Slide
1 and Slide 2:
Thank you David for giving me this opportunity to address the membership
of the ISMRM about UHFMRI and heat transfer in solids, liquids and
gases. UHF MRI at 8 Tesla
is characterized with excellent signal to noise and lower than expected
RF power requirements.
Slide
3 and Slide 4:
In the left slide, a high resolution image obtained at 8 Tesla is
displayed. This image is
surprisingly homogenous. It reveals a great deal of vascular details as
demonstrated in the expanded version on the right.
Slide
5 and Slide 6:
For comparison, a low flip angle gradient recalled echo1.5 Tesla image
is shown on the left with a 512 x 512 resolution and a 2 mm slice
thickness. On the right the
comparable 2k x 2k image obtained at 8Tesla is presented.
While this image has 16 times the resolution it easily surpasses
the 1.5 T image in terms of ISNR.
Slide
7 and Slide 8:
Another example is displayed here, along with its expanded
version. Now, lets get to
the question at hand. What
is the underlying explanation for the excellent ISNR at 8 Tesla.
I believe, unlike my colleagues, that the answer can only come
from a complete review of Thermal processes.
Slide
9 and Slide 10:
Thus, to fully understand MRI, it is important to reexamine what
it means when we say that NMR is a thermal process.
This, of course, brings us back to Planck.
Most believe that Planck’s work is relevant only in the
infrared. Such a limitation
however is without scientific basis.
In fact, everything depends on the phase and nature of what is
being studied.
Slide
11 and Slide 12:To
understand Planck, lets consider a non-metallic solid at 0 K.
This solid has no energy within it other than relativistic
energy, which we ignore for our discussion.
Now, lets place a hypothetical little heat engine inside the
solid. The heat engine is
acting as a heat source. As
the solid is heated, the atoms begin to vibrate, filling the vibrational
degrees of freedom. These
vibrations are associated with the phonons within the solid.
As soon as the atoms begins to vibrate, the solid will
try to dissipate its energy, both within the lattice through thermal
conduction and to the outside world through thermal emission.
The later is the cause of noise in NMR.
Slide
13 and Slide 14:
As more heat is dumped into the solid, thermal conductivity will try to
bring to entire solid to the same temperature.
This is also making recourse to phonons and the vibrational
degrees of freedom.
Slide
15 and Slide 16:
Some emitting solids, can be considered a blackbodies.
For such a body, Kirchhoff’s Law of thermal emission states
that emissivity will depend only on the frequency and temperature. An
object is considered a blackbody if it perfectly absorbs radiation
incident on its surface. Kirchhoff’s law, formulated in 1859, was
thought by Planck to be universally applicable. However, I believe that
Kirchhoff’s law is properly applied in a very limited range and only
to certain solids. In the
mid-1800’s graphite was used as a blackbody since it could produce
reasonable results in the regions of interest.
However, when Kirchhoff’s Law was formulated, very little was
know about matter. Indeed,
scientists were writing papers rating the quality of black paints for
producing blackbodies. At
this stage, it was discovered that some objects were graybodies with an
emissivity lower than theoretically predicted.
Slide
17 and Slide 18:
The total emission for a blackbody (or the area under the curve)
increases as the fourth power of the temperature.
This is summarized in Stephan’s Law of Emission.
The peak of emissivity is also related to a temperature, called
the Wien’s temperature, by a relationship called Wien’s Law of
Displacement.
Thus, if the peak of the emission is known, so is the Wien
temperature. Note however
that this Wein’s temperature was set only by the vibrational degrees
of freedom.
Slide
19 and Slide 20:
Planck formulated the equation for blackbody radiation in 1900.
This equation quantized physics and brought us the dual nature of
all electromagnetic radiation. The
classical region of Planck’s blackbody radiation curve is called the
Rayleigh-Jeans region. It
is in this region that the classical Maxwell treatment holds.
Beyond this limit however, Maxwell’s equations collapse since
these equations are not quantized.
Slide
21 and Slide 22:
Thus we see in this slide the full Planckian treatment for noise
voltage produced by a graphite resistor.
If the resistor is considered a blackbody, then this equation for
noise voltage will be valid over the entire spectral range.
The equation for Johnson’s noise is displayed in the right
slide. This equation is
actually the Rayleigh-Jeans limit of the Planckian equation for noise in
a graphite based resistor. The
question then becomes if and when this equation is valid in NMR.
Slide
23 and Slide 24:
In these two slides the normal spectral emissivity is ploted for various
forms of graphite under varying conditions both as a function of
temperature at one frequency (on the left) and as a function of
wavelength (on the right). Ideally
of course, for a perfect blackbody, normal spectral emissivity should be
1 under all circumstances. We
clearly see in these plots however that this condition is not achieved
even with graphite. As
such, the Johnson’s noise equation has limited validity even for a
substance always considered to very closely approach a blackbody.
So now, what about the validity of applying such an equation for
the human body, for liquids in general and for gases?
Slide
25 and Slide 26:
As more heat is dumped into our system, a point will eventually be
reached where thermal conductivity can no longer handle the increased
heat. The atoms can no
longer increase their vibrations. The
vibrational degrees of freedom are filled.
As seen on the right, thermal conductivity thus rises to a
maximum and then begins to drop. The
solid must find other degrees of freedom to handle the inflowing heat.
Eventually, therefore, our solid either melts, or in the case of
graphite, sublimes.
Slide
27 and Slide 28:
Melting or sublimation brings in both translational and
rotational degrees of freedom. The
atoms gain absolute translational motion within the lattice as depicted
in these two slides. Little
if anything is known about thermal emissivity in liquids.
Although unlike most solids, emissivity in the few liquids
studied (things like molten sodium for instance) does not increase with
temperature. This fact
provides for our society an important caution.
Physics knows essentially nothing about thermal emission from a
liquid. As such, there is
no physical evidence what so ever justifying the application of the
Johnson’s noise equation for liquid samples and especially for human
tissue. I highlight, that
liquids cannot produce a Planckian spectrum reporting a correct
temperature since most of the energy in a liquid is likely to be tied up
not in vibrational degrees of freedom but rather in translational and
rotational degrees of freedom. The rotational and translational degrees
of freedom are not associated with vibrational phonons and as such, they
have no means of supporting Planckian thermal emission.
Slide
29 and Slide 30:
Let us turn for an instant to RF power requirements in MRI.
It turns out that this power is directly related to the noise
power. Indeed, RF power can
be viewed as the absorptive component and noise power as the emissive
component. Both of them are
tied to the same processes within the lattice.
Now, prior to the arrival of the 8 Tesla system, several groups
had theorized that RF power in MRI would increase with the square of the
field. Balaban and his
group confirmed this up to 4 Tesla using a surface coil placed on the
human chest. This behavior
of course constitutes Rayleigh-Jeans behavior.
To extend this behavior forever is a violation of thermodynamics.
Then, with the building of the world’s first UHF scanner, I
reported that RF power requirements where lower than expected at 8
Tesla. If we assume that
MRI is a thermal process, then we can use thermodynamics and set a
Wien’s displacement temperature for the MRI scanners of the world.
That temperature works out to be an extremely low temperature of
approximately 0.0025 K. Can
there be any justification for such an illogical Wien’s temperature?
Let us look at the two most important Planckian curves in nature
for guidance. The first
deals with the temperature of the sun’s photosphere, the second deals
with the temperature of the universe.
Slide
31 and Slide 32:
In the mid 1880’s, Langley measured the thermal emission of the
photosphere. Since that
time, the temperature of the photosphere has been held at ~6,000 K.
Now, physicists recognize that the interior of the sun is at
temperatures in excess of 10,000,000K.
The photosphere, which is only about 3,000 km thick is then said
to be at ~6,000 K. Finally,
the corona in the mid-1950’s was found to be at temperatures of 1-2
million degrees at 1.5 R. How
could it be that the photosphere was cooler than the corona.
Clearly, heat could not be crossing a cooler region to produce a
more distant hotter region.
Everyone recognizes that this would constitute a violation of
the 2nd law of thermodynamics.
As such, in order to maintain Langley’s 6,000K temperature,
physicists are now searching for two means of producing heat in the sun.
The first is thermal nuclear energy within the sun.
However, they are also telling us that massive amounts of heat
must be produced independently in the corona as a result of ion flow
through magnetic fields. Moreover,
the photosphere simply cannot be heated.
But what if the photosphere is reporting an incorrect
temperature? The sun is
known to have huge convection currents.
It is much more reasonable that the real temperature of the
photosphere is not 6,000 K but rather at least 1,000 times this value.
Like human MRI, the photosphere may well be providing an example
of an unreasonably low Wein’s temperature.
This might well occur however in a liquid photosphere.
Slide
33 and Slide 34:
The second most important thermal curve is that discovered in 1965 by
Penzias and Wilson and assigned to the temperature of the universe.
Could it be that there is something wrong with this curve as well
and that it also reports an incorrect temperature.
Let us briefly recall the story.
In the mid-1960’s astrophysists discovered a source of thermal
noise at 3.5 K and assigned this temperature to a cosmic origin.
After all, nothing on earth was at 3 K.
The COBE satellite would end up providing for us a map of this
radiation. The signal to
noise on the data mapping the so-called temperature of the universe was
so high that the error bars are lost in the linewidth of the theoretical
curve. Indeed,
astrophysicist have had to cope with the fact that there was not enough
matter in the known universe to account for this ISNR.
Now, physics believes that they have measured the temperature of
the entire universe with a signal to noise beyond the dreams of anyone
who has ever used an NMR spectrometer.
What if this signal has nothing to do with the universe, but
rather, that it is of liquid origin?
Indeed, what if the oceans are reporting a Wein’s temperature
of 2.725 K and that is why they have such a high SNR.
The earth’s oceans may well be the source of this signal.
Once again this would provide an example of an unreasonably low
Wien’s temperature as a result of a liquid sample.
So
you see that there are at least two other areas in physics were
illogical Wien’s temperatures may indeed be present as a result of
liquid samples. Let us now
close by looking briefly at gases.
Slide
35 and Slide 36:
In these two slides the total emissivity for CO2 and water vapor
are displayed as a function of temperature for various pressures.
Remember in the solid that total emission had followed
Stephan’s Law moving with the fourth power of the temperature.
In sharp constrast, in gases, emissivity can actually drop
sharply with temperature. Stephan’s
law fails, and with it Kirchhoff’s law, Wein’s Law and Planck’s
law. All these laws break
down in gases. Indeed, if
you look for a Planckian spectrum reporting a correct temperature from
either a liquid or a gas you will not find such curves anywhere.
Slide
37 and Slide 38:
Importantly, gases do not behave in a Planckian manner.
Diatomic gases absorb radiation in several bands corresponding to
quantized rotational-vibrational modes that are either fundamental (as
shown on the left side) or overtones (as shown on the right slide).
Slide
39 and Slide 40:
Polyatomic gases absorb radiation in complex manner with bands of
absorption at various frequencies as show in these two slides and the
next two slides (Slide
41 and Slide 42).
In these slides we see the absorption bands for various gaseous
molecules. Note that in no
case is a Planckian spectrum obtained.
As such, experimental evidence indicates that gases simply
cannot produce Planckian absorption (and consequently emission) under
any circumstance. We
therefore see that the equation for Johnson’s noise cannot be applied
under any circumstances when dealing with gases.
Slide
43 and Slide 44:
I close by reminding everyone that Felix Bloch referred to the T1
relaxation constant as the Thermal Relaxation constant.
MRI is first and foremost a thermal method.
Along with T1 relaxation, signal, noise, RF power and RF
penetration are properly viewed as thermal properties.
Slide
45, Slide 46
and Slide 47:
Conclusions
This
lecture was presented on Monday June 25, 2001 to the International
Society of Magnetic Resonance Meeting on the Limits of Signal Detection
held in Berkeley, CA.
Published
Electronically on June 23, 2001
www.thermalphysics.org