Experimental study of underwater transmission characteristics of high-frequency 30 MHz polyurea ultrasonic transducer

In this paper, we present the transmission characteristics of a polyurea ultrasonic transducer operating in water. In this study, we used a polyurea transducer with fundamental resonance at approximately 30 MHz. Firstly, acoustic pressure radiated from the transducer was measured using a hydrophone, which has a diameter of 0.2 mm. The transmission characteristics such as relative bandwidth, pulse width, and acoustic sensitivity were calculated from the experimental results. The results of the experiment showed a relative bandwidth of 50% and a pulse width of 0.061 μs. The acoustic sensitivity was 0.60 kPa/V with good linearity, where the correlation coefficient R in the fitting calculation was 0.996. A maximum pressure of 13.1 kPa was observed when the transducer was excited at a zero-to-peak voltage of 21 V. Moreover, we experimentally verified the results. The results of the pulse/echo experiment showed that the estimated diameters of the copper wires were 458 and 726 μm, where the differences between the actual and measured values were 15% and 4%, respectively. Acoustic streaming was also observed so that a particle velocity map was estimated by particle image velocimetry (PIV). The sound pressure calculated from the particle velocity obtained by PIV showed good agreement with the acoustic pressure measured using the hydrophone, where the differences between the calculated and measured values were 12–19%.     

High repetition rate Q-switched microchip Nd:YVO4 laser with pulse duration as short as 1.1 ns

We have demonstrated a compact and an efficient passively Q-switched microchip Nd:YVO₄ laser by using a composite semiconductor absorber as well as an output coupler. The composite semiconductor absorber was composed of an LT (low-temperature grown) In_0.25Ga_0.75As absorber and a pure GaAs absorber. To our knowledge, it was the first demonstration of the special absorber for Q-switching operation of microchip lasers. Laser pulses with durations of 1.1 ns were generated with a 350 μm thick laser crystal and the repetition rate of the pulses was as high as 4.6 MHz. The average output power was 120 mW at the pump power of 700 mW. Pulse duration can be varied from 1.1 to 15.7 ns by changing the cavity length from 0.45 to 5 mm. Pulses with duration of 1.67 and 2.41 ns were also obtained with a 0.7 mm thick laser crystal and a 1 mm thick laser crystal, respectively.     

Heart ablation using a planar rectangular high intensity ultrasound transducer and MRI guidance

The aim of this study was to evaluate a flat rectangular (3 × 10 mm²) MRI compatible transducer operating at 5 MHz. The main task was to explore the feasibility of creating deep lesions in heart at a depth of at least 15 mm. The size of thermal necrosis in heart tissue was estimated as a function of power and time using a simulation model. The system was then tested in an excised lamb heart. In this study, we were able to create lesions of 15 mm deep with acoustic power of 6 W for an exposure of approximately 1 min. The contrast to noise ratio (CNR) between lesion and heart tissue was evaluated using fast spin echo (FSE). The CNR value was approximately 22 using T1 W FSE. Maximum CNR was achieved with repetition time (TR) between 300 and 800 ms. Using T2W FSE, the corresponding CNR was approximately 13 for the 14 in vivo experiments. The average lesion depth was 11.93 mm with a standard deviation of 0.62 mm. In vivo irradiation conditions were 6 W for 60 s. The size of the lesion in the other two dimensions was close to 3 × 10 mm² (size of the transducer element).     

Impact of thermal effects induced by ultrasound on viability of rat C6 glioma cells

In order to have consistent and repeatable effects of sonodynamic therapy (SDT) on various cancer cells or tissue lesions we should be able to control a delivered ultrasound energy and thermal effects induced. The objective of this study was to investigate viability of rat C6 glioma cells in vitro depending on the intensity of ultrasound in the region of cells and to determine the exposure time inducing temperature rise above 43 °C, which is known to be toxic for cells. For measurements a planar piezoelectric transducer with a diameter of 20 mm and a resonance frequency of 1.06 MHz was used. The transducer generated tone bursts with 94 μs duration, 0.4 duty-cycle and initial intensity I_SATA (spatial averaged, temporal averaged) varied from 0.33 W/cm² to 8 W/cm² (average acoustic power varied from 1 W to 24 W). The rat C6 glioma cells were cultured on a bottom of wells in 12-well plates, incubated for 24 h and then exposed to ultrasound with measured acoustic properties, inducing or causing no thermal effects leading to cell death. Cell viability rate was determined by MTT assay (a standard colorimetric assay for assessing cell viability) as the ratio of the optical densities of the group treated by ultrasound to the control group. Structural cellular changes and apoptosis estimation were observed under a microscope. Quantitative analysis of the obtained results allowed to determine the maximal exposure time that does not lead to the thermal effects above 43 °C in the region of cells for each initial intensity of the tone bursts used as well as the threshold intensity causing cell death after 3 min exposure to ultrasound due to thermal effects. The averaged threshold intensity was found to be about 5.7 W/cm².     

Comparison of continuous-wave (CW) and tone-burst (TB) excitation modes in vibro-acoustography: Application for the non-destructive imaging of flaws

This paper describes the application of continuous-wave (CW) and tone-burst (TB) vibro-acoustography (VA) experiments for imaging a flawed composite plate. For both modes, the ultrasound frequency is set at f₁ = 3 MHz and f₂ = 3 MHz + ∣Δf∣. The plate was placed at the focus of the transducer and scanned point-by-point over an area of 60 mm by 50 mm on its frontal face with an increment step equal to 0.25 mm/pixel. The resulting acoustic emission amplitude at ∣Δ f∣ is recorded. For the CW mode the difference frequency was set at ∣Δf∣ = 12.9 kHz. For the TB mode, the burst-emitted signal was 100 μs long at a pulse repetition frequency (PRF) of 100 Hz corresponding to bursts of 300 cycles at 3 MHz, and the difference frequency was set at ∣Δf∣ = 44 kHz. The resulting VA images readily show the shape of the flaws. The images also reveal considerable detail of internal substructures such as the fibers used to reinforce the plate. However, the CW VA image shows an artifact caused by the effect of ultrasound standing waves established between the plate and the concave surface of the transducer, resulting in masking some of the flaws. On the other hand, the TB-VA image is free from such artifact. Despite some advantages of using TB-VA, there are some limitations related to this mode. Advantages and limitations of using the two modes are discussed.     

Reflector-based phase calibration of ultrasound transducers

Recently, the measurement of phase transfer functions (PTFs) of piezoelectric transducers has received more attention. These PTFs are useful for e.g. coding and interference based imaging methods, and ultrasound contrast microbubble research. Several optical and acoustic methods to measure a transducer’s PTF have been reported in literature. The optical methods require a setup to which not all ultrasound laboratories have access to. The acoustic methods require accurate distance and acoustic wave speed measurements. A small error in these leads to a large error in phase, e.g. an accuracy of 0.1% on an axial distance of 10 cm leads to an uncertainty in the PTF measurement of ±97° at 4 MHz. In this paper we present an acoustic pulse-echo method to measure the PTF of a transducer, which is based on linear wave propagation and only requires an estimate of the wave travel distance and the acoustic wave speed. In our method the transducer is excited by a monofrequency sine burst with a rectangular envelope. The transducer initially vibrates at resonance (transient regime) prior to the forcing frequency response (steady state regime). The PTF value of the system is the difference between the phases deduced from the transient and the steady state regimes. Good agreement, to within 7°, was obtained between KLM simulations and measurements on two transducers in a 1-8 MHz frequency range. The reproducibility of the method was ±10°, with a systematic error of 2° at 1 MHz increasing to 16° at 8 MHz. This work demonstrates that the PTF of a transducer can be measured in a simple laboratory setting.     

Minimization of treatment time for in vitro 1.1 MHz destruction of Pseudomonas aeruginosa biofilms by high-intensity focused ultrasound

Medical implants are prone to colonization by bacterial biofilms. Normally, surgery is required to replace the infected implant. One promising noninvasive modality is to destroy biofilms with high-intensity focused ultrasound. In our study, Pseudomonas aeruginosa biofilms were grown on implant-mimicking graphite disks in a flow chamber for 3 days prior to exposing them to ultrasound pulses. Exposure time at each treatment location was varied between 5, 15 and 30 s. Burst period was varied between 1, 3, 6 and 12 milliseconds (ms). The pulses were 20 cycles in duration at 1.1 MHz from a spherically focused transducer (f/1, 63 mm focal length), creating peak compressional and rarefactional pressures at the graphite disk surface of 30 and 13 MPa, respectively. P. aeruginosa were tagged with green fluorescent protein, and killed cells were visualized using propidium iodide before determining the extent of biofilm destruction. The exposure-induced temperature rise was measured to be less than 0.2 °C at the focus, namely the interface between graphite disk and water. Then, the temperature rise was measured at the focus between the graphite disk and a tissue-mimicking phantom to evaluate therapy safety. Two thresholds, of bacteria destruction increase and of complete bacteria removal, respectively, were identified to divide our eight exposure conditions. Results indicated that 30-s exposure and 6-ms pulse period were sufficient to destroy the biofilms. However, the 15-s exposure and 3-ms pulse period were viewed as optimum when considering exposure time, efficacy, and safety.     

Lead-free KNLNT piezoelectric ceramics for high-frequency ultrasonic transducer application

This paper presents the latest development of a lead-free piezoelectric ceramic and its application to transducers suitable for high-frequency ultrasonic imaging. A lead-free piezoelectric ceramic with formula of (K_0.5Na_0.5)_0.97Li_0.03(Nb_0.9 Ta_0.1)O₃ (abbreviated as KNLNT-0.03/0.10) was fabricated and characterized. The material was found to have a clamped dielectric constant ε₃₃^S/ε₀ = 890, piezoelectric coefficient d₃₃ = 245 pC/N, electromechanical coupling factor k_t = 0.42 and Curie temperature T_c > 300 °C. High-frequency (40 MHz) ultrasound transducers were successfully fabricated with the lead-free material. A representative lead-free transducer had a bandwidth of 45%, two-way insertion loss of -18 dB. This performance is comparable to reported performances of popular lead-based transducers. The comparison results suggest that the lead-free piezoelectric material may serve as an alternative to lead-based piezoelectric materials for high-frequency ultrasonic transducer applications.     

Properties and characteristics of P(VDF/TrFE) transducers manufactured by a solution casting method for use in the MHz-range ultrasound in air

Highly effective piezoelectric polymer transducers operating in air at high frequencies have been successfully made by casting a solution of ferroelectric poly(vinylidene fluoride-co-trifluoroethylene) P(VDF/TrFE) directly on a backing metal plate, and their performance has been evaluated. By utilizing this method, it has been possible to develop the three kinds of transducers that operate respectively at 4, 6 and 10 MHz in air. For precise evaluation of the performance of the P(VDF/TrFE) transducers, the absorption loss in air was measured up to 10 MHz. It was confirmed that the empirical formula obtained from the measured absorption values in air at high frequencies was in alignment with its theoretical value. In addition, a high lateral resolution acoustic image of a ROM-Chip (amplitude-image) at 6 MHz in air was successfully displayed using an air coupled concave type P(VDF/TrFE) transducer by bonding an epoxy adhesive.     

Exvivo ultrasound attenuation coefficient for human cervical and uterine tissue from 5 to 10 MHz

Attenuation estimation and imaging in the cervix has been utilized to evaluate the onset of cervical ripening during pregnancy. This feature has also been utilized for the acoustic characterization of leiomyomas and myometrial tissue. In this paper, we present direct narrowband substitution measurement values of the variation in the ultrasonic attenuation coefficient in ex vivo human uterine and cervical tissue, in the 5-10 MHz frequency range. At 5 MHz, the attenuation coefficient values are similar for the different orientations of uterine tissue with values of 4.1-4.2 dB/cm, 5.1 dB/cm for the leiomyoma, and 6.3 dB/cm for the cervix. As the frequency increases, the attenuation coefficient values increase and are also spread out, with a value of approximately 12.6 dB/cm for the uterus (both parallel and perpendicular), 16.0 for the leiomyoma, and 26.8 dB/cm for the cervix at 10 MHz. The attenuation coefficient measured increases monotonically over the frequency range measured following a power law.     

Study of ultrasound stiffness imaging methods using tissue mimicking phantoms

A pilot study was carried out to investigate the performance of ultrasound stiffness imaging methods namely Ultrasound Elastography Imaging (UEI) and Acoustic Radiation Force Impulse (ARFI) Imaging. Specifically their potential for characterizing different classes of solid mass lesions was analyzed using agar based tissue mimicking phantoms. Composite tissue mimicking phantom was prepared with embedded inclusions of varying stiffness from 50 kPa to 450 kPa to represent different stages of cancer. Acoustic properties such as sound speed, attenuation coefficient and acoustic impedance were characterized by pulse echo ultrasound test at 5 MHz frequency and they are ranged from (1564 ± 88 to 1671 ± 124 m/s), (0.6915 ± 0.123 to 0.8268 ± 0.755 db cm^-1 MHz^-1) and (1.61×10⁶ ± 0.127 to 1.76 × 10⁶ ± 0.045 kg m^-2 s^-1) respectively. The elastic property Young’s Modulus of the prepared samples was measured by conducting quasi static uni axial compression test under a strain rate of 0.5 mm/min upto 10 % strain, and the values are from 50 kPa to 450 kPa for a variation of agar concentration from 1.7% to 6.6% by weight. The composite phantoms were imaged by Siemens Acuson S2000 (Siemens, Erlangen, Germany) machine using linear array transducer 9L4 at 8 MHz frequency; strain and displacement images were collected by UEI and ARFI. Shear wave velocity 4.43 ± 0.35 m/s was also measured for high modulus contrast (18 dB) inclusion and X.XX m/s was found for all other inclusions. The images were pre processed and parameters such as Contrast Transfer Efficiency and lateral image profile were computed and reported. The results indicate that both ARFI and UEI represent the abnormalities better than conventional US B mode imaging whereas UEI enhances the underlying modulus contrast into improved strain contrast. The results are corroborated with literature and also with clinical patient images.     

Investigation of rat bone fracture healing using pulsed 1.5 MHz, 30 mW/cm burst ultrasound – Axial distance dependency

This study investigated the effect of LIPUS on fracture healing when fractures were exposed to ultrasound at three axial distances: z = 0 mm, 60 mm, and 130 mm. We applied LIPUS to rat fracture at these three axial distances mimicking the exposure condition of human fractures at different depths under the soft tissue. Measurement of LIPUS shows pressure variations in near field (nearby transducer); uniform profile was found beyond it (far field). We asked whether different positions of the fracture within the ultrasound field cause inconsistent biological effect during the healing process. Closed femoral fractured Sprague–Dawley rats were randomized into control, near-field (0 mm), mid-near field (60 mm) or far-field (130 mm) groups. Daily LIPUS treatment (plane, but apodized source, see details in the text; 2.2 cm in diameter; 1.5 MHz sine waves repeating at 1 kHz PRF; spatial average temporal average intensity, I_SATA = 30 mW/cm²) was given to fracture site at the three axial distances. Weekly radiographs and endpoint microCT, histomorphometry, and mechanical tests were performed. The results showed that the 130 mm group had the highest tissue mineral density; and significantly higher mechanical properties than control at week 4. The 60 mm and 0 mm groups had significantly higher (i.e. p < 0.05) woven bone percentage than control group in radiological, microCT and histomorphometry measurements. In general, LIPUS at far field augmented callus mineralization and mechanical properties; while near field and mid-near field enhanced woven bone formation. Our results indicated the therapeutic effect of LIPUS is dependent on the axial distance of the ultrasound beam. Therefore, the depth of fracture under the soft tissue affects the biological effect of LIPUS. Clinicians have to be aware of the fracture depth when LIPUS is applied transcutaneously.     

Dual-mode transducers for ultrasound imaging and thermal therapy

Medical imaging is a vital component of high intensity focused ultrasound (HIFU) therapy, which is gaining clinical acceptance for tissue ablation and cancer therapy. Imaging is necessary to plan and guide the application of therapeutic ultrasound, and to monitor the effects it induces in tissue. Because they can transmit high intensity continuous wave ultrasound for treatment and pulsed ultrasound for imaging, dual-mode transducers aim to improve the guidance and monitoring stages. Their primary advantage is implicit registration between the imaging and treatment axes, and so they can help ensure before treatment that the therapeutic beam is correctly aligned with the planned treatment volume. During treatment, imaging signals can be processed in real-time to assess acoustic properties of the tissue that are related to thermal ablation. Piezocomposite materials are favorable for dual-mode transducers because of their improved bandwidth, which in turn improves imaging performance while maintaining high efficiency for treatment. Here we present our experiences with three dual-mode transducers for interstitial applications. The first was an 11-MHz monoelement designed for use in the bile duct. It had a aperture that was cylindrically focused to 10 mm. The applicator motion was step-wise rotational for imaging and therapy over a 360°, or smaller, sector. The second transducer had 5-elements, each measuring for a total aperture of . It operated at 5.6 MHz, was cylindrically focused to 14 mm, and was integrated with a servo-controlled oscillating probe designed for sector imaging and directive therapy in the liver. The last transducer was a 5-MHz, 64-element linear array designed for beam-formed imaging and therapy. The aperture was with a pitch of 0.280 mm. Characterization results included conversion efficiencies above 50%, pulse-echo bandwidths above 50%, surface intensities up to , and axial imaging resolutions to 0.2 mm. The second transducer was evaluated in vivo using porcine liver, where coagulation necrosis was induced up to a depth of 20 mm in 120 s. B-mode and M-mode images displayed a hypoechoic region that agreed well with lesion depth observed by gross histology. These feasibility studies demonstrate that the dual-mode transducers had imaging performance that was sufficient to aid the guidance and monitoring of treatment, and could sustain high intensities to induce coagulation necrosis in vivo.     

An investigation of a fiber-optic air-backed mandrel hydrophone

In this work, a optical-fiber air-backed mandrel hydrophone is proposed and investigated both analytically and experimentally. The two-dimensional and three-dimensional quasistatically theoretical models of the hydrophone is created and compared, and the phase sensitivity of the hydrophone is analyzed. The theoretical result of phase sensitivity with three-dimensional model is −153.3 dB re rad/μPa. Twenty-two hydrophones of this type according to the model presented are constructed and tested. The experiment results show that experimental results of mean values of phase sensitivity are about −153 ± 0.5 dB re rad/μPa and have the close agreement with the estimation of theoretical models. The size of the fiber sensor is ∅12 × 55 mm, the normal phase sensitivity achieves −308 dB re 1 μPa⁻¹, the 3 dB effective bandwidth of the frequency response is 30 kHz, and the responsivity decreases less than 0.5 dB when static pressure is 2 MPa (200 m water depth). The hydrophone is easy to constructed at low cost with simple structure, and some new type of it with the required performances could be designed according to the model presented.     

Influence of ophthalmic lenses in the illuminance originated at a peripheral glare source and reaching the eye

To study the influence of glare on the visual performance of a subject wearing an ophthalmic lens, it is useful to know how the lens affects the illuminance reaching the eye. In this paper, considering spherical standard ophthalmic lenses and defining the relative illuminance, E_r, as the quotient between the illuminance at the cornea with and without lens, a methodology to evaluate E_r in terms of easily determined parameters is developed. Three effects are considered, pupil size variation of the system with and without lens; lateral shifts of rays transmitted through the lens and reflections at the lens. Calculations are experimentally verified employing 5 organic ophthalmic lenses of ±6; ±4 and 0.12 dioptres and 2 glass plane parallel plates 1.95 and 6.6 mm thick. Using a photometer whose sensor is 12 mm apart from the lens and 740 mm apart from a glare source subtending an eccentricity angle of 9.6°, it results E_r=1.204 for the 6 dioptres lens and E_r=0.803 for the −6 dioptres one if sensor diameter is 10 mm while, for a 719 mm distance and a 10° angle, E_r=0.922 for the thin plate and a 30 mm sensor and E_r=1.006 for the thick plate and a 10 mm sensor. Experimental and theoretical results differ in less than 3%.     

High power diode-pumped passively Q-switched and mode-locking Nd:GdVO4 laser at 912 nm

A high power diode-end-pumped passively Q-switched and mode-locking (QML) Nd:GdVO₄ laser at 912 nm was demonstrated for the first time, to the best of our knowledge. A Z-type laser cavity with Cr⁴⁺:YAG crystals as the intracavity saturable absorber were employed in the experiments. Influence of the initial transmission (T_U) of the saturable absorber on the QML laser performance was investigated. Using the T_U = 95% Cr⁴⁺:YAG, as much as an average output power of 2.0 W pulsed 912 nm laser was produced at an absorbed pump power of 25.0 W, then the repetition rates of the Q-switched envelope and the mode-locking pulse were ~ 224 kHz and ~ 160 MHz, respectively. Whereas the maximum output power was reduced to 1.3 W using the T_U = 90% Cr⁴⁺:YAG, we obtained a 100% modulation depth for the mode-locking pulses inside the Q-switched envelope.     

Ultrafast laser pulses generated from the chromium-doped cunyite laser

Femtosecond pulses were generated from a Cr⁴⁺: Cunyite laser using a combination of a broadband semiconductor saturable absorber mirror (SESAM), chirped mirrors, and passive mode locking. The astigmatically compensated asymmetric X-cavity with a 4.5-mm-long Cr⁴⁺:Ca₂GeO₄ sample was operated with a 2.5% output coupler. Dispersion compensation was achieved using chirped mirrors. During self-starting mode-locked operation, pulses as short as 365 fs were generated at a pulse repetition rate of 100 MHz with output power of 70 mW and a spectral bandwidth of 5.2 nm at the center wavelength of 1432 nm.     

Improvement of frequency sensitivity of series photodetector frequency circuit system and its application for Cy5 fluorescence detection

This study elucidated the frequency characteristics of series photodetector frequency circuit system for detection of DNA probe ET996 marked with fluorescence dye Cy5. We developed 48 MHz series photodetector frequency circuit system with good sensitivity for fluorescence detection. In accordance with the theory of series photodetector frequency circuit system, the frequency sensitivity can be improved by adjusting circuit parameters such as A (tan θ), C_q, C₀, and C_p. In this research of A adjustment, the capacitance parameter C_m of 48 MHz series photodetector frequency circuit system was adjusted to improve the frequency sensitivity for detection of fluorescence dye concentration; moreover, the bias of photodetector was also adjusted to improve the frequency sensitivity. In the optimal conditions of capacitance match and photodetector bias, the detection limit of ET996-Cy5 fluorescence dye concentration 2 pmol/L can be measured by 48 MHz sensor system. The results of fluorescence experiment also demonstrated that the frequency shift of 48 MHz sensor system was linearly related to the logarithm of fluorescence dye concentration from 200 nmol/L to 2 pmol/L. The frequency method can be applied simply and the detection limit of ET996-Cy5 fluorescence dye concentration was lower than the conventional fluorescence technique by 2 orders.     

Influence of temperature variations on the entropy and correlation of the Grey-Level Co-occurrence Matrix from B-Mode images

In this work, the feasibility of texture parameters extracted from B-Mode images were explored in quantifying medium temperature variation. The goal is to understand how parameters obtained from the gray-level content can be used to improve the actual state-of-the-art methods for non-invasive temperature estimation (NITE). B-Mode images were collected from a tissue mimic phantom heated in a water bath. The phantom is a mixture of water, glycerin, agar-agar and graphite powder. This mixture aims to have similar acoustical properties to in vivo muscle. Images from the phantom were collected using an ultrasound system that has a mechanical sector transducer working at 3.5 MHz. Three temperature curves were collected, and variations between 27 and 44 °C during 60 min were allowed. Two parameters (correlation and entropy) were determined from Grey-Level Co-occurrence Matrix (GLCM) extracted from image, and then assessed for non-invasive temperature estimation. Entropy values were capable of identifying variations of 2.0 °C. Besides, it was possible to quantify variations from normal human body temperature (37 °C) to critical values, as 41 °C. In contrast, despite correlation parameter values (obtained from GLCM) presented a correlation coefficient of 0.84 with temperature variation, the high dispersion of values limited the temperature assessment.     

Development of nanocrystalline Mn-Zn ferrites for high frequency transformer applications

Microwave-Hydrothermal (M-H) method has been successfully used for the synthesis of nanocrystalline Mn-Zn ferrites which are used for high-frequency applications. As synthesized powders were characterized using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The nanopowders were annealed at 600 °C/20 min using the microwave sintering method. The frequency dependence of dielectric constant (ε′) was measured in the range of 10 Hz-1.3 GHz and initial permeability (μ_i) was measured in the range of 10 Hz-1 MHz. The total power loss (P_t) was measured on the annealed samples at 100 kHz and 200 mT condition. Conductor-embedded-ferrite transformers were fabricated and output power (P_o), efficiency (η) and temperature rise (ΔT) were measured at sinusoidal voltage of 25 V at 1 MHz. The transformer efficiency (η) was found to be high and surface rise of temperature (ΔT) is very low.