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Patent No. 4324255
Method and apparatus for measuring
magnetic fields and electrical currents in biological and other systems (Barach,
et al., Apr 13, 1982)
Abstract
A method and apparatus for measuring magnetic fields and electric current flow in biological systems and other systems employing a room temperature pick-up probe connected to a superconducting quantum interference device (SQUID).
Notes:
Description
This invention relates generally to a method for measuring electric currents
produced in biological systems such as nerve and muscle fibers by measuring
the magnetic field produced by such currents.
The prior art can be divided into three distinct areas: the measurement of biological
magnetic fields, the direct measurement of the electric currents associated
with nerve and muscle tissue, and the measurement of electric currents by measurement
of their magnetic field.
Present day Superconducting Quantum Interference Device (SQUID) magnetic field
detectors built for biomagnetic measurements are limited in that the magnetic
field sensing coils have to be operated at cryogenic temperatures and as a result
must be placed in an insulated vacuum enclosure such as a dewar. Because of
the thickness of the dewar walls, the coils are at least one cm from the magnetic
field source being studied. As long as the systems being studied are large as
compared to one cm, this is not a serious limitation. However, typical nerve
bundles, large single axons, and cardiac muscle fibers are approximately 0.5
mm in diameter, so that at a distance of one cm, the peak magnetic field from
them is on the order of 1 picoTesla (pT). This field strength is barely at the
level of detectability for a SQUID operating with a 1 kHz bandwidth. Furthermore,
many details of the spatial variation of the magnetic field outside the nerve
are not observable at distances greater than several nerve radii. While such
a SQUID magnetometer can detect the magnetic field of an isolated frog sciatic
nerve, its one cm coil-to-nerve separation, the intrinsic SQUID noise and environmental
noise preclude any detailed or useful measurements.
These difficulties have been overcome by the present invention, which uses a
small room temperature toroidal coil placed around the nerve, with the toroid
connected to the SQUID. By detecting the magnetic field within one mm or less
of the nerve surface rather than at one cm, a hundred-fold or larger increase
in field strength can be obtained. The resulting combination of a room temperature
toroidal coil and a superconducting magnetometer has sufficient spatial resolution
and sensitivity to detect the 100 pT magnetic field of an isolated frog sciatic
nerve with at least a forty-to-one signal to noise ratio (with signal averaging
less than 1000 repetitive signals). If this measurement was attempted with a
conventional SQUID magnetometer as used for measuring biomagnetic fields from
the heart, the sensitivity of the SQUID magnetometer to external magnetic noise
would require that the measurements be made in a magnetically quiet environment.
The present invention overcomes this limitation because the toroidal pickup
coil is insensitive to magnetic field sources external to the toroid and it
is possible to shield the SQUID sensor from magnetic noise and thereby utilize
its full 6.times.10.sup.-12 A/Hz.sup.-1/2 sensitivity for measurements in a
typical laboratory.
Furthermore, by using a toroid split into two semicircular halves, it is possible
to clip the toroid around an exposed nerve or muscle fiber in vivo without requiring
access to one end for threading through the toroid. Thus, this invention provides
a means for measuring the magnetic field from electric currents as small as
10.sup.-8 Amps with a 500 Hz measuring bandwidth.
Much of the knowledge about the function of nerve and muscle cells has come
from measurement of the electric fields that they produce when stimulated. However,
it has proven difficult to measure electric current flow within these cells.
It is possible to use voltage clamp techniques to measure transmembrane currents
in large nerve axons, but a serious assumption must be made. These measurements
of currents cannot be made during an action potential but must be measured when
the transmembrane potential is held (clamped) at a particular fixed value. If
has been assumed that the currents and membrane conductance are the same in
the clamped state as during the action potential. In this invention, the internal
currents are measured directly and can be determined during an action potential.
If a transmembrane potential is measured simultaneously, it is also possible
to compute the instantaneous membrane conductance. The voltage clamp technique
per se cannot be applied to cardiac muscle, but the corresponding sucrose gap
techniques for muscle often lead to ambiguous results. Also, muscle contraction
following stimulation can break the microelectrodes.
The apparatus of the present invention is easier to use than a glass microelectrode.
The toroid pickup coil and SQUID sensor combination of the present invention
is significantly more sensitive than previously available current measuring
devices and has the added advantage of not requiring puncture of the cell membrane.
For example, it will be possible to monitor the function of nerves exposed during
surgery without damage to or puncture of the nerve. The toroidal coil of the
present invention can be surgically and permanently implanted around an intact
human or animal nerve for monitoring the function of that nerve, either for
diagnostic purposes or for controlling a prosthetic device. If the nerve is
in fact a bundle of smaller nerve fibers, the magnetic measurement will be able
to detect all of the fibers with more uniformity than could electric potential
measurements on the outside of the nerve bundle.
Furthermore, the apparatus allows bioelectric signals to be monitored directly
in the conducting fluid; unlike electrical signals, they are not shorted out
by high conductivity fluid surrounding the nerve or muscle fiber. Nerves in
air may produce millivolt potential differences along their surface. Immersed
in a solution or medium with an electrical conductivity typical of living systems,
a nerve will produce potentials on the membrane surface that are on the microvolt
level. Thus, it is difficult to measure electrical signals of intact nerves.
The magnetic method described by this invention functions when the nerve is
immersed in conducting fluid, and is ideally suited for studying intact nerves
in vivo. Equally important, this technique measures current density directly
(properly it measures curl J but in simple axon geometries one uses Stokes'
theorem at once) and allows determination of current profiles without assumptions
about conductivity and electric boundary conditions that are necessary to unfold
the nerve current from voltage recordings. Since the magnetic trace is very
close to an actual current measurement, it is therefore a particularly strong
complement to the electrical record.
Although the electrical potentials produced by a propagating nerve action potential
have been measured, the accompanying magnetic fields have never been observed
directly prior to this invention. The failure of previous attempts is readily
understood. The nerve action potential has the form of a moving, azimuthally-symmetric
solitary wave which can be modeled as two opposing current dipoles driven by
a potential change on the order of 70 mV. The peak currents range from 5 to
10 .mu.A. The external magnetic field B can be estimated using Ampere's law
in which I is the net axial current enclosed by a closed path of integration
c: ##EQU1## If the nerve is immersed in a conducting medium, the maximum magnetic
field of 100 pT occurs at the nerve surface (r<0.3 mm for nerve bundles,
r<<0.3 mm for single vertebrate nerves), with the particular detailed
values depending upon the preparation used. The nerve is physically small and,
moreover, the current distribution outside the nerve is largely quadrupolar
so that the field falls off steeply with distance. Thus the magnetic field will
decrease in proportion to (r/R.sub.n).sup.-f where r is the distance from the
nerve, R.sub.n is the nerve radius, and 1<f<3. As the distance from the
nerve is increased, an increasing fraction of the external current returns within
c, so that the field at 1 cm is a few pT and decreases thereafter in proportion
to the inverse cube of the distance. The weakness of the magnetic field, its
rapid falloff with distance, and the required 1 to 2 kHz bandwidth place the
signal at the limit of detectability of magnetometers currently used for biomagnetic
measurements.
Room temperature coils and conventional amplifiers have been used to obtain
signals interpreted as the magnetic field from the action potential of an isolated
frog sciatic nerve. These signals did not exhibit the expected reversal of polarity
upon reversal of the direction of impulse propagation, which lead the investigators
and others to question the validity of the results.
Because sciatic nerves produce readily measured potentials only if the nerve
is in air, these investigators attempted to measure the magnetic field of a
nerve supported in air. As a result, all of the electrical currents were confined
to the nerve bundle and the coaxial layer of moist electrolyte surrounding it.
As a consequence, there was no magnetic field in the air outside such a nerve.
The previous attempts could not have detected a magnetic field and did not.
These previous measurements were also sensitive to capacitative coupling, since
three electrostatically-shielded pickup coils of adequate sensitivity were unable
to detect the magnetic field of a moist nerve in air.
This invention avoids these difficulties by using a nerve naturally immersed
in a natural, conducting medium.
The apparatus of the present invention has several major advantages over previous
magnetic devices to measure weak electric currents. The most important is its
high sensitivity to currents threading the toroid and low sensitivity to external
currents and their magnetic fields. Prior art devices that utilize toroidal
pickup coils to measure currents have all used conventional vacuum-tube or semiconductor
amplifiers to measure the voltages induced in the pickup coil. For a fixed amount
of current passing down a wire or nerve threading a toroid, the signal-to-noise
ratio is determined by the effective radius of the toroid, the number of turns
in the coil, the Johnson noise in the coil and the amplifier noise. There are
several design criteria that result in compromising tradeoffs. First, the toroid
dimensions should be small to allow coupling to the large magnetic field close
to the surface of the nerve or wire. Secondly, conventional vacuum tube or semiconductor
amplifiers are optimized for measuring voltages across sources with a high resistance.
The impedance matching criteria can in theory be met by utilizing a large number
of turns of wire in the coil, but as the number of turns increases, so must
the size of the toroid. Decreasing the wire size to allow small toroids results
in a corresponding increase in coil resistance. Furthermore, a large number
of turns introduces significant capacitance, which combines with the necessarily
large inductance of the detector to form an LC resonant circuit with extremely
limited band-pass and impulse response characteristics. As a result, it is difficult
to build a toroid/conventional amplifier system capable of detecting currents
smaller than 10.sup.-6 amps in the bandwidth of 1 Hz to 2 Khz. These limitations
are overcome by the present invention, since the SQUID is optimal for measuring
currents from sources with a large inductance and a low resistance. Thus toroids
can be constructed with only a small number of turns, thereby minimizing the
resistance of the coil with its associated Johnson noise and allowing construction
of extremely small toroids of high sensitivity.
It is an object of this invention to provide an improved method and apparatus
for measuring the magnetic fields and electric currents in nerves, muscles,
and other electrical systems.
It is another object of this invention to provide a method for determining the
instantaneous conductance of a nerve membrane.
It is a further object of this invention to provide a method for determining
the internal currents in nerve and muscle cells.
It is another object of this invention to provide an apparatus for measuring
the magnetic fields of biological systems.
It is another object of this invention to provide an improved, compact apparatus
for measuring weak electric current flow in wires and microcircuits.
The foregoing and other objects of the invention are achieved by an apparatus
including a supercooled vacuum enclosure containing a SQUID sensor and a room
temperature toroidal pick-up coil connected to the SQUID sensor.
FIG. 1 is a schematic diagram showing an apparatus in accordance with the present
invention including a toroidal pick-up probe surrounding a nerve or wire carrying
a current I.sub.o (t).
FIG. 2 is an equivalent circuit of a toroidal pick-up coil connected directly
to a SQUID.
FIG. 3 is an equivalent circuit similar to FIG. 2 with a transformer having
primary inductance L.sub.1 and secondary inductance L.sub.2 connected between
the pick-up coil and the SQUID.
FIG. 4 is a schematic diagram of a toroidal pick-up probe including a gap in
the toroidal core for detecting adjacent currents.
FIG. 5 is a schematic diagram of the apparatus used in measurements already
completed, with a nerve and pick-up core immersed in a conductive solution .
The apparatus of the present invention has three main parts as shown in FIG.
1: the toroidal probe 11, an impedance matching transformer 12 (optional), and
the SQUID sensor 13. The supercooled environment required for the operation
of the SQUID can be provided by a small cryogenic dip-probe to house the SQUID
sensor and to allow its operation in a liquid helium storage dewar flask. The
dip-probe consists of a 1/2 inch diameter metal tube approximately 1 m long
with the SQUID located in a super-conducting lead shield at the bottom, connected
to a junction box at the top via two small coaxial cables. One of these cables
connects the SQUID sensor to the SQUID electronics, the other connects the SQUID
to the toroidal pick-up probe 11. The dip-probe also contains a liquid helium
level detector to allow determination of the storage dewar helium volume without
removing the probe. Depending upon the inductance of the toroid coil and the
SQUID sensor, an impedance matching network or transformer 12 may be added between
the toroidal probe and the SQUID. The toroidal probe is operated at ambient
temperature and thus is not superconducting. The probe is connected to the impedance
matching network by a coaxial cable 16 to prevent currents from being induced
by stray magnetic fields. All or part of the impedance matching network can
be operated in the superconducting state at cryogenic temperatures to utilize
the absence of electrical resistance and the associated Johnson noise. If the
impedance matching transformer is not used, the coaxial cable can be connected
directly to the SQUID. In either case, care must be taken to prevent coupling
radio frequency interference to tne SQUID. The toroidal probe includes a core
18 with a winding 19. Ferrite toroids with a 2.6 mm diameter may be used for
the core, which supports the pickup coils 19. By using molypermalloy toroids,
higher permeabilities can be achieved, allowing the use of fewer turns without
an increase in the effects of stray inductance. Fabrication of the molypermalloy
cores is straightforward and only requires careful annealing prior to their
use. By fabricating cores split into two halves 20 and 21, it is possible to
make pickup coils that can be clipped around nerves, muscles, and other systems
carrying electrical current without damage or interruption of the system or
the current it carries. If desired, the entire core can be covered with a grounded
electrostatic shield or an insulating layer (not shown).
The equivalent circuit of a toroid connected directly to a SQUID current sensor
is shown schematically in FIG. 2. The toroid is represented by a voltage source
E.sub.T that corresponds to the emf induced in the toroid by the time varying
currents I.sub.o (t), FIG. 1, threading it, by an inductance L.sub.T, and by
a resistor R. The resistor has a Johnson noise voltage E.sub.R associated with
it. The leads connecting the toroid to the SQUID have an inductance L.sub.L
; the resistance of the leads is assumed to be contained in R. The SQUID is
treated as a perfect ammeter A with an inductance L.sub.S. The intrinsic noise
of the SQUID and its electronics are indicated by the voltage source E.sub.S.
For this analysis, we will assume that the SQUID noise appears only on the output
of the SQUID and does not reflect back into the input circuit.
The voltage induced in the toroid by a current I.sub.o sin (.omega.t) threading
the toroid can be determined by using Ampere's law to compute the flux linking
the coil and Faraday's law to obtain the amplitude E.sub.T of the sinusoidal
electromotive force given by
where N is the number of turns in the toroidal coil 19, .mu..sub.o is the permeability
of free space, .mu. is the relative permeability of the toroid core, t is its
thickness and r.sub.1 and r.sub.2 are the inner and outer radii of the toroid.
The inductance of the toroid is L.sub.T. The magnitude I.sub.1 of the current
induced in the circuit by the sinusoidal voltage E.sub.T is determined by the
impedance Z.sub.1 of the entire circuit
where the inductance L.sub.E1 is
Equation (3) shows that the circuit acts as a low-pass filter with the half-power
point occuring where .omega.L.sub.E1 /R=1. However, the voltage induced in the
circuit by the toroid, as given by Eq. (2), is proportional to .omega. so Eq.
(3) can be written as
This indicates that the entire circuit behaves as a high-pass filter for currents
I.sub.o sin (.omega.t) threading the toroid, with the half-power point at .omega.L.sub.E1
/R=1. At frequencies well above the half-power point, the last term on the right
approaches unity. In this limit, the current induced in the circuit is proportional
to 1/N times the current threading the toroid: the circuit serves as a 1:N step-down
current transformer so that less current is induced in the circuit than threads
the toroid. Since the SQUID is a current sensing device rather than a voltage
sensing one, it is important to maximize the current measured by the SQUID by
minimizing the number of turns on the toroid. The practical limit of this occurs
when the inductance of the coil coupling to the ferrite core approaches the
stray inductance of the circuit.
Given this description of the system response to current threading the toroid,
we can add the effects of noise to estimate the signal-to-noise ratio of the
system. The Johnson noise from the resistor can be described in terms of a spectral
power density.
where T is the absolute temperature and k is Boltzman's constant. The LR circuit
acts as a low-pass filter on this voltage, so that the spectral power density
of the noise currents is given by
This implies that the SQUID will detect signals preferentially at frequencies
above .omega.=R/L.sub.E1 and detect the Johnson noise preferentially below that
frequency. The effects of the noise is the output can be further reduced without
affecting the signal by limiting the output bandwidth of the SQUID to frequencies
above .omega.=R/L.sub.E1.
The intrinsic SQUID noise can be conveniently described in terms of an effective
noise power density <i.sub.S.sup.2 > at the input. Typically, input noise
current densities as low as 6.times.10.sup.-12 AHz.sup.-1/2 can be obtained
at 1 kHz. The total RMS noise current I.sub.N in a measuring bandwidth .omega..sub.1
<.omega.<.omega..sub.2 is thus ##EQU2## If we assume that the SQUID current
noise is white in the frequency range of interest, and that the Johnson current
noise is given by Eq. (7), then Eq. (8) can be integrated to yield
with the toroid cut-off frequency .omega..sub.o equal to R/L.sub.E1.
Equations (5) and (9) can be combined to estimate the ultimate sensitivity of
a toroidal coil to current threading it. The minimum detectable current (I.sub.o).sub.min
can be defined as the value of I.sub.o in Eq. (5) for which I.sub.1 equals I.sub.N
in Eq. (9), i.e.
This equation suggests the complexity of optimizing the system parameters. For
example, decreasing N will improve the sensitivity, but will decrease R, which
is some linear function of N and also decrease L.sub.T, which is a quadradic
function of N, thereby shifting the cut-off frequency .omega..sub.o. This equation
also provides the motivation for the high permeability core: it provides a large
inductance with few turns, which is crucial for high sensitivity and wide bandwidth.
To elucidate the nature of the dependence of (I.sub.O).sub.min on experimental
parameters, consider a case in which the bandpass is from .omega..sub.1 =.omega..sub.o
/2 to .omega..sub.2 =2.omega..sub.o, with .omega..sub.o =R/L.sub.E1. Further,
let us require that L.sub.T be large enough that it dominates L.sub.E1. Then
This equation shows that the best sensitivity occurs at the higher frequencies
from .omega.=.omega..sub.o to 2.omega..sub.o. To the extent that L.sub.T.perspectiveto.AN.sup.2
and that R.perspectiveto.BN, where A and B are constants, .omega..sub.o =(B/A)(1/N)
and (I.sub.o).sub.min rises as .sqroot.N so that the minimum turn number is
indeed desired.
A typical toroid has a 1.3 mm mean radius, a 1.2 mm thickness, and a .mu./.mu..sub.o
of 6800, for an L.sub.T of 27 .mu.H and an R of 0.1.OMEGA., giving a cut-off
frequency of .omega..sub.o =590 Hz. The RMS current noise I.sub.N in a 500 to
1500 Hz bandwidth is given by Eq. (9) and is 1.2.times.10.sup.-7 A, with the
Johnson noise power a factor of 10.sup.5 greater than that for the SQUID noise.
With this 1000 Hz measuring bandwidth, a 1000 Hz sinusoidal current of 6.1.times.10.sup.-7
A can be detected by the toroid with a unity signal-to-noise ratio. This represents
at least a three order of magnitude increase in sensitivity compared to commercially
available current probes. As we will now show, further improvements in sensitivity
can be realized by using an impedance matching transformer.
If a superconducting impedance matching transformer is added, the equivalent
circuit can be modified as shown in FIG. 3 to include separate primary and secondary
circuits connected only by an electromotive force E.sub.2 in the secondary due
to currents in the primary. Since we will assume the secondary to be super-conducting,
it has no resistance and thus it has a flat frequency response. The effective
inductance of the primary circuit will be ##EQU3## where L.sub.1 and L.sub.2
are the transformer inductances on the toroid and SQUID sides of the transformer,
respectively, and k is the transformer coupling constant which is equal to the
mutual inductance M divided by (L.sub.1 L.sub.2).sup.1/2. The second term in
the brackets accounts for the loading of the primary circuit by the secondary.
Similarly, the effective inductance L.sub.E2 of the secondary circuit will be
##EQU4## The current induced in the primary is given by Eq. (3). The voltage
E.sub.2 induced in the secondary is
The current induced in the secondary is
The minimum detectable signal is given by Eq. (10) with an additional multiplicative
factor of (L.sub.E2 /M), and the RMS noise current is given by Eq. (9) with
a factor of (M/L.sub.E2) multiplying the second term in the braces. For the
same SQUID and toroid inductances used previously, a transformer witn a primary
inductance L.sub.1 of 45 .mu.H, a secondary inductance L.sub.2 of 3.3 .mu.H,
and a coupling coefficient of 0.8 will provide a minimum detectable current
at 1000 Hz of 2.2.times.10.sup.-8 A in a 500 to 1000 Hz bandwidth, a factor
of five improvement over the unmatched case. Further improvements should be
possible by optimizing toroid and SQUID parameters.
The response of the toroid-SQUID system in FIGS. 2 and 3 to a time-varying current
threading the toroid is given by the differential equation describing the current
induced in the primary circuit
which can be integrated to yield ##EQU5## The second term on the right side
of this expression represents the correction that must be applied to the signal
to account for the low-frequency cut-off of the resistive pick-up coil.
There are several adaptations of this preferred embodiment that greatly extend
the utility of this invention. By immersing the toroid in a conducting medium,
it is possible to map out the electric current distribution in that medium.
By rotating the toroid about an axis through a major diameter, it is possible
to measure the steady current distribution as well as the time-varying one.
If the coil form, either in the form of a toroid or another shape, has a section
of its circumference with low magnetic permeability in contrast to the remainder
of the form with high permeability, possibly as the gap 23 provided in the core
18, FIG. 4, it will become sensitive to currents flowing adjacent to the low-permeability
section but not necessarily threading the form. While this will increase the
sensitivity to external fields, this modification will greatly increase the
flexibility of the method in that the coil could be brought up adjacent to a
nerve that has been exposed.
In summary, this invention provides a means for measuring weak electrical currents
in biological and other electrical systems by using a toroidal probe that detects
the magnetic field produced by the time-varying electric current passing through
the center of the toroid. If a wire or an electrically active biological preparation
is threaded through the toroid, the device can measure the net current being
conducted along the wire or preparation. If a split toroid is used, the device
can be placed around the wire or biological preparation without requiring access
to one end for threading through the toroid. For example, it will be possible
to use this device to monitor the functional integrity of an in vivo human nerve
bundle during surgery without damage to or puncture of the nerve bundle once
it has been exposed.
While the apparatus measures the magnetic field linking the ferrite core, Ampere's
law provides a one-to-one correspondence between that field and the net current
threading the toroid. Thus the system is the first to provide direct, quantitative
interpretation of biomagnetic signals in terms of their bioelectric current
densities. In the case of a single nerve axon, the current density within the
nerve axoplasm is several orders of magnitude larger than that immediately outside
the nerve. If a small toroid is placed around such a nerve immersed in a conducting
medium, the net current linking the toroid will primarily be due to intracellular
currents; most extracellular currents will flow outside the toroid. For this
reason, the system provides a technique for measuring intracellular current
densities without puncturing the cell membrane. This technique allows determination
of current profiles without the assumptions regarding conductivity and electric
boundary conditions that are required to determine intracellular currents from
extracellular voltage recordings. When combined with transmembrane potential
measurements, this invention provides a method for direct measurement of transmembrane
conductance during an action potential.
In one example, sciatic nerves from bullfrogs (Rana catesbeiana) were dissected
and placed in a dish containing aerated Ringer's (saline) solution, FIG. 5.
The magnetic fields were recorded with a SHE Model BMP-55 SQUID magnetometer
(1.3.times.10.sup.-14 T(Hz).sup.-1/2 sensitivity, 18.7 mV per flux quantum calibration).
The SQUID magnetometer utilizes a Superconducting Quantum Interference Device
to detect magnetic flux changes through a superconducting pick-up coil in a
liquid helium environment. At the closest coil-to-nerve separation of 15 mm,
the nerve magnetic field could barely be detected.
Considerable effort was thereby expended to increase the signal-to-noise ratio.
The distance between the nerve and the detector coil was reduced an order of
magnitude by threading the nerve through a toroidal probe in accordance with
the invention. The probe consisted of four turns of No. 38 wire wound on a 1.2
mm thick ferrite core of minor diameter 1.2 mm, major diameter 2.6 mm, and effective
relative permeability at 2000 Hz of 6800. The effective cross sectional area
of this toroidal pick-up coil was 3.9.times.10.sup.-2 m.sup.2. The toroid was
inductively coupled (mutual inductance 5.4 nH) to the magnetometer face coil
via a transfer coil wrapped around the outside of the dewar. The signals induced
in the nerves were detected and analyzed.
This invention represents the first SQUID magnetometer utilizing a miniature,
room temperature pickup coil. While the Johnson noise associated with such a
resistive coil may prove disadvantageous in other applications, the filter-like
behavior of the LR circuit that comprises the pickup coil minimizes or eliminates
this problem for this application. Because the SQUID is optimized for measuring
currents from high inductance, low resistance sources, the application of a
SQUID instead of conventional amplifiers provides for a substantial increase
in sensitivity over that which can be obtained using previously available devices.