The invention addresses methods and instrumentation for using ultrasound vibrations of intra-capillary micro-bubbles to increase fluid to gas phase transition of fluor-carbon (FC) droplets in humans.
Liquid to gas phase transition of perfluor-carbon nano- and micron- droplets is an emerging field for improving ultrasound diagnosis and assisted therapy of diseases such as cancer, inflammation, atherosclerosis, and myocardial infarction.
Ultrasound stimulated phase transition of ~ 3 µm diameter Per-Fluor-Carbon (PFC) droplets produces micro-bubbles of ~ 15 µm diameter in larger arteries. In capillaries with typical diameters ~ 6 - 10 µm, such gas bubbles fills the capillary for ~ 30 - 100 µm length with a slow absorption decay into blood over some minutes. Ultrasound vibration of the intra-capillary bubbles produces vibration of the extra-capillary tissue ~ 1 µm and has shown to increase efficacy of cancer chemotherapy in pre-clinical studies. There are also indications that such intra-capillary bubble vibrations can increase the immune response to a particular cancer in association with other therapies, and reduce myocardial hypoxia after coronary reopening after a cardiac ischemia attack.
The therapeutic effect depends on adequate amplitude of the capillary wall vibrations. Bubbles obtained by evaporation of PFC droplets of ~ 3 µm diameter produce resonance frequencies around ~ 500 kHz, and to obtain desirable vibration amplitude of the capillary wall one wants to vibrate the bubbles close to their resonance frequency. The vibration amplitude depends on the amplitude and frequency of the incident ultrasound drive wave, the capillary dimension, and particularly also the shear stiffness of the extra capillary tissue. Especially can both the capillary diameter and the shear stiffness and absorption of the extra-capillary tissue vary by a large amount between different cases. It is therefore desirable to have an online assessment of the vibration amplitude of bubbles that fills the capillary. The invention presents new methods and instrumentation that produces estimates of both the bubble vibration amplitude and its resonance frequency, and also extracts elastic information of tissue surrounding the bubbles.
An overview of the invention is presented, where the overview is a short form and by no means represents limitations of the invention, which in its broadest aspect is defined by the claims appended hereto.
The invention presents methods and instrumentation for estimation of vibration amplitude of intra-capillary micro-bubbles that fills the capillary for a length and are driven to vibrate with an incident ultrasound wave of given amplitude and frequency. The estimated amplitude is for example used to adjust the drive amplitude of the incident wave to obtain a desired vibration amplitude of the extra-capillary tissue.
The estimation method comprises
The invention further includes instrumentation for carrying through the methods of estimation in a practical situation.
This section gives a more detailed description of example embodiments of the invention, where the examples by no means represents limitations of the invention, which in its broadest aspect is defined by the claims appended hereto.
The invention presents methods and instrumentation for extracting information about ultrasound driven vibrations of micro-bubbles in tissue, and also to use this information for estimation of tissue properties, such as elastic properties, and properties relating to elastic properties.
The invention is relevant for micro-bubbles with diameter less than the capillaries, and also bubbles that in large arteries have a spherical shape with radius a ~ 5 - 30 µm that gives a bubble volume Vb = 4πα3/3, while in capillaries with radii av ~ 3 - 5 µm the larger bubbles fill at least part of the capillary. Examples of the larger bubbles are shown in
There is spatially distributed elasticity and mass density of the tissue, the blood, and the gas, that implies wave propagation with reflection at boundaries. The tissue and the blood have both a high volume compression stiffness λt = 1/κt(κt- volume compressibility) that upholds pressure waves with propagation velocity cp ≈1500 m/s for both tissue and blood. The tissue has in addition a low shear/deformation stiffness µt that produces tissue shear/deformation waves with no volume compression and low propagation velocity cs ~ 2 - 20 m/s. The blood and the gas have negligible shear stiffness, and hence no shear waves. The bubble gas has a low volume compression stiffness, but the mass density is also so low that the gas pressure can be approximated as constant across the bubble volume. The bubble gas pressure depends on the bubble volume and its variation as
where P0 ~100 kPa is the environmental pressure, Vb is the equilibrium bubble volume, δV is the change in bubble volume, Cp and Cvare the heat capacities at constant pressure and volume. Typical gases have large molecules that makes Cp ≈ Cv and γ≈ 1. The volume-pressure relation is inherently nonlinear for larger changes in the volume, but we shall in our work use the approximate linear variation with δV/Vb, to study fundamental aspects of the bubble vibration.
The low tissue shear stiffness allows large deformations of the cylindrical bubble surface 111, with large amplitude, short-range shear deformation of the surrounding tissue with comparatively low volume compression. The large vibration amplitude of the close surrounding tissue produces an outward acoustic radiation force (ARF) that has interesting applications for drug transport both across the capillary wall, through the interstitial space between the tissue cells, and across membranes of the cells and other tissue structures. In this context it is important to obtain adequate bubble/tissue vibration amplitude (~ 1 µm) and one target of this invention is to use ultrasound scattering from vibrating bubbles to measure the bubble vibration amplitude produced by an incident ultrasound wave. The invention further uses the measured bubble vibration amplitude to set the amplitude of the incident vibration wave to achieve desired bubble vibration amplitude in the surrounding tissue to achieve the desired therapeutic effect.
A bubble in a large vessel, as 101 in 100, has a practically spherical shape with a spherical vibration pattern. A drive pressure Pd that is the difference between the gas pressure Pg and the pressure P∞ at a point so distant from the bubble that one can neglect the tissue shear vibration, produces a complex volume vibration amplitude □Vc of the bubble as [1]
where ρb and ηb are the mass density and coefficient of viscosity of the surrounding blood, and Est is the Youngs module of the blood/gas surface layer. We refer to Hd as the direct drive transfer function, and ωd as the direct drive angular resonance frequency produced by the interaction between the co-oscillating mass of the surrounding blood and the elasticity of the blood/gas surface layer. Viscous friction in the blood and the surface layer is given by ηb.
An incident acoustic wave with pressure amplitude Pi and angular frequency ω produces a variation in the bubble volume and the gas pressure that produces drive pressure amplitude Pd as
which gives the complete transfer function HV(ω) from the incident pressure amplitude Pi to the complex relative volume amplitude as
With the 2nd order form of the Hd(ω) in Eq.(2), we get the following form of HV(ω)
For a bubble that partially fills a capillary with a large cylindrical region as 111 in
The
Eqs.(12,13,19) shows that for a bubble with dimensions adequately smaller than the incident wavelength the scattered signal is determined by the bubble volume Vb and bubble volume compressibility κb. We note from
where 2 L is the length of a cylindrical bubble in a capillary with the same volume Vb. The vibrating area of the cylindrical bubble is
We notice that Ac is
which is ⅓ of the surface area of the end spheres. However, the effect of this error is reduced because the displacement of the semi-spherical end surfaces is less than the radial vibration of the cylinder surface as shown in
Analysis of vibration and scattering from the cylindrical bubble is carried through in Appendix A. We note from 210 in
from Eq.(A10, A12) of Appendix A for 1c/av=5. The dotted lines show the magnitude |Ĥv(ω)| (302) and the phase θ̂v(ω) (303) of the 2nd order approximation |Ĥv(ω)| of Eq.(A14). The approximation of the 2nd order function to Eq.(A12) is done in the following steps:
In the example in
To observe the LF vibration amplitude of a bubble driven by the incident LF wave with angular frequency ωL , the invention presents methods and instrumentation building on U.S. Pat. 8,550,998; 9,291,493; 9,939,413; 10,578,725 and 7,727,156; 10,879,867.
An LF pulse shown by example as 401 or 405 in
In many situations, for example trans-abdominal and trans-costal applications, the access window to the therapeutic region is limited, and it is desirable to have a HF transmit and receive beam arrangement with the same direction as the LF beam as illustrated in
With adequate ultrasound access windows, it can be useful to use crossing multi/depth focused HF receive beams exemplified by 514 and the dots 515 in
In a particular solution, one transmits a set SN of N≥ 1 groups Gn pulse complexes where one for each group Gn transmits at least two pulse complexes comprising a LF manipulation pulse and a HF observation pulse where the LF pulse varies in one of amplitude, and polarity, and phase between each pulse complexes, where the LF pulse might be zero for one pulse complex, and the LF pulse is non-zero for at least one pulse complex. The LF pulses 401 and 405 in
The time between transmit of the HF pulses is determined so that it is larger than the round trip propagation time TR from HF transmit transducer to the micro-bubble and to the HF receive transducer. In particular solutions where one wants long duration LF transmit vibration of the bubble we can use LF pulses with long duration time TL, for example longer than NTR where N is the the number of groups Gn. Several groups Gn of HF transmit pulses are then transmitted with time distance larger than TR and tn defining the detailed phase relation between the HF pulse and the LF oscillation of the bubble when the HF pulse hits the bubble.
It is also interesting the use a HF transmit beam 513 that crosses the LF beam 501 in the same direction as the set of HF receive beams 514/515.
For therapy we generally drive the bubble with the low frequency (LF) pressure wave with angular frequency ωL, typically in the neighborhood of the bubble resonance frequency to produce large therapeutic cylindrical radius vibration amplitude (~ 1 µm). The LF pulse has an amplitude envelope pPLe(t), where p is a polarity parameter of the LFwave. p = 1 implies positive LF amplitude (e.g. 401), p = -1 implies inverted LF amplitude (e.g. 405), while p = 0 implies zero LF amplitude. Other values/sequences of the polarity parameter can be used to enhance the signal processing, where the cited patents show examples of p = 0, ±1; p = ±1, ±2, for example to improve suppression of tissue noise and/or compensate for bubble movements between the HF pulses.
The LF pulse produces a vibration in bubble volume as
Where θ(ωL)=∠H(ωL) is the phase of H(ωL), and τe(ωL)≈θʹ(ωL) is an approximate delay of the envelope produced by the transfer function H(ω) for an adequately narrow band HF pulse. The last approximation of δVLe(t) assumes that he envelope varies slowly relative to the ωL oscillation. To measure the bubble vibration amplitude we transmit HF observation pulses as described in
The scattered pressure field of an incident ultrasound pressure wave with angular frequency ω and amplitude Pi from a bubble with volume Vb and adequately less extension than the incident wavelength λ, is by the Born approximation obtained as
where
The term κb/κt represents scattering due to the deviation of the bubble volume compressibility from the tissue volume compressibility, and the term esei represents scattering due the relative difference between the bubble mass density (≈ 0) and the tissue mass density ρt. In a typical situation |κb(ω)/κt|>>|esei|, and the term esei can be neglected. Using
we modify Eq.(6) to
Both for contrast agent bubbles and bubbles for therapy, we are generally interested in vibrating the bubbles in the low frequency (LF) range Ω0 around the bubble volume vibration resonance frequency, where the 2nd order transfer functions of Eqs.(5,A14) are useful. To measure the bubble vibration amplitude at ωL we transmit in addition high frequency (HF) observation pulses with angular center frequency ωH ~10ωL >> ω0 as illustrated in
Spherical Bubble:
Cylindrical Bubble:
where it is shown the major dependencies of the receive signal Y(D;ω) on the bubble dimensions D. For the spherical bubble D is the bubble radius a, while for the bubble filling parts of the capillary D is (av,L) or (av, a) by Eq.(7). A change in the bubble dimension/volume at the HF/LF time reference tm when the HF pulse hits the bubble, produces a change in the amplitude of the HF receive signal. For polarity p of the LF pulse the major change in bubble dimensions are
The spatial average
where c0 is the low amplitude linear propagation velocity, PL is the pressure of the low frequency wave at the location of the HF pulse, β is a nonlinearity parameter of the tissue bulk compression, and p is a scaling parameter defined in relation to Eqs.(10,11). This nonlinear propagation effect gives a non-linear propagation delay (NPD) to the HF pulse, pτn(r), and a weaker pulse form distortion (PFD) that increases with the propagation distance r is before scattering, as described in the cited patents. When the transmitted HF pulse is at the crest or through of the LF wave, the NPD has a larger effect than the PFD that generally can be neglected. When the transmitted HF pulse is at a zero crossing of the LF wave, the PFD has a larger effect than the NPD that generally can be neglected.
The back scattered HF signal will generally in addition to the scattering from the bubbles contain considerable scattering from tissue surrounding the bubble, and it is devised to suppress the tissue signal, for example by correcting the received signal for adequate NPD and/or PFD according to the methods in the cited patents, or using the 2nd harmonic component of the received HF signal, or a combination of both. We notice, however that the transmitted LF amplitude to vibrate bubbles is generally lower than for imaging, and both the NPD and the PFD have less effect, and corrections for NPD and/or PFD can in many cases be neglected. Before further processing, we assume that the received HF signals are adequately corrected with the NPD and PFD, as described in the cited patents, and in the notation for the received HF signals below, we assume that that adequate correction have been done.
For illustration of a simplest form, we linearize the receive signals and form a detection signal Dm with p = ±1 as
where the subscript n indicates the time point tn in
Components for Ys and Yc in Eqs.(14,15) that have low variation with bubble dimension variations are shorted in the ratio of Dm. In particular has Hb low sensitivity to variations in bubble dimensions that are small compared to the wave length. Hb(K) is the Fourier transform of the bubble volume with Fourier vector K=k(ei-es). The largest magnitude Kmax=2kei=4π/λ)ei is found for back-scattering where es= –ei, which the situation in
We notice that for the sphere we have for back scattering Ka=(4πa/cp)·f where f is the frequency and cp ≈ 1500 m/s is the propagation velocity of the pressure wave.
Scattering from the cylindrical bubble in
ΔHb/Hb0 is analyzed in
For this situation ΔHb/Hb0<0.02 is obtained for f = 2.5 and 5 MHz. Reducing □av to 0.5 □m we have ΔHb/Hb0<0.02 up to 7.5 MHz for all situations.
We expect capillaries and hence also bubbles to have random position within the tumor, and if we select the bubbles with the strongest back-scatter, i.e. incident wave normal to the capilary length and φ close to ± π/2 eg , we can assume that the variation of Hb for the variations of the bubble dimension produced by the LF pulse is negligible for all the given bubble lengths and frequencies HF < 15 MHz.
We note that when the incident HF beam hits close to the short axis of the bubble, both Hb0 and ΔHβ/Hb0 are approximately independent of the dimension variations for HF < 15 MHz When we can neglect the changes in Hb with the bubble dimension variations produced by the polarity change in the incident LF pulse, Hb is essentially canceled in the fraction of Dm in Eq.(18). Neglecting Hb in the expression for Ys, Yc in Eq.(14,15) we see that Dm of Eq.(18) gives
where KpH(L/av) is given in Eq.(15, A17). We note that ψcm is the spatial average of the normal displacement ψr for the cylinder, as shown in Eq.(A12), while ψsm is the maximal displacement of the spherical bubble radius, as the bubble displacement is constant across the bubble surface. Acm as a function of lc/av is shown as 700 in
The relative volume variation δV/Vb can be approximated from the relative displacement for the spherical and cylindrical bubbles with the linear approximations as
Considering measurements errors and relative displacement magnitudes, these approximate expressions have good practical value. More accurate nonlinear expressions between δV/Vb and the displacements can be calculated by anyone skilled in the art.
For the 2nd order transfer functions in Eqs.(5,A14) it is possible to measure/estimate the three major parameters, w0, ζ, and KV, for example in the following way. We get a phase estimate θ(ωL)=∠H(ωL) of the transfer function at ωL for the tn = tm that gives maximum of δVb in Eq.(11), i.e.
Measuring θ̂(ωL1) and θ̂(ωL2) from Eq.(22) for two low frequencies ωL1 and ωL2 where we get the maximal detection signal for tm1 and tm2, we can for example though linear interpolation, indicated as 703 in
At the resonance frequency □0 we shall have θ(ω0) = -π/2 which gives an estimated resonance frequency from Eq.(23) as
Matching the differential of the phase in Eq.(5,A14) at ω= ω0 to Eq.(24) we get an estimate for the absorption losses in the tissue vibrations as
Another estimate of the absorption factor ζ is from Eq.(5) also found for a single low frequency ωL as
The parameter KV can for example be found by the angular frequency ωm that gives maximal amplitude of HV(ω). From the estimates of ω̂0 and ζ̂ we can obtain an estimate of
where we measure |HV| at the estimated angular frequency ωm. If we do not have an estimate of ζ̂, we can search for the ωm that gives max|HV| and do the following calculations
Estimating the phases θ̂n = θ̂(ωLn) at more than two frequencies ωLn, n=1, 2, ... , N, we can improve the estimate of ω̂0 with more complex interpolations, as known by any-one skilled in the art. By example, for n = 1, ... , N we the set of measured frequencies by the vector ωL = {ωL1,...ωLn,...ωLN} and the set of estimated phases by ωL = {ωL1,...ωLn,...ωLN}, we can then form an estimate of ω̂0 and ζ̂ω̂0 through minimization of a mean square functional as
Other forms of functionals for minimization, also including added information, can be formed by any-one skilled in the art.
From Eq.(5-7) we notice that for θ̂(ωL)+ωLtm≈ 0 the amplitude of the received HF signal takes the form
and we can for example include the amplitude of the received signal ~|Hv(ωLn)| for the different {ωL1,...ωLn} in addition to the phase in the functional for parameter estimation in Eq.(29).
The extra capillary tissue is determined by the mass density, ρt, and the real and imaginary part, µtr and µti of the complex shear stiffness of the tissue, as shown in Eq.(A6, A7). We can approximate ρt≈ 1100 kg/m3 for most solid tumor tissues, and hence it is µtr and µti which are the most sought after tissue parameters. From the measured/estimated ω̂0 and k̂v, we see from Eq.(A18) that we can obtain an estimate of ω̂d as
where γ ≈ 1 and P0 ≈ 101 kPa.
From Fd(x) in Eq.(A11) we obtain estimated xd(lc/av) from Re{Fd(xd)=0.
which allows us to calculate
The power dissipated by the surface vibration at a surface area element d2r is
We assume Pi approximately constant across the bubble surface, and integrated across the whole bubble surface gives the following power dissipation that provides a heating energy per unit time
Inserting the transfer function from Eq.(5), we get
Hence, from estimation of ω0 and ζ and assessment of the bubble volume and the incident pressure amplitude, we can assess the dissipated power from the bubble on the surrounding tissue at ω= ωL. Because ωL is low, we can estimate the low frequency amplitude Pi = PL using an assessment of the low absorption. From the ultrasound image (2D or 3D) we can automatically estimate the number of bubbles N per unit volume and assess the total heat generation as
that can be used to estimate temperature increase in the tissue to avoid uncontrollable results.
For 3D scanning of the ultrasound beams, the linear array 901 can in this example embodiment be rotated around the long axis 904 that provides a mechanical scanning of the LF/HF beam in an elevation direction, indicated by the arrows 905. For each elevation position of the array, one does electronic scanning of LF/HF transmit beams in an azimuth direction indicated by the arrows 906, through electronic selection of transmitting LF and HF elements, and transmitting combined LF/HF pulse complexes for example as shown in
At least two pulse complexes with different LF pulses, for example as illustrated in
Two versions of the instrument are useful, where the first version 903 comprises beam former for HF receive cross-beams, illustrated as 914 in the 2D scan plane 908, and HF back scatter receive beams with the same axis as the HF transmit beam 907, shown in further detail in
The processor 911 typically comprises at least one multicore central processing unit (CPU) and at least one graphics processor unit (GPU) that are SW programmable, according to known methods. The processor receives user inputs from a user/operator input unit 913 that operates according to known methods, and displays image data and other information necessary for communication with the user/operator through a combined display and audio unit 912, according to known methods.
In the second version of the instrument, the digital HF receive signals from each HF receive elements and each transmitted pulse complex are via the high-speed bus 910 transferred to the processor 911 for storage and further processing. For 2D imaging in the second version, a SW program in the processor unit 911 combines HF receive signals from multiple HF receive elements to produce both HF backscatter receive beams and HF receive cross-beams crossing each HF transmit beam in the 2D set, for example as shown as 914 and in more detail in
One use of the cross-beam (914) HF receive signals is to estimate the nonlinear propagation delay at a multitude of depths along the HF transmit beam with low influence of multiple scattered noise, as described in U.S. Pat. Appl. 2020/0405268. A set of cross beams is also useful to provide better suppression of signal from tissue, that is noise for detecting bubbles, vibration amplitudes, and tissue parameters. When we have imaging situations where the level of multiple scattering noise in the back-scatter HF receive signal is low compared to the 1st order scattered signals, the nonlinear propagation delay at multitude of depths along the HF transmit beam (907) can be obtained from the back-scatter HF receive signal, as described in the above cited US Patents, and the beam former for HF receive cross-beams, has less importance and can be omitted.
The processor 911 further comprises means, for example implemented as SW programs, to carry through the processing as described above to estimate
The method and instrument is useful for estimating vibration amplitudes of bubbles of any dimension at an angular frequency we define as the low frequency, ωL. For spherical bubbles we have a good analytic relationship of a 2nd order transfer function, Eq.(5) between the bubble radius and the scattered wave over a large frequency range from well below to well above the resonance frequency. For Bubbles that fill a capillary, like in
Thus, while there have shown and described and pointed out fundamental novel features of the invention as applied to preferred embodiments thereof, it will be understood that various omissions and substitutions and changes in the form and details of the devices illustrated, and in their operation, may be made by those skilled in the art without departing from the spirit of the invention.
It is also expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results, are within the scope of the invention. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or embodiment of the invention may be incorporated in any other disclosed or described or suggested form or embodiment as a general matter of design choice. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.
For the vibration field outside the cylindrical capillary from the vibrating bubble in
where λ = 2πcp/ω is the wavelength of the pressure wave with propagation velocity cp. The particle vibration displacement ψ and the pressure P in the co-oscillating mass are obtained from A as
Fourier transform along the z-axis gives
Setting x = kzr and A(r,kz) = y(kzr) we get the modified Bessel equation with the solution K0(x)
With A defined for r= av and a tissue mass density ρ, we get the following field amplitudes in the tissue outside the capillary
Inside the co-oscillating mass the incompressible tissue deformation produces shear stresses, which balances to zero inside the tissue, but at the boarder to the bubble at the capillary wall we get a stress contribution to the tissue surface as
where µt = µtr + iµti = µtr(1 +iη) is the complex shear stiffness of the tissue where the imaginary component produces absorption of oscillation power. At the bubble-tissue surface interface this stress adds to the pressure in Eq.(A5) to the following pressure from the cylindrical bubble surface towards the tissue
When the bubble cylindrical length 2/c is adequately larger than the capillary radius av, we can approximate the bubble with semi-spherical end surfaces with radius av with a cylinder with length 2L as shown in Eqs.(7, 8) above. Pd (av,kz is the z-Fourier transform of a spatially constant drive pressure amplitude Pd relative to infinity in the interval (- L, L), and zero outside
The ψr vibration amplitude at the cylindrical part of the bubble amplitude, gives a volume change of the cylinder
Changing integration coordinates q = kzav, kz = q/av , dkz = dq/av we get the direct drive transfer function Hd as
where cs is the shear wave velocity and ωs is the shear wave angular frequency. Introducing x = ω/ ωs we obtain the scaled direct drive transfer function Fd as
Note that for the cylindrical bubble in a capillary we have above put the surrounding tissue real shear stiffness µtr outside Hd and Fd. This gives Fd the nice property that it does not depend on µtr and ωs, only on η. We assume a linear variation η with frequency, i.e. η = 2αx. The resonance frequency of Fd is defined as the value xd that gives the real part of Fd equal zero, i.e. Re{Fd(xd;L/av}.
Including gas elasticity according to Eq.(3) we get the complete transfer function from incident pressure to relative volume amplitude
Due to the frequency variation of the displacement along the bubble surface as shown in 212 of
With the 2nd order approximation of Hv in Eq.(A14) we can from Eq.(13) approximate the scattered field in the low frequency range as
For detection of the low frequency LF vibration amplitude we transmit a high frequency (HF) pulse, HF ~ 10*LF or more, i.e. ω>> ω0, as described in relation to Eqs.(12-19) and
Inserted into Eq.(13) we then get the approximation to the scattered field for the ΩH frequency range as
The received HF amplitude is then proportional to
With the 2nd order approximation of Hv in Eq.(A14) the angular frequency ωm for max|Hv (ω)| is given by
1. Lars Hoff: “Acoustic Characterization of Contrast Agents for Medical Ultrasound Imaging” Springer Science + Business Media. 2001
This application claims priority from U.S. Provisional Pat. application No. 63/248,180 filed on Sep. 24, 2021, the entire content of which is incorporated by reference.
Number | Date | Country | |
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63248180 | Sep 2021 | US |