Heavy water coupling gel for short-wave infrared photoacoustic imaging.

Significance: Changes in lipid, water, and collagen (LWC) content in tissue are associated with numerous medical abnormalities (cancer, atherosclerosis, and Alzheimer's disease). Standard imaging modalities are limited in resolution, specificity, and/or penetration for quantifying these changes. Short-wave infrared (SWIR) photoacoustic imaging (PAI) has the potential to overcome these challenges by exploiting the unique optical absorption properties of LWC>1000 nm. Aim: This study's aim is to harness SWIR PAI for mapping LWC changes in tissue. The focus lies in devising a reflection-mode PAI technique that surmounts current limitations related to SWIR light delivery. Approach: To enhance light delivery for reflection-mode SWIR PAI, we designed a deuterium oxide (D2O, "heavy water") gelatin (HWG) interface for opto-acoustic coupling, intended to significantly improve light transmission above 1200 nm. Results: HWG permits light delivery >1 mJ up to 1850 nm, which was not possible with water-based coupling (>1 mJ light delivery up to 1350 nm). PAI using the HWG interface and the Visualsonics Vevo LAZR-X reveals a signal increase up to 24 dB at 1720 nm in lipid-rich regions. Conclusions: By overcoming barriers related to light penetration, the HWG coupling interface enables accurate quantification/monitoring of biomarkers like LWC using reflection-mode PAI. This technological stride offers potential for tracking changes in chronic diseases (in vivo) and evaluating their responses to therapeutic interventions.

Acoustoelectric Time-Reversal for Ultrasound Phase-Aberration Correction.

Acoustoelectric imaging (AEI) is a technique that combines ultrasound (US) with radio frequency recording to detect and map local current source densities. This study demonstrates a new method called acoustoelectric time reversal (AETR), which uses AEI of a small current source to correct for phase aberrations through a skull or other US-aberrating layers with applications to brain imaging and therapy. Simulations conducted at three different US frequencies (0.5, 1.5, and 2.5 MHz) were performed through media layered with different sound speeds and geometries to induce aberrations of the US beam. Time delays of the acoustoelectric (AE) signal from a monopole within the medium were calculated for each element to enable corrections using AETR. Uncorrected aberrated beam profiles were compared with those after applying AETR corrections, which demonstrated a strong recovery (29%-100%) of lateral resolution and increases in focal pressure up to 283%. To further demonstrate the practical feasibility of AETR, we further conducted bench-top experiments using a 2.5 MHz linear US array to perform AETR through 3-D-printed aberrating objects. These experiments restored lost lateral restoration up to 100% for the different aberrators and increased focal pressure up to 230% after applying AETR corrections. Cumulatively, these results highlight AETR as a powerful tool for correcting focal aberrations in the presence of a local current source with applications to AEI, US imaging, neuromodulation, and therapy.

Ultrasound, photoacoustic, and magnetic resonance imaging to study hyperacute pathophysiology of traumatic and vascular brain injury.

BACKGROUND AND PURPOSE: Cerebrovascular dynamics and pathomechanisms that evolve in the minutes and hours following traumatic vascular injury in the brain remain largely unknown. We investigated the pathophysiology evolution in mice within the first 3 hours after closed-head traumatic brain injury (TBI) and subarachnoid hemorrhage (SAH), two significant traumatic vascular injuries. METHODS: We took a multimodal imaging approach using photoacoustic imaging, color Doppler ultrasound, and MRI to track injury outcomes using a variety of metrics. RESULTS: Brain oxygenation and velocity-weighted volume of blood flow (VVF) values significantly decreased from baseline to 15 minutes after both TBI and SAH. TBI resulted in 19.2% and 41.0% ipsilateral oxygenation and VVF reductions 15 minutes postinjury, while SAH resulted in 43.9% and 85.0% ipsilateral oxygenation and VVF reduction (p < .001). We found partial recovery of oxygenation from 15 minutes to 3 hours after injury for TBI but not SAH. Hemorrhage, edema, reduced perfusion, and altered diffusivity were evident from MRI scans acquired 90-150 minutes after injury in both injury models, although the spatial distribution was mostly focal for TBI and diffuse for SAH. CONCLUSIONS: The results reveal that the cerebral oxygenation deficits immediately following injuries are reversible for TBI and irreversible for SAH. Our findings can inform future studies on mitigating these early responses to improve long-term recovery.

Temporal evaluation of efficacy and quality of tissue repair upon laser-activated sealing.

Injuries caused by surgical incisions or traumatic lacerations compromise the structural and functional integrity of skin. Immediate approximation and robust repair of skin are critical to minimize occurrences of dehiscence and infection that can lead to impaired healing and further complication. Light-activated skin sealing has emerged as an alternative to sutures, staples, and superficial adhesives, which do not integrate with tissues and are prone to scarring and infection. Here, we evaluate both shorter- and longer-term efficacy of tissue repair response following laser-activated sealing of full-thickness skin incisions in immunocompetent mice and compare them to the efficacy seen with sutures. Laser-activated sealants (LASEs) in which, indocyanine green was embedded within silk fibroin films, were used to form viscous pastes and applied over wound edges. A hand-held, near-infrared laser was applied over the incision, and conversion of the light energy to heat by the LASE facilitated rapid photothermal sealing of the wound in approximately 1 min. Tissue repair with LASEs was evaluated using functional recovery (transepidermal water loss), biomechanical recovery (tensile strength), tissue visualization (ultrasound [US] and photoacoustic imaging [PAI]), and histology, and compared with that seen in sutures. Our studies indicate that LASEs promoted earlier recovery of barrier and mechanical function of healed skin compared to suture-closed incisions. Visualization of sealed skin using US and PAI indicated integration of the LASE with the tissue. Histological analyses of LASE-sealed skin sections showed reduced neutrophil and increased proresolution macrophages on Days 2 and 7 postclosure of incisions, without an increase in scarring or fibrosis. Together, our studies show that simple fabrication and application methods combined with rapid sealing of wound edges with improved histological outcomes make LASE a promising alternative for management of incisional wounds and lacerations.

Thermal and Acoustic Stabilization Of Volatile Phase-Change Contrast Agents Via Layer-By-Layer Assembly.

OBJECTIVE: Phase-change contrast agents (PCCAs) are perfluorocarbon nanodroplets (NDs) that have been widely studied for ultrasound imaging in vitro, pre-clinical studies, and most recently incorporated a variant of PCCAs, namely a microbubble-conjugated microdroplet emulsion, into the first clinical studies. Their properties also make them attractive candidates for a variety of diagnostic and therapeutic applications including drug-delivery, diagnosis and treatment of cancerous and inflammatory diseases, as well as tumor-growth tracking. However, control over the thermal and acoustic stability of PCCAs both in vivo and in vitro has remained a challenge for expanding the potential utility of these agents in novel clinical applications. As such, our objective was to determine the stabilizing effects of layer-by-layer assemblies and its effect on both thermal and acoustic stability. METHODS: We utilized layer-by-layer (LBL) assemblies to coat the outer PCCA membrane and characterized layering by measuring zeta potential and particle size. Stability studies were conducted by; 1) incubating the LBL-PCCAs at atmospheric pressure at 37∘C and 45∘C followed by; 2) ultrasound-mediated activation at 7.24 MHz and peak-negative pressures ranging from 0.71 - 5.48 MPa to ascertain nanodroplet activation and resultant microbubble persistence. The thermal and acoustic properties of decafluorobutane gas-condensed nanodroplets (DFB-NDs) layered with 6 and 10 layers of charge-alternating biopolymers, (LBL6NDs and LBL10NDs) respectively, were studied and compared to non-layered DFB-NDs. Half-life determinations were conducted at both 37∘C and 45∘C with acoustic droplet vaporization (ADV) measurements occurring at 23∘C. DISCUSSION: Successful application of up to 10 layers of alternating positive and negatively charged biopolymers onto the surface membrane of DFB-NDs was demonstrated. Two major claims were substantiated in this study; namely, (1) biopolymeric layering of DFB-NDs imparts a thermal stability up to an extent; and, (2) both LBL6NDs and LBL10NDs did not appear to alter particle acoustic vaporization thresholds, suggesting that the thermal stability of the particle may not necessarily be coupled with particle acoustic vaporization thresholds. CONCLUSION: Results demonstrate that the layered PCCAs had higher thermal stability, where the half-lifes of the LBLxNDs are significantly increased after incubation at 37∘C and 45∘C. Furthermore, the acoustic vaporization profiles the DFB-NDs, LBL6NDs, and LBL10NDs show that there is no statistically significant difference between the acoustic vaporization energy required to initiate acoustic droplet vaporization.

Current Source Density Imaging Using Regularized Inversion of Acoustoelectric Signals.

Acoustoelectric (AE) imaging can potentially image biological currents at high spatial (~mm) and temporal (~ms) resolution. However, it does not directly map the current field distribution due to signal modulation by the acoustic field and electric lead fields. Here we present a new method for current source density (CSD) imaging. The fundamental AE equation is inverted using truncated singular value decomposition (TSVD) combined with Tikhonov regularization, where the optimal regularization parameter is found based on a modified L-curve criterion with TSVD. After deconvolution of acoustic fields, the current field can be directly reconstructed from lead field projections and the CSD image computed from the divergence of that field. A cube phantom model with a single dipole source was used for both simulation and bench-top phantom studies, where 2D AE signals generated by a 0.6 MHz 1.5D array transducer were recorded by orthogonal leads in a 3D Cartesian coordinate system. In simulations, the CSD reconstruction had significantly improved image quality and current source localization compared to AE images, and performance further improved as the fractional bandwidth (BW) increased. Similar results were obtained in the phantom with a time-varying current injected. Finally, a feasibility study using an in vivo swine heart model showed that optimally reconstructed CSD images better localized the current source than AE images over the cardiac cycle.

Emerging photoacoustic and thermoacoustic imaging technologies for detecting primary and metastatic cancer and guiding therapy.

In recent years, there has been a progressive trend towards less invasive technologies for detecting metastatic cancer and guiding therapy with the goal of lower morbidity, better outcomes, and superior cosmetic appearance than traditional methods. This mini-review examines three emerging noninvasive hybrid technologies for detecting primary cancer, metastasis and guiding thermal therapy. Real-time thermoacoustic imaging and thermometry potentially provides valuable and critical feedback for guiding focused microwave ablation therapy. Label-free photoacoustic monitoring of cancer cells is a promising clinical diagnostic and theranostic tool for detecting metastatic disease and monitoring the response to therapy. Finally, immunologically targeted gold nanoparticles combined with photoacoustic imaging is able to detect lymph node micrometastasis in mouse models of breast cancer. These emerging techniques have the potential to improve the decision to biopsy, provide more accurate prognosis, and enhance the efficacy of therapy for early and late stage cancers.

Introduction to novel developments in radio-imaging and radiotherapy.

Radiation therapy has long been known to be a very effective form of therapy in relieving symptoms and prolonging the life of patients with brain metastases. Novel developments in this field have allowed oncologists to improve on older forms of radiation therapy; these recent advances in radiotherapeutic techniques (stereotactic radiosurgery and hippocampal-avoidant whole brain radiation therapy) allow sparing of the healthy brain from receiving unnecessary radiation while delivering effective treatment to the metastases, thus improving the quality of life for surviving patients. Furthermore, multiple clinical trials have documented the increased loco-regional control in the brain when radiosurgery is interdigitated with immune check point inhibitors for treatment of melanoma brain metastases. Mild hyperthermia has been used for decades as an adjuvant to radiotherapy in the treatment of radiation resistant cancers; lately, however, thermal therapies, such as hyperthermia, cryoablation, radiofrequency ablation and high intensity focused ultrasound are being investigated to provide a new ablative approach to cancer while thermoacoustic imaging and thermometry have recently been proposed as new techniques for monitoring tissue temperature in the breast during ablation treatment. In addition, other hybrid techniques have emerged that combine ultrasounds with other forms of energy such as light to provide a more accurate diagnosis and enhance the efficacy of therapy for early and late stage cancers.

Shear wave elastography detects novel imaging biomarkers of aromatase inhibitor-induced joint pain: a pilot study.

AIM: To determine whether differences in joint and tendon stiffness as measured by ultrasound shear wave elastography are present in breast cancer patients with aromatase inhibitor-associated arthralgias compared to age-comparable healthy control women. METHODS: Postmenopausal women with stage I-III breast cancer who were taking adjuvant aromatase inhibitors and complained of joint pain were enrolled (n = 6). Postmenopausal women with no history of breast cancer, hormone treatment, or joint pain served as controls (n = 7). All subjects had bilateral hands and wrists evaluated by gray-scale and power Doppler ultrasound, and shear wave elastography ultrasound. RESULTS: Patients with AI-associated arthralgias had significantly stiffer tendons than controls in the 1st extensor compartment (long axis; p = 0.001), 4th extensor compartment (long axis; p = 0.014), 3rd metacarpophalangeal joint (p = 0.002), the pooled values of the extensor compartments, both long (p = 0.044) and short axes (p = 0.035), and the pooled values for the metacarpophalangeal joints (p = 0.002). On ultrasound, the patients (but not controls) presented with hyperemia and increased tenosynovial fluid in the flexor and extensor tendon sheaths, and the median nerves were symptomatic and bifid; however, these differences were not statistically significant. CONCLUSIONS: This is the first study to identify increased tendon stiffness as a putative physiological characteristic of aromatase inhibitor-associated arthralgias. Future studies should determine whether increased tendon stiffness is a risk factor for the development of aromatase inhibitor-associated arthralgias, or a result of aromatase inhibitor treatment.

Real-Time Volumetric Thermoacoustic Imaging and Thermometry Using a 1.5-D Ultrasound Array.

Noninvasive thermal therapies for the treatment of breast cancer depend on accurate monitoring of tissue temperature to optimize treatment and ensure safety. This work describes a real-time system for 3-D thermoacoustic imaging and thermometry (TAI-TAT) for tracking temperature in tissue samples during heating. The study combines a 2.7-GHz microwave pulse generator with a custom 1.5-D 0.6 MHz ultrasound array for generating and detecting TA signals. The system is tested and validated on slabs of biological tissue and saline gel during heating. Calibration curves for relating the TA signal to temperature were calculated in saline gel (3.40%/°C), muscle (1.73%/°C), and fat (1.15%/°C), respectively. The calibrations were used to produce real-time, volumetric temperature maps at ~3-s intervals with a spatial resolution of approximately 3 mm. TAT temperature changes within a region of interest were compared to adjacent thermocouples with a mean error of 17.3%, 13.2%, and 20.4% for muscle, gel, and fat, respectively. The TAT algorithm was also able to simultaneously track temperatures in different tissues. With further development, noninvasive TAI-TAT may prove to be a valuable method for accurate and real-time feedback during breast cancer ablation therapy.

In vivo acoustoelectric imaging for high-resolution visualization of cardiac electric spatiotemporal dynamics.

Acoustoelectric cardiac imaging (ACI) is a hybrid modality that exploits the interaction of an ultrasonic pressure wave and the resistivity of tissue to map current densities in the heart. This study demonstrates for the first time in vivo ACI in a swine model. ACI measured beat-to-beat variability (n=20) of the peak of the cardiac activation wave at one location of the left ventricle as 5.32±0.74µV, 3.26±0.54mm below the epicardial surface, and 2.67±0.56ms before the peak of the local electrogram. Cross-sectional ACI images exhibited propagation velocities of 0.192±0.061m/s along the epicardial-endocardial axis with an SNR of 24.9 dB. This study demonstrates beat-to-beat and multidimensional ACI, which might reveal important information to help guide electroanatomic mapping procedures during ablation therapy.

Acoustoelectric imaging of deep dipoles in a human head phantom for guiding treatment of epilepsy.

OBJECTIVE: This study employs a human head model with real skull to demonstrate the feasibility of transcranial acoustoelectric brain imaging (tABI) as a new modality for electrical mapping of deep dipole sources during treatment of epilepsy with much better resolution and accuracy than conventional mapping methods. APPROACH: This technique exploits an interaction between a focused ultrasound (US) beam and tissue resistivity to localize current source densities as deep as 63 mm at high spatial resolution (1 to 4 mm) and resolve fast time-varying currents with sub-ms precision. MAIN RESULTS: Detection thresholds through a thick segment of the human skull at biologically safe US intensities was below 0.5 mA and within range of strong currents generated by the human brain. SIGNIFICANCE: This work suggests that 4D tABI may emerge as a revolutionary modality for real-time high-resolution mapping of neuronal currents for the purpose of monitoring, staging, and guiding treatment of epilepsy and other brain disorders characterized by abnormal rhythms.

Real-time 3D thermoacoustic imaging and thermometry using a self-calibration technique.

Thermoacoustic (TA) imaging is a modality where pulsed microwaves are used to generate ultrasound waves in tissue, which are highly correlated with temperature. This study uses a self-calibration approach to improve the estimation of temperature using 3D real-time TA thermometry in porcine tissue during localized heating. The self-calibration method estimated temperatures at eight embedded thermocouple locations with a normalized root-mean-square error of 3.25±2.08%. The results demonstrate that the method has the suitable accuracy and resolution to provide feedback control for breast cancer ablation therapy.

High resolution transcranial acoustoelectric imaging of current densities from a directional deep brain stimulator.

OBJECTIVE: New innovations in deep brain stimulation (DBS) enable directional current steering-allowing more precise electrical stimulation of the targeted brain structures for Parkinson's disease, essential tremor and other neurological disorders. While intra-operative navigation through MRI or CT approaches millimeter accuracy for placing the DBS leads, no existing modality provides feedback of the currents as they spread from the contacts through the brain tissue. In this study, we investigate transcranial acoustoelectric imaging (tAEI) as a new modality to non-invasively image and characterize current produced from a directional DBS lead. tAEI uses ultrasound (US) to modulate tissue resistivity to generate detectable voltage signals proportional to the local currents. APPROACH: An 8-channel directional DBS lead (Infinity 6172ANS, Abbott Inc) was inserted inside three adult human skulls submerged in 0.9% NaCl. A 2.5 MHz linear array delivered US pulses through the transtemporal window and focused near the contacts on the lead, while a custom amplifier and acquisition system recorded the acoustoelectric (AE) interaction used to generate images. MAIN RESULTS: tAEI detected monopolar current with stimulation pulses as short as 100 µs with an SNR ranging from 10-27 dB when using safe US pressure (mechanical indices <0.78) and injected current of ~2 mA peak amplitude. Adjacent contacts were discernable along the length and within each ring of the lead with a mean radial separation between contacts of 2.10 and 1.34 mm, respectively. SIGNIFICANCE: These results demonstrate the feasibility of tAEI for high resolution mapping of directional DBS currents using clinically-relevant stimulation parameters. This new modality may improve the accuracy for placing the DBS leads, guide calibration and programming, and monitor long-term performance of DBS for treatment of Parkinson's disease.

Selective Mapping of Deep Brain Stimulation Lead Currents Using Acoustoelectric Imaging.

We describe a new application of acoustoelectric imaging for non-invasive mapping of the location, magnitude and polarity of current generated by a clinical deep brain stimulation (DBS) device. Ultrasound at 1MHz was focused near the DBS device as short current pulses were injected across different DBS leads. A recording electrode detected the high-frequency acoustoelectric interaction signal. Linear scans of the US beam produced time-varying images of the magnitude and polarity of the induced current, enabling precise localization of the DBS leads within 0.70mm, a detection threshold of 1.75mA at 1 MPa and a sensitivity of 0.52 ± 0.07 µV/(mA*MPa). Monopole and dipole configurations in saline were repeated through a human skullcap. Despite 13.8-dB ultrasound attenuation through bone, acoustoelectric imaging was still >10dB above background with a sensitivity of 0.56 ± 0.10 µV/(mA*MPa). This proof-of-concept study indicates that selective mapping of lead currents through a DBS device may be possible using non-invasive acoustoelectric imaging.

Frontiers of cancer imaging and guided therapy using ultrasound, light, and microwaves.

This review describes emerging techniques within the last 5 years that employ ultrasound for detecting and staging malignancy, tracking metastasis, and guiding treatment. Ultrasound elastography quantifies soft tissue elastic properties that change as a tumor grows and proliferates. Hybrid imaging modalities that combine ultrasound with light or microwave energy provide novel contrast for mapping blood oxygen saturation, transport of particles through lymphatic vessels and nodes, and real-time feedback for guiding needle biopsies. Combining these methods with smart nanoparticles and contrast agents further promotes new paradigms for cancer imaging and therapy.

Tissue Acoustoelectric Effect Modeling From Solid Mechanics Theory.

The acoustoelectric (AE) effect is a basic physical phenomenon, which underlies the changes made in the conductivity of a medium by the application of focused ultrasound. Recently, based on the AE effect, several biomedical imaging techniques have been widely studied, such as ultrasound-modulated electrical impedance tomography and ultrasound current source density imaging. To further investigate the mechanism of the AE effect in tissue and to provide guidance for such techniques, we have modeled the tissue AE effect using the theory of solid mechanics. Both bulk compression and thermal expansion of tissue are considered and discussed. Computation simulation shows that the muscle AE effect result, conductivity change rate, is 3.26×10-3 with 4.3-MPa peak pressure, satisfying the theoretical value. Bulk compression plays the main role for muscle AE effect, while thermal expansion makes almost no contribution to it. In addition, the AE signals of porcine muscle are measured at different focal positions. With the same magnitude order and the same change trend, the experiment result confirms that the simulation result is effective. Both simulation and experimental results validate that tissue AE effect modeling using solid mechanics theory is feasible, which is of significance for the further development of related biomedical imaging techniques.

Shear-Wave Elastography: Basic Physics and Musculoskeletal Applications.

In the past 2 decades, sonoelastography has been progressively used as a tool to help evaluate soft-tissue elasticity and add to information obtained with conventional gray-scale and Doppler ultrasonographic techniques. Recently introduced on clinical scanners, shear-wave elastography (SWE) is considered to be more objective, quantitative, and reproducible than compression sonoelastography with increasing applications to the musculoskeletal system. SWE uses an acoustic radiation force pulse sequence to generate shear waves, which propagate perpendicular to the ultrasound beam, causing transient displacements. The distribution of shear-wave velocities at each pixel is directly related to the shear modulus, an absolute measure of the tissue's elastic properties. Shear-wave images are automatically coregistered with standard B-mode images to provide quantitative color elastograms with anatomic specificity. Shear waves propagate faster through stiffer contracted tissue, as well as along the long axis of tendon and muscle. SWE has a promising role in determining the severity of disease and treatment follow-up of various musculoskeletal tissues including tendons, muscles, nerves, and ligaments. This article describes the basic ultrasound physics of SWE and its applications in the evaluation of various traumatic and pathologic conditions of the musculoskeletal system. ©RSNA, 2017.

Tracking delivery of a drug surrogate in the porcine heart using photoacoustic imaging and spectroscopy.

Although the drug-eluting stent (DES) has dramatically reduced the rate of coronary restenosis, it still occurs in up to 20% of patients with a DES. Monitoring drug delivery could be one way to decrease restenosis rates. We demonstrate real-time photoacoustic imaging and spectroscopy (PAIS) using a wavelength-tunable visible laser and clinical ultrasound scanner to track cardiac drug delivery. The photoacoustic signal was initially calibrated using porcine myocardial samples soaked with a known concentration of a drug surrogate (DiI). Next, an in situ coronary artery was perfused with DiI for 20 min and imaged to monitor dye transport in the tissue. Finally, a partially DiI-coated stent was inserted into the porcine brachiocephalic trunk for imaging. The photoacoustic signal was proportional to the DiI concentration between 2.4 and 120 ?? ? g / ml , and the dye was detected over 1.5 mm from the targeted coronary vessel. Photoacoustic imaging was also able to differentiate the DiI-coated portion of the stent from the uncoated region. These results suggest that PAIS can track drug delivery to cardiac tissue and detect drugs loaded onto a stent with sub-mm precision. Future work using PAIS may help improve DES design and reduce the probability of restenosis.

An Instrumental Electrode Configuration for 3D Ultrasound Modulated Electrical Impedance Tomography.

Ultrasound modulated electrical impedance tomography (UMEIT) is a novel hybrid imaging technique, which utilizes coupling between electric and acoustic modalities. Based on the forward solver along different current directions, an instrumental electrode configuration is proposed for 3D UMEIT. The proposed electrode configuration can produce a similar longitudinal current, making the power density distribution on the x-y plane approximately consistent with the corresponding conductivity distribution. Then, this satisfying power density is adopted to reconstruct a higher-resolution conductivity distribution. Therefore, the proposed electrode configuration contributes to improving the image reconstruction quality of UMEIT. Also, to clearly demonstrate its meaning in theory, the forward solver results are analyzed from an electrical point of view. In addition, the nonlinear partial differential equation (PDE) relating the power density to the measured data is derived again with a more reasonable expression. Finally, simulation with realistic geometry model of human breast is done and feasibility verifying experiment is made. Both simulation and experimental results validate the feasibility of the proposed electrode configuration.