffusion sensitized spin-echo images (repetition time TR=800 ms, echo time TE=140 ms, lZ8 x 128 acqui~i-tion matrix) allowing images to be obtained with a 2 mm x 2 mm spatial resolution. The acquisition time for each image is 3 min 25 s.
These diffusion images are calculated in real time from the spin-echo images according to equation (5) above using a computer program loaded on a DEC VAX 11/730 computer coupled with a MSP-3000 array processor. Dif-fusion images are obtained before and during the presence of the thermal gradient.
The relative changes in the diffusion coefi-cients D are then averaged from the diffusion images every 5 mm in the direction of the thermal gradient using 0.8 cm regions of interest (ROI). The following two ;~ series of tests are performed: ~-ll) the first test i5 centered about room temperature (To=23.8C), and (2) the second test centered about normal body temperature ~To=36.7C) at which the gel is first uni-formly heated.
A plot of the relative change (D-Do)/Do in the diffusion coefficient with (T-To) is shown in Figure 1 (corre~ponding to the second test). As expected, the relation i~ found to be linear. The activation energy E
of water in the gel is ob~ained from the slope of the ~ 35 plot using equation (3) above. The values obtained are : O.212 0.004 eY at To=23.8C and 0.54~0.004 eV to To=36.7C. The values obtained agree very well with * Trade-mark , ~

.: . . , - , , ., . .

~32222~

published data (0.21 eV at 20C) normally associated with the diffusion coefficient of water (Simpson/ J.~., Carr, H.Y., Phys. Rev. 111:1201-1202 (1958~).
The diffusion coefficient Do is 1.76 x 103 mm2/s and 2.22 x 103 mm2/s at 23.8C and 36.7C, respectively. The measuremen~ error in determining the relative change in the diffusion coefficients D using 0.8 cm2 ROIs is 1~ which corr~sponds to a 0.5C uncertainty for the temperature.
The invention now being fully described, it will be apparent to one of ordinary skill in the art that many changes and modifications can be made there~o with-out departing from the spirit or scope of the invention as set forth herein.

Claims (22)

Claims

1. A method of determining and imaging the temperature or the temperature change of an object by nuclear magnetic resonance comprising (a) placing the object in a magnetic field Bo at a temperature To;
(b) subjecting the thus positioned object to a first series of magnetic resonance imaging sequences to obtain first numerical values or images of molecular diffusion coefficients Do for various points of the object or of a limited volume thereof;
(c) maintaining at least part of the object including the points measured in step (b) at a temperature T or waiting for a spontaneous change to said temperature n said part of the object;
(d) subjecting the thus positioned object to a second series of magnetic resonance imaging sequences to obtain second numerical values of molecular diffusion coefficients Di for the same points of the object or of a limited volume thereof measured in step (b);
(e) comparing point-by-point said first numerical values measured in step (b) with said second numerical value obtained in step (d) in order to deter-mine and to generate a third series of values representing temperature changes dTi between steps (b) and (d) for each point of the object or of a limited volume of the object measured in steps (b) and (d) from the formula dTi = (kTo2/E) Log (D/Do)i wherein k is Boltzman's constant (1.38 10-23 J/K) and E
is the activation energy (?0.2 eV at 20°C), provided dT
<< To and E ? constant;
(f) repeating steps (c) to (e) so that temperature changes dTi can be monitored;
(g) determining the absolute temperature T? for each measured point of the object or of a limited volume of the object so that by repeating steps (b) to (f) the absolute temperature Ti can be determined and volume thereof from the formula Ti = Tio + dTi where dT is determined and imaged in step (e).

2. The method of claim 1, wherein the dif-fusion coefficients D and Do are determined from Nuclear Magnetic Resonance Spin-Echo sequences.

3. The method of claim 1, wherein the dif-fusion coefficients D and Do are determined from Nuclear Magnetic Resonance Stimulated Echo sequences.

4. The method of claim 1, wherein the dif-fusion coefficients D and Do are determined from Nuclear Magnetic Resonance Steady-State Free Precession sequences.

5. The method of claim 1, wherein the object is selected from the group consisting of living objects.

G. The method of claim 5, wherein the living object is an animal.

7. The method of claim 6, wherein the animal is a human.

8. The method of claim 5, wherein the Nuclear Magnetic Resonance excitation sequences and recording of the Magnetic Resonance signals are synchronized with the heart beats of the living object.

9. The method of claim 5, wherein the dif-fusion values are freed from blood microcirculation interference by using longer and/or more powerful field gradient pulses in the Nuclear Magnetic Resonance sequences obtained from Spin Echo sequences.

10. The method of claim 5, wherein the dif-fusion values are freed from blood microcirculation interference by using longer and/or more powerful field gradient pulses in the Nuclear Magnetic Resonance sequences obtained from stimulated Echo sequences.

11. The method of claim 5, wherein diffusion measurements are freed from blood microcirculation inter-ference by using longer and/or more powerful field gradient pulses in the Nuclear Magnetic Resonance sequences obtained from steady state free precession sequences.

12. The method of claim 1, wherein the object is selected from the group consisting of solid and liquid objects.

13. The method of claim 1, wherein the dif-fusion values and temperature measurements derived there-from are processed into a one-, two- or three-dimensional image.

14. The method of claim 13, wherein the dif-fusion values and the temperature measurements derived therefrom are obtained for any desired part of the object.

15. The method of claim 13, wherein the dif-fusion values and the temperature measurements obtained therefrom are obtained for any orientation of the object.

16. The method of claim 1, wherein steps (b), (d) and (e) are conducted with the aid of a computer program.

17. The method of claim 1, wherein the overall thermal state or thermal change of an object is deter-mined.

18. The method of claim 1, wherein a thermal state or a thermal change in an animal is determined.

19. The method of claim l wherein the temper-ature of a medium comprising a compound selected from the group consisting of water, fat molecules, lactates, or lactic acid molecules, 31p compounds, 13C compounds and 19F compounds is determined.

20. The method of claim 19 wherein said medium is water.

21. The method of claim 1, wherein said first numerical values are processed into a one, two, or three-dimensional image.

22. The method of claim 1, wherein said second numerical values are processed into a one, two, or three-dimensional image.