Methods for assessing hemostatic function

Abstract

This paper discloses a method for evaluating hemostatic function, comprising: applying a force waveform to a test sample in a test chamber; the force waveform applying an acoustic radiation force to the test sample, thereby inducing movement; ultrasonic sensing pulses being applied to the test sample, and the differences in their echoes providing information about the movement of the test sample, wherein these differences include phase changes or time shifts, either of which are related to displacement; and comparing the characteristics of these differences with an analytical or computational model to estimate the mechanical properties of the test sample, thereby evaluating the hemostatic function. This invention enables timely and accurate evaluation of hemostatic function by measuring the mechanical properties of blood samples during coagulation.

Description

[0001] This application is a divisional application of patent application No. 201680015219.6, filed on March 17, 2016, entitled "Determining Mechanical Properties by Ultrasonic Induced Resonance". This application is also a divisional application of patent application No. 201910203968.7, filed on March 17, 2016, entitled "Apparatus for Evaluating Hemostasis".

[0002] Cross-referencing of related patent applications

[0003] This application claims priority to U.S. Patent Application 14 / 660,700, entitled “Determining Mechanical Properties via Ultrasound-Induced Resonance,” filed March 17, 2015, the entire contents of which are incorporated herein by reference. Background Technology

[0004] Hemostasis is the physiological process of stopping bleeding. Functional hemostasis requires a balanced combination of plasma clotting factors to initiate coagulation, sufficient fibrinogen to form the fibrin network, platelets to regulate factor function and mechanically strengthen the fibrin network, and fibrinolytic enzymes to dissolve the clot at the end of its lifespan. Disruption of any of these subsystems can interrupt hemostasis, either by hindering the cessation of bleeding or by initiating coagulation when unnecessary. Interruption of hemostasis can have a significant impact on morbidity and mortality in patients with heart disease, stroke, traumatic injuries, cancer, and sepsis.

[0005] While hemostatic dysfunction can affect a wide range of medical conditions, it has been particularly well-studied in cardiac surgery. Coronary artery bypass surgery is often accompanied by significant postoperative bleeding. This is due to a combination of factors including platelet damage from the bypass pump, depletion of factors and fibrinogen associated with surgical trauma, and the occasional presence of residual anticoagulants. Several strategies are currently used to address this dysfunction. The most primitive strategy is the "shotgun approach"; infusing different combinations of fresh frozen plasma, cryoprecipitate, or fibrinogen concentrate, along with platelet concentrate. This approach is often successful in controlling bleeding, but unnecessary transfusions can incur substantial financial costs and increase patient morbidity and mortality. Recognizing the risks associated with excessive transfusions has led to the development of increasingly specific and detailed guidelines for transfusion management. These guidelines require the implementation of timely and accurate bedside assessments of hemostatic function to guide transfusions.

[0006] Various methods have been proposed to meet the needs of bedside hemostasis testing. These techniques can be categorized into several types: coagulation time assays, platelet-specific assays, and viscoelasticity assays. Coagulation time assays can be performed in simple systems; however, rapidly formed clots may not be physiologically useful, thus limiting the clinical value of coagulation time results. Furthermore, coagulation time assays are typically performed on plasma rather than whole blood, thus often overlooking important interactions between plasma clotting factors and platelets. Platelet-only assays provide useful information but are also limited because they ignore interactions between platelets and plasma clotting factors. Viscoelasticity assays have been shown to provide very useful data. However, their procedural complexity has traditionally limited their bedside applicability. Currently, no available bedside assay can adequately and accurately assess hemostasis in a timely manner. Therefore, a rapid and accurate assay remains needed to fill this gap.

[0007] Other systems, methods, features, and / or advantages will or may become apparent to those skilled in the art upon review of the following drawings and detailed description. All such additional systems, methods, features, and / or advantages are intended to be included within this description and are protected by the appended claims. Summary of the Invention

[0008] This document discloses an apparatus for estimating the mechanical properties of a sample. The apparatus may include: a chamber configured to hold a sample; a transmitter configured to emit a plurality of waveforms, including at least one force waveform; and a transducer assembly operatively connected to the transmitter and configured to convert the emitted waveforms into ultrasonic shapes. The transducer assembly may also emit and receive the ultrasonic shapes within and outside the chamber, and convert at least two received ultrasonic shapes into received electrical waveforms. The apparatus further includes a data processor capable of: receiving the received electrical waveforms; estimating a difference in the received electrical waveforms at least partially caused by movement of the sample; and estimating the mechanical properties of the sample by comparing at least one feature of the estimated difference with at least one predicted feature, wherein the at least one predicted feature is based on a model of the effects of the chamber walls. Finally, the apparatus may also include a controller configured to control the timing of the ultrasonic transmitter and the data processor.

[0009] In one specific implementation, at least one predictive feature predicted by the data processor is based on a model of aspects of induced movement caused at least in part by the boundary effects of the chamber walls.

[0010] In another specific implementation, at least one predictive feature predicted by the data processor is based on a model of aspects of induced movement caused at least in part by resonance within the cavity.

[0011] In yet another specific implementation, at least one predictive feature predicted by the data processor is based on a model of an aspect of induced movement caused at least in part by the reflection of induced shear waves from the chamber wall.

[0012] A device for estimating the mechanical properties of a sample is also disclosed. The device may include: a chamber configured to hold the sample; a transmitter configured to emit a plurality of waveforms, including at least one force waveform; and a transducer assembly operatively connected to the transmitter and configured to convert the emitted waveforms into ultrasonic shapes. The transducer assembly may also emit and receive the ultrasonic shapes within and outside the chamber, and convert at least two received ultrasonic shapes into received electrical waveforms. The device further includes a data processor capable of: receiving the received electrical waveforms; estimating a difference in the received electrical waveforms at least partially caused by sample resonance; and characterizing the mechanical properties of the sample based on at least one feature of the estimated difference. Finally, the device may also include a controller configured to control the timing of the ultrasonic transmitter and the data processor.

[0013] Other implementation schemes, specific implementations and / or examples are also provided below. Attached Figure Description

[0014] The following detailed description will be better understood when read in conjunction with the accompanying drawings, which illustrate one or more of various embodiments of the present disclosure. However, it should be understood that the various embodiments of the present disclosure are not limited to the precise arrangements and means shown in the drawings.

[0015] Figure 1 This is an exemplary schematic diagram of a device used to measure the mechanical properties of a sample.

[0016] Figure 2 Is using Figure 1 An exemplary schematic diagram of the specific implementation of signal processing and data acquisition process.

[0017] Figure 3 Representative experimental time-displacement curves obtained from coagulated human blood are shown.

[0018] Figure 4 Representative time-modulus and time-viscosity curves estimated using computer models are shown.

[0019] Figure 5 An exemplary contour plot shows the correlation between experimental time-displacement data and computer models for a range of moduli and viscosities.

[0020] Figure 6 A representative time-modulus curve estimated using a computer model assuming constant viscosity is shown.

[0021] Figure 7 An example of using correlation masking to remove marginal modulus estimates is shown.

[0022] Figure 8 An exemplary embodiment of this disclosure is shown, in which a focusing element is associated with a transducer assembly.

[0023] Figure 9 An exemplary embodiment of this disclosure is shown, wherein an acoustic coupling agent is inserted between the transducer assembly and the test chamber.

[0024] Figure 10 An exemplary embodiment of this disclosure is shown, wherein a focusing element is associated with a transducer assembly, and an acoustic coupling agent is inserted between the transducer assembly and the test chamber.

[0025] Figure 11 An exemplary embodiment of this disclosure is shown, wherein a focusing element is associated with a test chamber, and an acoustic coupling agent is inserted between the transducer assembly and the test chamber.

[0026] Figure 12 An exemplary embodiment of the present disclosure, incorporating multiple additional elements, is shown.

[0027] Figure 13 An exemplary embodiment of this disclosure is shown, wherein the transducer assembly includes two separate transducer elements.

[0028] Figure 14 An embodiment of this disclosure is shown, wherein the transducer assembly includes two separate transducer elements, one dedicated to waveform transmission and the other dedicated to waveform reception.

[0029] Figure 15 A computational grid for the finite difference time-domain method described in this disclosure is shown.

[0030] Figure 16 A representative time-modulus curve estimated using the analytical model is shown.

[0031] Figure 17 The Kelvin-Voigt model (Example 1) and the Jeffrey model (Example 2) used in this disclosure are shown. Detailed Implementation

[0032] Hemostatic function can be assessed in a timely and accurate manner by measuring the mechanical properties of blood samples during coagulation. For example, the shear modulus of a blood sample over time can be measured during the coagulation process. In this application, "shear modulus" is used interchangeably with "modulus". The terms "rigid" and "stiffness" also refer to modulus.

[0033] In the embodiments described in this disclosure, a force-applying ultrasonic waveform is applied to a sample within a test chamber. This force waveform exerts an acoustic radiation force on the sample, thereby causing motion. This motion is influenced by the presence of the test chamber walls. Ultrasonic sensing pulses are applied to the sample, and the differences in their echoes provide information about the sample's movement. These differences may include phase changes or time shifts, either of which can be related to displacement. Finally, characteristics of these differences, such as the oscillation period of the sample motion, are compared with an analytical or computational model to estimate the mechanical properties of the sample.

[0034] The implementation schemes described in this disclosure may include Figure 1 The components are shown. Transmitter 112 emits an electrical waveform including at least one applied force waveform. These electrical waveforms are converted into ultrasonic waves by transducer assembly 114. The applied force waveform induces sample motion within test chamber 116. The returned ultrasonic echoes are converted back into electrical waveforms by transducer assembly 114. These electrical waveforms are analyzed by data processor 118 to estimate the mechanical properties of the sample. The details of this and other embodiments can be understood through the following detailed description. The timing of transmission, reception, and data processing is controlled by controller 110.

[0035] This disclosure utilizes the phenomenon of ultrasonic radiation force, sometimes referred to as acoustic radiation force. Ultrasonic radiation force is a body force acting in the same direction as the propagation of the ultrasonic wave. It is a result of momentum transfer that occurs as the traveling ultrasonic wave is absorbed or reflected. The ultrasonic radiation force is confined within the ultrasonic beam; the magnitude of the force is proportional to the intensity of the ultrasonic beam. Therefore, a focused ultrasonic beam can be used to apply a local acoustic radiation force field. In this disclosure, the applied radiation force field is typically smaller than the test chamber to which it is applied. The sample motion induced by the radiation force field is initially confined to the force field region. However, over time, the displacement field propagates outward from the force application region.

[0036] In the embodiments described in this disclosure, ultrasonic radiation force is used to generate shear waves within a blood sample. A shear wave is a mechanical wave in which the displacement direction of particles is perpendicular to the direction of wave motion. The shear waves of this disclosure can be generated by guiding ultrasound waves of sufficient magnitude into the sample via a "force waveform." The force waveform carries sufficient energy for absorption and reflection within the test sample to generate an acoustic radiation force. This acoustic radiation force is induced along the direction of ultrasound propagation and can be considered as a body force acting on a certain volume of a medium limited by the size of the ultrasound beam.

[0037] Induced shear waves travel within the test chamber and are reflected from one or more walls. In some embodiments, a single reflected shear wave can be detected, and its arrival time at the ultrasonic sensing beam can form the basis for estimating the sample's modulus. For some combinations of chamber geometry and sample mechanical properties, reflected shear waves may not be detectable. For example, the sample viscosity may be too high for it to generate a shear wave, although it may not possess easily distinguishable characteristics, and therefore the reflection of the shear wave from the walls cannot be easily measured. Nevertheless, the sample motion induced by acoustic radiation forces will exhibit disturbances caused by the interaction of the induced shear wave with the chamber walls. The characteristics of this sample motion can form the basis for estimating the sample's mechanical properties, even if the shear wave itself is not clearly distinguishable during the induced sample motion. In other cases, the shear wave may repeatedly reflect within the chamber, generating resonances that can form the basis for estimating the sample's modulus.

[0038] In this specification, the terms “test chamber,” “resonance chamber,” “resonance chamber,” and “chamber” are used interchangeably without loss of generality.

[0039] In this disclosure, the terms "force waveform" and "force pulse" are used interchangeably without loss of generality. Similarly, the terms "sensing pulse" and "sensing waveform" are used interchangeably without loss of generality.

[0040] The motion of induced shear waves, including perturbations of the shear waves associated with reflection and / or reverberation, can be estimated by considering the difference between the echoes from the sensed waveform. The difference does not imply attenuation; rather, the term is used broadly to indicate any aspect that is not identical between waveforms. The term "sensed waveform" is used here to indicate an ultrasonic shape whose magnitude is too small to generate a significant acoustic radiation force and therefore too small to induce a significant shear wave, but large enough to return an ultrasonic echo for difference analysis. In an alternative embodiment, one or more of the same waveforms may be used for force application and sensing.

[0041] Shear modulus can be correlated with other mechanical property measures such as Young's modulus and Lamé constant. Therefore, while this disclosure focuses on the measurement of shear modulus, these estimates can be transformed to provide estimates of other mechanical properties.

[0042] In one embodiment, an apparatus is provided for transmitting a force waveform and multiple sensed waveforms into a sample within a resonant cavity and processing the echoes returned from the sensed waveforms. The apparatus distinguishes the mechanical characteristics of the sample based on resonant features. For example, the apparatus may include at least a controller, a transmitter, a transducer assembly, a resonant cavity, and a data processor.

[0043] Figure 1A high-level block diagram of an exemplary embodiment of the present disclosure is shown. In this embodiment, controller 110 is provided to manage the timing of various aspects of the detection process. For example, controller 110 may control the timing of transmit data digitization and data processing. Controller 110 may be a general-purpose computer. In other embodiments, controller 110 may be a dedicated controller, such as, for example, a field-programmable gate array (FPGA). In one specific embodiment, a Xilinx Spartan 6 FPGA may be utilized. Alternatively, an embedded processor or DSP chip may be used as the controller.

[0044] Controller 110 can control the timing of transmitter 112 among other things. Transmitter 112 can be used to transmit voltage waveforms. Controller 110 can guide transmitter 112 to connect and disconnect power relative to transducer components at specific time intervals. In one exemplary embodiment, transmitter 112 can transmit desired waveforms including positive voltages, negative voltages, and / or neutral voltages at specific time intervals to achieve transmission between voltage levels. In other embodiments, the transmitter may be able to have multiple voltage amplitude levels, thereby enabling the generation of a wider range of waveform shapes. In one embodiment, transmitter 112 includes a Supertex MD1810 level shifter to control a Supertex TC6320 MOSFET to switch + / -100V power and to control a Supertex TC2320 to clamp the transmitted waveform to ground. Various hardware devices, firmware and / or software, or combinations thereof, can also be used. Input signals to transmitter 112 can be obtained from controller 110.

[0045] exist Figure 1In one embodiment, transmitter 112 transmits a voltage waveform to transducer assembly 114. In this embodiment, transducer assembly 114 is an ultrasonic transducer. Transducer assembly 114 can convert the transmitted voltage waveform into an ultrasonic wave and convert the ultrasonic echo into a received voltage waveform. In one exemplary embodiment, the ultrasonic transducer is a unit-piece composite piston transducer. However, other types of ultrasonic transducers can be used, and these ultrasonic transducers may include hardware, firmware and / or software, or combinations thereof. In alternative embodiments, the transducer may include piezoelectric materials (including single-crystal materials), CMUT (capacitive micromachining ultrasonic transducer), relaxor ferroelectric transducers, thermoacoustic sources or voice coils, and other transducer technologies. In another alternative embodiment, ultrasonic emission is performed using a thermoacoustic method, wherein rapid heating causes thermal expansion, which in turn generates ultrasonic waves. Transducer assembly 114 may also include an active transducer element (e.g., a piezoelectric material) mounted to a single acoustic matching layer, which may then be mounted to a polymer support. In one embodiment, the transducer employs air backing to improve electromechanical efficiency. In an exemplary embodiment, the transducer element of transducer assembly 114 has a wide bandwidth and a sensitivity between approximately 5 MHz and 12 MHz. In some embodiments, a series matching inductor is placed between transducer assembly 114 and transmitter 112 to eliminate the dummy component of the transducer impedance. Other circuitry can be demonstrated to facilitate matching the impedances of the transmitter, transducer, and receiver.

[0046] In one exemplary embodiment, a test sample is placed within chamber 116 for testing. Transducer assembly 114 directs ultrasonic energy through the test sample held within chamber 116. In some embodiments, chamber 116 is axisymmetric and has a major axis collinear with the propagation vector of the ultrasonic beam. In an alternative embodiment, only a portion of chamber 116 is axisymmetric, while other portions have arbitrary geometry as needed to support the filled sample and avoid obstructing the ultrasonic beam.

[0047] In some implementations, chamber 116 is made of a material that is substantially more rigid (with a higher shear modulus) than the material being characterized. Therefore, for the purpose of analyzing blood clots, a resonant chamber made of polystyrene or a similarly rigid material can be effectively considered to have infinite rigidity. For example, chamber 116 can be thousands, hundreds of thousands, or even millions of times harder than the sample within it. For instance, blood clots typically have a shear modulus of several thousand Pascals. Thermoplastics such as polystyrene have a shear modulus of approximately one gigapascal.

[0048] In some implementations, a "force waveform" and a "sensing waveform" can be directed into the test sample within chamber 116. The force waveform can be an ultrasonic waveform capable of inducing shear waves in the sample via acoustic radiation force, while the sensing waveform can be a lower-energy waveform used to sense various aspects of the sample at a given point in time. These waveforms and their uses are described in more detail below. The modulus of the sample can be estimated by analyzing the resonance of the ultrasonically induced shear waves within chamber 116.

[0049] In some implementations, the data processor 118 incorporates multiple functions to perform analysis of the received echoes. For example, the data processor 118 may incorporate a receiver and a digitizer, which together provide digital signals to a general-purpose processor for data analysis. In this implementation, the receiver of the data processor 118 receives and amplifies the electrical signal corresponding to the ultrasonic echo within chamber 116. In this implementation, the receiver is operatively coupled to a transducer. The receiver may also include protection circuitry to prevent high-voltage waveforms from overwhelming one or more amplifiers of the receiver. An example of such protection circuitry is the Supertex MD0100. In some implementations, the input of the protection circuitry is connected to the transducer, while the output of the protection circuitry is coupled to a low-noise amplifier, which is then coupled to a variable-gain amplifier. Filtering stages may also be interpolated to eliminate out-of-band noise. For example, in one implementation, an analog device, the AD8334 LNA / VGA combination, is used to amplify the input signal.

[0050] In one implementation, the receiver can be operatively coupled to the digitizer. Specifically, the output of the amplifier can form the input of the digitizer. The digitizer converts analog signals into digital signals. In one exemplary implementation, a 12-bit analog-to-digital converter (ADC), such as the analog device AD9238, is used.

[0051] exist Figure 1In an exemplary embodiment, the received echo data can be stored in a memory within the data processor 118. This memory can capture the digital output from the digitizer. The data processor 118 may include an FPGA, a general-purpose processor, a dedicated DSP processor, or some combination thereof. For example, the data processor 118 may include an FPGA storage unit where the echo data is temporarily buffered before being transmitted to an embedded processor. In this case, the data is buffered again in the embedded processor before being transmitted to an embedded PC for processing and modulus estimation. In one exemplary embodiment, the data processor 118 estimates the modulus through two distinct and interconnected steps. First, the data processor 118 analyzes the input echo signal to determine the displacement between echoes returned from various sensed waveforms. In a second step, the data processor 118 compares the characteristics of the measured displacement with predicted characteristics predicted by an analysis or computer model for a given cavity 116 geometry, thereby estimating the modulus of the sample within the cavity 116.

[0052] Figure 2 An example of the estimation process is shown, including data acquisition step 202, motion estimation step 204, and modulus estimation step 206. Figure 2 A graph 224 showing the modulus as a function of time is also shown, including data point 222, whose estimates are represented in more detail in panels 202, 204, and 206. Data acquisition panel 202 illustrates the data acquisition process. A series of ultrasonic waves are emitted into the test chamber. This series of ultrasonic wave shapes is: (1) sensing pulse 210; (2) force pulse 211; (3) sensing pulse 212; (4) sensing pulse 213; (5) sensing pulse 214; and (6) sensing pulse 215. These waveforms are merely examples, and this disclosure is not limited to the specific number or order of the waveforms shown.

[0053] In some exemplary embodiments, the sensing pulse is designed to apply minimal acoustic radiation force to the sample while returning an echo with a high signal-to-noise ratio and bandwidth. Sensing pulse 210 can be used to establish a baseline echo of the sample before applying the applied force waveform. On the other hand, the applied force pulse 211 is designed to apply a large acoustic radiation force field. Following the applied force pulse 211, a series of low-intensity sensing pulses (212 to 215) are emitted into the sample. The timing between the various sensing pulses is controlled to maintain the accuracy of downstream signal processing steps.

[0054] In an alternative embodiment, all these waveforms have sufficient energy to exert an acoustic radiating force. In this specific embodiment, these force-applying waveforms also effectively function as sensing waveforms. Received echoes from any or all of these waveforms can be processed to estimate the modulus using the methods and apparatus of this disclosure. It is further contemplated that this disclosure includes any combination of force-applying waveforms, sensing waveforms, and the combined use of force-applying waveforms / sensing waveforms.

[0055] Uninterrupted clotting of healthy blood samples results in the formation of hard clots. However, if the same sample is subjected to mechanical stress during clotting, the formed fibrin network may be damaged, leading to soft clots. Therefore, any measurement of mechanical properties applied during clotting with significant mechanical effects is likely to disrupt the evolution of the mechanical properties being measured. This bias effect in viscoelastic clot measurements is particularly likely to disrupt measurements of soft clots formed in the blood of patients with dysfunctional hemostasis. This problem has previously been addressed by an adaptive force measurement method disclosed in patent application PCT / US2010 / 049342. This application discloses a coagulation measurement system in which the magnitude of the applied force is adjusted to limit the magnitude of the induced displacement. When the clot is soft, the applied force is reduced to avoid damaging the clot. When the clot is hard, the applied force is increased to maximize the sensitivity of the mechanical property estimation. This adaptive force method is equally applicable to this disclosure and is contemplated for use in conjunction with this disclosure.

[0056] In one exemplary embodiment, the sensing waveform is emitted at intervals of approximately 122 microseconds, providing a sampling frequency of approximately 8.2 kHz. Other interrogation frequencies may also be used. Generally, interrogation of harder materials requires higher interrogation frequencies due to the high frequency of shear wave resonances (assuming constant resonant chamber geometry). By using lower interrogation frequencies, more accurate results can be obtained in softer materials, the cumulative radiative force from the sensing waveform is minimized, and data can be acquired over longer time periods for a fixed data storage size. For example, for blood samples, suitable interrogation frequencies range from approximately 2 kHz to approximately 16 kHz.

[0057] The combination of a single applied force waveform and multiple sensed waveforms can be referred to as an "ensemble". In one embodiment, the ensemble includes approximately 500 sensed waveforms. However, in other embodiments, the ensemble may include between approximately 16 and approximately 2048 sensed waveforms. Other ensemble sizes can be used to measure materials with higher or lower stiffness. An ensemble is processed to produce a single modulus estimate.

[0058] In some implementations, the acquisition time for a single ensemble is approximately 62 milliseconds. However, the acquisition time can be shorter or longer. For example, accurate results can be obtained by using an acquisition time of approximately 20 to 30 milliseconds for a single ensemble. Even shorter acquisition times, such as 10 milliseconds, can also be used. Longer ensemble durations enable accurate measurements of a wider range of moduli. In some implementations, ensembles can be repeated at a rate of approximately 16 Hz to measure rapidly changing moduli. In other implementations, the physical process under examination (coagulation) is slow enough that ensembles can be repeated at a rate of only six seconds, still providing data that accurately reflects changes in modulus.

[0059] In some implementations, it may be advantageous to limit the range of mechanical properties considered in a given ensemble based on previously measured mechanical properties for the same test chamber. For example, during coagulation, it can be expected that, assuming measurements are taken at sufficiently small time intervals, the shear modulus will change very smoothly over time. For instance, if the modulus is 1.0 kPa in a given measurement, it may be advantageous to limit the possible modulus range in consecutive measurements to between 0.5 kPa and 2.0 kPa. Even where the modulus range is not explicitly limited, it may be advantageous to smooth the modulus estimate over time using linear filtering (convolution with a filter kernel) or nonlinear filtering methods (such as median filtering) or a combination of both.

[0060] Each transmitted waveform in the transmitted waveform travels from left to right along the hourglass-shaped beam, such as... Figure 2 The vertical lines within the test chamber of panel 202 are shown in the diagram. When interrogated by the sensed waveform 210, the sample is stationary. Due to the inertia of the sample material, the sample remains stationary when impacted by the applied force waveform 211. However, immediately after the applied force waveform passes, the acoustic radiation force exerted by the applied force waveform 211 immediately causes the sample material along the beam to move in the propagation direction of the applied force waveform 211. Figure 2 In this embodiment, the motion is first visible when the sample is interrogated by the sensed waveform 212. This motion is shown in the figure as a shaded area located below the ultrasonic beam.

[0061] When the sensing waveform 213 is emitted, the radiation-induced displacement begins to propagate outward from the sound beam toward the test chamber wall. This displacement propagates primarily in the form of a shear wave. Over time, the shear wave reflects off the wall, propagates back through the sound beam, and then reflects off the wall again. This repeated reflection represents the resonance of the shear wave within the test chamber. As viscous losses and other losses within the sample weaken the propagating shear wave, the reverberation eventually subsides. It should be noted that for some combinations of modulus, viscosity, and resonant chamber velocity, the induced shear wave can reach the chamber wall so quickly that an observer would not see its propagation. Instead, it appears as if the entire internal chamber is oscillating rhythmically. Although different in nature from a propagating shear wave, this standing wave mode is an example of resonance and is contemplated in this disclosure. In other combinations of modulus, viscosity, and chamber geometry, the excited shear wave may be quite discrete in time and space, and the shear wave reflected from the wall is a spatially and temporally discrete waveform. Measuring the modulus by examining the arrival times of these different pulses is one possible embodiment of this disclosure. In this implementation, the shear wave echo arrival time is one aspect of the difference in the received waveform compared to the same aspect of the modeling difference (shear wave reflection arrival time).

[0062] In other specific implementations, chamber 116 is so small relative to the shear wavelength that no real shear wave is generated. In this case, it can be said that there is no resonance for this combination of modulus and chamber geometry. However, in reality, the induced displacement is still affected by the presence of the chamber walls. This boundary effect is used to change the induced displacement compared to what is expected when the same force is applied to an infinite or semi-infinite medium. This change can take the form of a change in time-dependent displacement relative to the displacement predicted for a semi-infinite medium. This change is an aspect of the estimated time-displacement caused at least in part by the boundary effect of the chamber walls. In this case, the time process of the induced displacement can be considered in conjunction with the chamber geometry to estimate the sample modulus. In one implementation, this modulus estimation is performed by comparing the measured displacement with displacements predicted by a series of computer models, as described in more detail below.

[0063] The presence or absence of resonance can be determined by either a general analysis of the difference in received echoes or, more specifically, by an analysis of estimated time-displacement. In one implementation, the time-displacement curve is analyzed to determine the presence of a trough (negative peak displacement). If such a trough is found, resonance can be inferred. If no trough (negative peak) is observed in the time displacement, resonance can be inferred to be absent. This conclusion regarding the presence or absence of resonance can be expressed as a parameter indicating the intensity of resonance. In this simple example, the parameter holds a value of 1 when a time-displacement trough is detected, and holds a value of 0 when no such trough is detected. This concept can be further extended by considering whether displacement peaks are detected in conjunction with displacement troughs, as this would indicate a stronger resonance. An alternative parameter indicating the intensity of resonance is the average value of the time-displacement curve. When resonance is absent, the time-displacement curve will be predominantly unipolar and therefore will have a high average value. Alternatively, when resonance is strong, the time-displacement curve will exhibit strong oscillations near zero and will therefore have a low average value. Another alternative parameter indicating the intensity of resonance is the ratio of the average displacement to the peak displacement on the measurement ensemble. A high value for this parameter indicates weak resonance. Other parameters can be calculated to indicate the resonance intensity.

[0064] Each sensing waveform in the sensing waveform returns an echo from impurities (acoustic scatterers) within the sample. In the case of whole blood, these impurities are primarily red blood cells. This disclosure can also be used to measure homogeneous materials, such as plasma, by adding polystyrene microspheres or other reagents that act as acoustic scatterers.

[0065] As the acoustic scatterer moves away from the ultrasonic transducer, the acoustic path length between the sensor and the scatterer increases. Assuming a constant speed of sound, this will result in the echo arriving later when the target is pushed further away by the resonant shear wave. Similarly, the echo will arrive earlier if the scatterer has moved closer to the ultrasonic transducer. These variations in echo arrival time are the differences between these waveforms that indicate the potential movement of the sample. If the ultrasonic propagation velocity (sound velocity c) is known or measurable in the sample, the measurement time delay can be related to the potential physical displacement according to the well-known relationship dx = c dt / 2.

[0066] In the preceding expressions, dt is the measurement time offset between echoes, c is the velocity of sound (ultrasound, not shear wave), and dx is the estimated relative displacement. However, it should be noted that this disclosure does not require knowledge of the velocity of sound, as the displacement characteristics used to estimate the modulus do not necessarily include absolute displacement. In one embodiment of this disclosure, the phase shift between various sensed waveform echoes is measured. These phase shifts are differences in the received waveforms due to potential movement of the sample. For resonant samples, these phase shifts will exhibit oscillatory characteristics with frequencies associated with the sample's modulus. The observed characteristics (oscillation frequencies) can be compared with predicted characteristics (oscillation frequencies predicted theoretically) to estimate the sample's modulus.

[0067] It is well known that the speed of sound in blood changes as blood clots. However, this evolving speed of sound has little or no effect on current measurements for at least two reasons. First, as mentioned above, many algorithms used to correlate measured displacement with modulus do not require knowledge of the actual displacement; only the relative displacement is needed. Second, the change in the speed of sound occurs over minutes, while the measurement ensemble described herein occurs over milliseconds. Therefore, the slowly evolving speed of sound has an imperceptible effect on the time delay estimation of any single ensemble.

[0068] The echo data from the ensemble is processed to find the differences between the received waveforms that indicate the target's motion along the ultrasonic beam. One process for analyzing these waveform differences is called "motion estimation," which... Figure 2 The motion estimation panel 204 is conceptually illustrated. Each echo generated by, for example, sensing pulses 212 to 215 is compared with a reference echo generated by sensing pulse 210 to discover the time delay between them. The time delay between the various echoes can be converted into displacement by using a measured or assumed sound velocity. All displacement estimates of a single ensemble are combined to form a time-displacement curve 220, as shown vertically on the right side of the motion estimation panel 204. This time-displacement curve is a characteristic indicative of the modulus of the sample. Note that the exemplary time-displacement curve shows oscillations associated with shear wave resonances and the attenuation of those oscillations associated with the chamber geometry and the inherent viscous damping of the medium.

[0069] Motion estimation algorithms used to calculate the differences in the received waveforms can be algorithms known in the art. Exemplary algorithms include those proposed by Kasai (C. Kasai, K. Namekawa, A. Koyano, and R. Omoto, “Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique”, IEEE Trans. Sonics Ultras., Vol. SU-32, pp. 458-464, 1985); Loupas et al., “Experimental evaluation of velocity and powerestimation for ultrasound blood flow imaging, by means of a two-dimensional autocorrelation approach”, IEEE Trans. Ultrason Ferroelect Freq Contr. 42:689-699, 1995); and Walker (US Patent 8,306,293).

[0070] Alternatively, waveform differences can be analyzed to estimate motion by finding the time delay corresponding to the peak of the correlation function between the various received echo signals. Direct measurement of the time delay can be extended to the measurement of the delay envelope of the demodulated waveform. As another alternative, the relative phase shift between the various received echo waveforms is a difference representing the motion of the sample. These phase shifts can be calculated digitally by comparing the complex Hilbert transforms of the waveforms associated with different transmissions. As yet another alternative, the received waveforms can be digitally sampled at intervals of approximately 1 / 4 period to approximate in-phase and quadrature (IQ) signals. This so-called Direct Sampling In-Phase and Quadrature (DSIQ) sampling scheme has previously been used to simplify ultrasonic beamformer design (US20070016022 A1) and can be applied to calculate the waveform differences representing motion in this disclosure. In another embodiment, the received ultrasonic waveform is processed via quadrature demodulation to produce a complex waveform, where the angle between the real and imaginary parts indicates the phase of the received signal. This phase is a difference indicating the motion of the sample.

[0071] Figure 3Experimental time-displacement curves obtained by this disclosure are shown. Waveform differences were analyzed to generate displacement estimates based on a series of 300 ensembles. Each ensemble consists of a single applied force waveform and 512 sensed waveforms emitted at a pulse repetition frequency of 8,206 Hz. Larger displacements and lower-frequency oscillations were detected earlier in the coagulation process. The first time-displacement curve 302 did not show oscillations, while the oscillations became clearer as the clot formed a higher modulus. A simple algorithm based solely on the mechanical resonant frequency would fail for the data in curve 302. This curve corresponds to a modulus for which the chamber geometry cannot support resonance. However, this disclosure can estimate the modulus even when no obvious oscillations are visible, as in the case of time-displacement curve 302. In this case, the modulus can be estimated by comparing the measured displacement (characteristic) with a computer model or analytical model (predictive characteristic) of the dynamic sample motion induced by the applied force waveform.

[0072] Figure 2The modulus estimation panel 206 illustrates an exemplary process for estimating the shear modulus of a sample based on a time-displacement curve 220 determined experimentally. The shape of the time-displacement curve 220 is a characteristic of the estimated displacement, which can further be described as a waveform difference. In one exemplary embodiment, a set of reference models has been generated using a computer model, where each reference model is a predicted time-displacement curve for a given shear modulus and viscosity for a specific test chamber geometry. These reference models incorporate predicted features associated with the modulus of the computer model. This computer model can utilize the finite-difference time-domain method, as described below. Alternatively, the model can be computed using the finite element method or boundary element method. The processor searches a library of reference models (predicted features) to find the reference model that best matches the experimentally measured time-displacement curve 220 (feature). In this embodiment, the library of reference models can be formed offline using a finite-difference time-domain (FDTD) model, as described below. Alternatively, the reference models can be computed using the finite element method or boundary element method. The reference models (predicted features) are shown as gray curves in the modulus estimation panel 206, each corresponding to a different shear modulus. Each reference model in the modulus estimation panel 206 is shown with a time-displacement curve 220 (feature) overlaid in black. In this specific exemplary embodiment, the reference model with a 3 kPa shear modulus best matches the time-displacement curve 220. The modulus and viscosity used to form this reference model are estimates of the modulus and viscosity of the sample. In other embodiments, the computer model calculates a series of models corresponding to the potential modulus and viscosity of a given time-displacement curve immediately after the curve is generated. However, this dynamic modeling approach can be computationally intensive compared to searching predefined reference models. Improvements in computing power or reductions in algorithmic complexity will enable dynamic computation of reference models. This approach will allow for more accurate estimation of modulus and / or viscosity. This approach can also be combined with a coarse-sampled (in terms of modulus dimension) library of reference models to strike a tradeoff between computational complexity and storage requirements.

[0073] It should be noted that the term "analytical model" can refer to something as simple as an expression relating resonant frequency to modulus, or something as complex as a full-time-displacement waveform predicted by an analytical expression. When using a full-time-displacement waveform as a model, it may be advantageous to evaluate the analytical expression and construct a set of reference models, similar to the methods described above for calculating the model.

[0074] In an alternative implementation, no explicit reference curve is used to estimate the modulus. Instead, characteristics of the time-displacement curve, such as its oscillation period, are calculated and used together with the oscillation period predicted by the analytical model (the predicted characteristic) to estimate the modulus. An exemplary analytical model is derived below. This model shows that the resonant frequency (the reciprocal of the period) is related to the resonant cavity radius, as well as the material modulus and density, through the following expression:

[0075]

[0076] This expression can be rearranged so that the modulus can be directly estimated based on the measurement period:

[0077]

[0078] Where T is the resonance period. Therefore, the oscillation period is a characteristic that can be compared with the predicted characteristic (the oscillation period of the analytical model) to estimate the modulus. Similarly, the oscillation period is an aspect of the induced motion caused at least in part by the resonance within the cavity. It should be noted that, in the case of the analytical model, it is not necessary to test a series of model predictions; instead, the step of comparing the predicted and experimental characteristics can be performed through a simple mathematical expression. This disclosure contemplates such a method. Alternatively, the resonance frequency can be used together with the above expression to estimate the modulus.

[0079] In some applications, estimating mechanical properties may not be necessary. Instead, characterizing mechanical properties can prove useful. In this context, we intend the concept of “estimating mechanical properties” to refer to a quantitative estimate of well-known mechanical properties such as shear modulus. Alternatively, we consider the concept of “characterizing mechanical properties” to mean determining something about mechanical properties without necessarily assigning units to them or even determining them in a directly proportional manner. For example, estimating the resonant frequency of a sample characterizes the mechanical properties of that sample without taking the extra step of mentioning the true modulus. It might be useful to generate a graph of “resonant frequency” versus time, rather than a graph of modulus versus time. Although “resonant frequency” is not the same as, and even not proportional to, modulus, tracking the resonant frequency will allow for the acquisition of important information about coagulation. Thus, we recognize the practicality of this characterization without needing to link it to fundamental mechanical properties such as shear modulus.

[0080] The resonant period is a characteristic that can be used as a basis for estimating or characterizing mechanical properties. Considering that the period is simply the reciprocal of the frequency, the estimation of the period equals the estimation of the frequency, and vice versa. The resonant period can be estimated in various ways based on the difference between received waveforms. For the purposes of this discussion, consideration of the difference between received waveforms is limited to motion estimation derived from the received waveforms, although other methods are envisioned, particularly those involving estimation of phase changes based on the received waveforms. We first consider time-displacement curves, such as… Figure 3 As shown, the oscillation period of this curve can be estimated by employing a Fast Fourier Transform (FFT) and estimating the frequency at which the energy reaches its peak. Alternatively, the average value can be subtracted from the time-displacement curve, and then an autoregressive power spectral density estimate can be performed using the Burg method. The frequency of the peak energy corresponds to the oscillation frequency. The ROOT-MUSIC algorithm can also be used to estimate the oscillation frequency. Other spectral estimation techniques can be used similarly.

[0081] The oscillation frequency can also be estimated in other ways. Specific algorithms for estimating the frequency of a decaying sine curve are known. (This information was published by DPRuiz et al.) IEEE Transactions on Signal Processing Such an algorithm is described in the paper "Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach" published in November 1995, Volume 43, Issue 11. T.P. Zieliński and K. Duda... Metrology and Measurement Systems The paper "Frequency and Damping Estimation Methods – An Overview" in Volume 18, Issue 4, 2011 presents a comprehensive overview of algorithms specifically addressing this problem. Other methods are also provided.

[0082] The oscillation period can be directly estimated from the time-displacement signal. In one approach, the time of the first trough in the displacement (maximum negative displacement) is used as an estimate of half the oscillation period. Since the time-displacement signal is discretely sampled in time, while the period can take continuous values, interpolation is advantageous. In one implementation, the time-displacement signal is directly interpolated to a higher sampling frequency before locating the trough time. This interpolation can be performed by resampling via FFT, piecewise cubic spline interpolation, or other known methods. Alternatively, discrete samples where troughs occur can be identified, and the true location of the trough can be found by analyzing the interpolation scheme. In one implementation, a parabola is fitted to the discrete trough value and its two nearest neighbors, and the time of the minimum value of the parabola is used as the estimated time of the trough. Alternatively, this interpolation can be performed using a higher-order function comprising piecewise cubic splines.

[0083] The period of displacement oscillation can also be estimated using other methods. In one alternative method, the positions of the first trough and the second peak are determined, and the time interval between them is an estimate of half the oscillation frequency. Note that the second peak is generally preferred because the timing of the first peak is distorted due to the application of the force pulse. This peak-finding strategy can be further extended by estimating the positions of multiple positive and negative peaks and combining these positions to estimate the period. In one implementation, the first and second troughs, as well as the second and third peaks, are identified. The time for considering the first trough is t. n1 The time of the second peak is t. p2 The time of the second trough is t. n2 And the time of the third peak is t. p3 In this case, the period can be related to each of these peaks and troughs, as follows:

[0084] t n1 =T / 2+e1

[0085] t p2 =T+e2

[0086] t n2 =3T / 2+e3

[0087] t p3 =2T+e4

[0088] Where e1, e2, e3, and e4 represent error terms caused by noise in the estimation of peak / trough locations. The oscillation period can be directly measured from the estimated times of these peaks and troughs using the following expression:

[0089]

[0090] This expression has the advantage of reducing the weighting of later peaks and troughs, which will have lower relative amplitudes and are therefore more susceptible to noise. Alternatively, the period can be estimated based on the same peak and trough times using the following expression:

[0091]

[0092] This disclosure contemplates other variations of the method, including more or fewer peaks and troughs, and alternative expressions for estimating the period based on the timing of peaks and troughs.

[0093] The oscillation period can also be estimated based on the location of the zero-crossing point of the time-displacement curve. While the time interval from peak to trough is 1 / 2 period, the zero-crossing interval is approximately half that, i.e., 1 / 4 period. The method described above for estimating the oscillation period by combining peak and trough times can be easily modified to incorporate the zero-crossing time, thereby estimating the oscillation period. Many algorithms for estimating the zero-crossing time are known. One method involves fitting a straight line to data points near the zero-crossing point and finding the time when the fitted line equals zero. Higher-order methods using polynomials or splines have also been envisioned.

[0094] In some implementations, the shear modulus estimate for each ensemble is plotted as a single point on a curve, such as... Figure 2 As shown. In this specific embodiment, exemplary calculations represented by panels 202, 204, and 206 generate data points 222. Repeated calculations of multiple ensembles over a period of time generate shear modulus curves 224.

[0095] In one exemplary implementation, a normalized correlation coefficient is used to quantify the similarity between the reference model and the experimentally determined time-displacement curve 220. The normalized correlation coefficient between two different signals a[n] and b[n] is given by the following formula:

[0096]

[0097] in and

[0098] Figure 4The results of modulus estimation as applied to coagulated human blood are shown. A small amount of kaolin was added to a human whole blood sample. The top graph shows the estimated modulus over time, with the reagent (kaolin) added to the blood sample at time zero. The middle graph shows the estimated viscosity over time. The bottom graph shows the normalized correlation between the experimental time-displacement curve and the time-displacement curve predicted by the finite-difference time-domain model described below. The model used in this figure considers modulus between 10 Pa and 10,000 Pa and viscosity between 0.025 Pa s and 0.8 Pa s. A total of 16,032 combinations of modulus and viscosity were modeled. All models are assumed to have a modulus of 1.06 g / cm³. 3 The density of the experimental chamber was determined. The geometry of our experimental chamber was modeled on a spatial grid sampled at 100 μm in each dimension. The resonant portion of the chamber consisted of a cylindrical region with a diameter of 4.2 mm and a length of approximately 1.5 mm, with a hemispherical cap having the same radius as the cylinder. The first 18 time-modulus estimates were removed from the experimental data and model, and the correlation between the experimental data and the model was then calculated. The best-fit line was removed from the experimental time-displacement and computer model time-displacement predictions, and the correlation was then calculated. Incorrect modulus estimations occurred in the early stages of clot formation because the model could not allow for liquid blood or blood with low modulus at the very early stages of clot formation.

[0099] Figure 4 The results shown are noteworthy, partly due to the relatively high correlation between the experimentally determined time-displacement curves and the predictions of the FDTD model. From Figure 4 As can be seen in the bottom figure, for well-formed clots, the correlation between the FDTD model and the experimentally measured time-displacement curves far exceeds 0.95. This provides a strong indication that the computational model is suitable for these experimental conditions. The correlation between the model and experimental data is much worse for the liquid blood phase. This is not surprising, as in this case, the softest model corresponds to a modulus of 10 Pa, which is far from the liquid state, which has a modulus of zero. Similar correlation tests were performed by numerically evaluating the formed time-displacement waveforms using the analytical model derived below. Although not shown, these results are closely related to the experiments; confirming the applicability of the analytical model. The correlation of the analytical model is somewhat worse than that of the FDTD model. This may be because the analytical model assumes an infinitely long cylinder, while FDTD assumes a covered cylinder similar to the experimental chamber used in real experiments.

[0100] The correlation between experimental time-displacement curves and a series of reference models can be plotted as a two-dimensional function of modulus and viscosity, such as... Figure 5The contour plot is shown below. This plot illustrates the normalized correlation between the experimental time-displacement curves and the time-displacement curves predicted by the finite-difference time-domain model described below. The model used in this plot considers moduli between 10 Pa and 10,000 Pa and viscosities between 0.025 Pa s and 0.8 Pa s. The best-fit lines were removed from the experimental time-displacement and computer model time-displacement predictions before the correlations were calculated. The peak correlation lies within the minimum ellipse marked 0.95 in this plot. The location of the peak corresponds to the estimated modulus and viscosity for a specific exemplary ensemble. The minimum ellipse (highest correlation) is an oblong shape, distributed across a wide range of viscosities and a smaller range of moduli. A small amount of noise can cause continuous estimates to linger around the peak correlation, although this may always be confined to the high-correlation contours. The shape of the 0.95 correlation contours suggests that viscosity estimates can include significant variations, as evidenced by the width of the contours in the viscosity dimension. Due to the narrower contours in this dimension, variations in modulus estimates will be relatively small. However, the correlation function is inseparable in the viscosity and modulus dimensions. Conversely, errors that shift the viscosity necessarily shift the modulus as well. This observation suggests that, by assuming the viscosity remains constant, this parameter can be fixed to obtain a more accurate and repeatable estimate of the shear modulus. This method of fixing the viscosity offers the advantage of limiting what is a two-dimensional search (modulus and viscosity) to a one-dimensional search (modulus), thereby improving computational efficiency.

[0101] Figure 6 The results of modulus estimation with constant viscosity are shown. The top plot shows the modulus estimation. The middle plot shows the viscosity, which is fixed at a value of 0.25 Pa s. The bottom plot shows the correlation between the model and experimental time-displacement. The models used for these estimations are in many respects the same as those used to obtain the results in Figure 4. There are two notable differences. First, the modulus varies between 0.01 Pa and 10,000 Pa. Second, the viscosity remains constant at a value of 0.25 Pa s. A total of 1,167 models were created. Figure 6 The results show a significant improvement in modulus estimation before the formation of a solid agglomerate. While the correlation of these early estimates is rather low, they are significantly higher than... Figure 4 This result is encouraging because it shows that adjusting the model range to introduce a lower modulus can produce a more accurate estimate of the mechanical properties when the sample has a low modulus. This is further confirmation of the validity of the computational model. Figure 6 The result requires less computation. Figure 4 The result is 1 / 10 of the original result, while there is no loss of quality.

[0102] The computational and analytical models described in this disclosure have multiple adjustable parameters that can be estimated or alternatively kept constant, depending on the specific sample and chamber geometry. In the foregoing examples, it has proven advantageous to keep the sample viscosity and density constant and to evaluate the model against a range of shear moduli. In human blood, keeping the density constant is reasonable because the differences between individuals are relatively small. While viscosity may vary slightly, the advantage of limiting the degrees of freedom in estimation may outweigh any absolute error in viscosity. For different samples, it may be advantageous to allow variations in viscosity or density while keeping the modulus constant. In other embodiments, the chamber geometry may not be precisely known, and the model may allow certain aspects of the chamber geometry to vary between models.

[0103] In some implementations, the value of the normalized correlation coefficient can be used to reject unreliable and unlikely-to-be-correct modulus and viscosity estimates. For example, the normalized correlation coefficient can be used to reject modulus and viscosity estimates where air bubbles in the acoustic path disrupt the potential ultrasonic echo. Processing this damaged echo data will produce a similarly noisy time-displacement curve. While the typical correlation between the optimal reference model and the experimental time-displacement curve can be 0.98, the correlation of damaged time-displacement data can drop to, for example, 0.40. This significant reduction in correlation clearly indicates that the measurement is unreliable and should be rejected. This process of rejecting estimates with low correlation can be called “masking.” An appropriate threshold can be empirically determined based on experimental tests, but a reasonable threshold is around 0.9.

[0104] To eliminate noisy estimates formed before blood has begun to clot, masking shear modulus estimates based on their peak correlation with a reference model is particularly valuable. For liquid blood, time-displacement estimates exhibit very large and often irregular displacements. The irregularity of these curves allows them to fit almost any reference model, although such a fit is merely coincidental rather than a true match. Furthermore, the reference model may not actually apply until the blood begins to form a solid "clot." For example, models based on viscoelastic solids are not suitable for liquid samples. In these cases, while a fit exists, the quality of the match and therefore the correlation coefficient will be quite low. By removing only modulus estimates with peak correlation below a reasonable threshold, erroneous modulus estimates associated with liquid blood can be directly eliminated.

[0105] Applying the concept of "correlation masking" to Figure 6 The experimental results are as follows: Figure 7As shown. The top plot shows the original modulus estimate; including the two data points at the start of the measurement. These data points are clearly incorrect. The middle plot shows the correlation between the experimental data and the best-fit model. A correlation threshold of 0.6 was chosen to remove obviously erroneous data points. Figure 7 The bottom plot shows the remaining modulus estimates after removing moduli with a correlation below 0.6. Two erroneous modulus estimates were eliminated.

[0106] The correlation between the model and the experimental time-displacement estimate can also be used for other purposes. In an alternative implementation, several different models are formed, with variations in mechanical properties and underlying assumptions. For example, a series of models can be developed where the sample is assumed to be a viscoelastic solid, while a second series of models assumes the sample is a liquid. Within each series, variations in mechanical properties are allowed. In this implementation, the data processor tests the correlation between each model in both series and the estimated time-displacement curve. The specific model with the best correlation to the time-displacement curve will indicate both the value of the mechanical property and the material type that best describes the sample. In this specific example, the material type is either a viscoelastic solid or a liquid.

[0107] The reference model library necessarily contains a finite number of reference models. In some implementations, the modulus estimate may fall among the reference models. This limitation can be overcome with less computational cost by interpolating the correlation coefficient around the measured peak to locate the shear modulus corresponding to the best correlation, regardless of whether a reference model is calculated for that modulus. In the simplest case, where viscosity remains constant and only the modulus is allowed to vary, the modulus estimate can be determined by locating the peak of the parabolic fit using the correlation of the best-fit reference model and the correlation of its two nearest neighbors. Other interpolation schemes, including spline-based and higher-order polynomial-based interpolation schemes, can produce more accurate results. Furthermore, the interpolation described herein can be applied to two-dimensional (modulus-viscosity) estimation using a two-dimensional interpolation scheme. The experimental results presented herein all use interpolation to form the modulus estimate.

[0108] Time-displacement curves determined experimentally can be corrupted by various physical and electronic effects. For test chambers of finite volume, the applied force waveform can generate significant reverberant ultrasonic echoes that can extend into the acquisition cycle of subsequent sensing waveforms. In one exemplary embodiment, the effect of reverberation can be mitigated by designing the frequencies of the applied force waveform and the sensing waveform to be in different frequency bands and then using analog or digital filtering to suppress the reverberation associated with the applied force waveform. In an alternative embodiment, sensing waveforms sent shortly after the applied force waveform can be removed from the time-displacement estimation curve, and then a reference model can be searched for a best fit. Methods for rejecting erroneous time-displacement estimates can be performed statically (e.g., assuming the first six estimates for each time-displacement curve are erroneous) or dynamically (e.g., calculating a quality metric for the time-displacement estimates and discarding estimates with a quality metric below a certain threshold).

[0109] Figure 16 The time-modulus curve, determined experimentally using an analytical expression to correlate the measured period of displacement oscillations with the shear modulus, is shown. This method uses Equation 58 to correlate the resonant frequency with the modulus. The resonant period is estimated based on the time difference between the first trough and the second peak of the displacement. This method produces a reliable estimate of the clot modulus, although it is challenged by the early liquid phase before the onset of coagulation. As described elsewhere in this disclosure, these erroneous estimates can be masked by parameters indicating the intensity of the resonant intensity. This analytical estimation of the modulus differs quantitatively from estimates based on computational models. This is likely due to the different geometric assumptions made by the two methods. The analytical model assumes an infinitely long cylinder, while the computational model assumes a covered cylinder similar to a test chamber used in experiments.

[0110] This disclosure contemplates the estimation of mechanical properties based on at least three distinct but interrelated modes of mechanical behavior. In the first mode, a force pulse is applied to the chamber, potentially exciting mechanical resonance in the sample constrained by the test chamber. In one embodiment, the resonant frequency is the basis for estimating the shear modulus of the sample. However, it should be noted that certain combinations of modulus, viscosity, density, and chamber geometry may not induce true resonance. For example, if the sample viscosity is higher than its modulus, the system will be underdamped and resonance will not occur. However, as the clot hardens, the modulus increases while the viscosity remains relatively constant. Therefore, the exemplary device disclosed herein will be able to detect the onset of resonance as the clot hardens. This shift provides a useful and simple indication of clot formation.

[0111] In another embodiment, the viscosity of the sample is low enough relative to its modulus that a well-defined shear wave (both spatially and temporally) can be induced within the sample. With the shear wave constrained in both time and space, the reflection of the shear wave from the chamber wall will be clear and easily detectable based on the difference between the echoes received from the scatterer within the sample. Once the chamber geometry (shear wave path length) is known, the shear wave velocity (and thus the modulus) can be directly estimated from the arrival time of the shear wave echo from the chamber wall. As with the previous resonance example, there may be certain combinations of mechanical properties and geometries for which a clearly measurable shear wave cannot be generated. Similar to the resonance example, the transition between a state where a clearly measurable shear wave cannot be generated and a state where a clearly measurable shear wave can be generated can provide a good substitute for the transition from liquid blood to formed clots. Therefore, the timing of this transition can provide a useful measure of clot formation time.

[0112] In the third embodiment, clear resonance or propagating shear waves are not easily measured. However, this does not preclude the estimation of the mechanical properties within the test chamber. For any sample within a finite chamber, the chamber walls will alter the apparent mechanical impedance of the sample. In this context, mechanical impedance describes the relationship between the applied force and the resulting displacement. A very soft sample in a very large test chamber will exhibit mechanical impedance very similar to that of a sample in an infinitely large test chamber. Alternatively, a rigid sample in a small test chamber will exhibit mechanical impedance very different from that observed in a larger test chamber. Under dynamic force application, the magnitude of the sample viscosity will further influence the perceived mechanical impedance. This disclosure anticipates comparing a model of the sample within the test chamber with experimental measurements to estimate the mechanical properties of the sample. In this embodiment, the effect of the walls (boundary effects) is explicitly considered. Since the effect of the boundaries (walls) of a given chamber geometry varies depending on the mechanical properties of the sample, the transition of boundary effects from insignificant to significant can serve as an alternative to the transition from a liquid blood sample to a formed clot.

[0113] exist Figure 8 In another embodiment shown, Figure 1 The transducer assembly 114 incorporates a focusing element 802. The addition of the focusing element increases the intensity of the applied force waveform and the intensity of the received echo. Furthermore, the use of the focusing element 802 allows for the use of a larger transducer element within the transducer assembly 114. Alternatives to this device are envisioned in detail herein.

[0114] exist Figure 9In one exemplary embodiment shown, the separable test chamber 116 is provided with coupling agent 902. Separable test chambers are particularly useful as consumable components in many commercial applications. In this application, we refer to the separable test chamber as a "consumable," while recognizing that it can be a reusable component. In the context of this embodiment, an acoustic path including transducer assembly 114 (instrument), coupling agent 902 (consumable), and test chamber 116 (consumable) is described. Additionally, a focusing element can be inserted between the transducer assembly and the coupling agent, or between the coupling agent and the test chamber. In an alternative embodiment (such as...) Figure 10 As shown), the focusing element 1004 is combined with the instrument, and the coupling agent 1002 is associated with the instrument or consumable. The acoustic path from the transducer assembly outward is: transducer assembly 114 (instrument), focusing element 1004 (instrument), coupling agent 1002 (instrument or consumable), and test chamber 116 (consumable). In yet another alternative embodiment, the focusing element is combined with a consumable, such as Figure 11 As shown. In this embodiment, the coupling agent 1102 may be associated with an instrument or consumable, while the focusing element 1104 may be associated with a consumable.

[0115] exist Figure 11 In an exemplary embodiment, the ultrasonic wave travels from the coupling agent 1102 to the focusing element 1104. The focusing element 1104 may be shaped such that it refracts the ultrasonic energy and focuses it as needed within the resonant test chamber. In some embodiments, the focusing element 1104 is a thermoplastic, but other suitable materials may be used instead of or supplement the thermoplastic. In one possible embodiment, the coupling agent 1102 may comprise a liquid such as water. In another possible embodiment, the coupling agent 1102 may comprise water-based or oil-based gels such as those commonly used in ultrasound imaging.

[0116] Focusing element 1104 focuses ultrasonic energy into chamber 116. Chamber 116 can also be interchangeably described as a resonant chamber, resonance chamber, or test chamber. Focusing element 1104 is designed such that its curvature and sound velocity act to refract the emitted ultrasonic waves into a focused beam. Focusing element 1104 can be designed to form a sharp-focused or broad-focused beam. Sharp focusing tends to exert a higher amount of radiating force; however, sharp focusing may make the entire system more sensitive to small errors in aligning the ultrasonic beam with resonant chamber 116. Alternatively, focusing element 1104 can be designed to more broadly focus the ultrasonic beam. This may generate a smaller amount of radiating force but make the system less sensitive to alignment errors between the ultrasonic beam and resonant chamber 116.

[0117] Figure 12An alternative embodiment including a durable instrument and a consumable test cartridge is shown. A controller 110, a transmitter 112, a transducer assembly 114, a data processor 118, a transducer alignment feature 1210, and a clamping mechanism 1214 are integrated into the instrument. A test chamber 116, a coupling agent 1202, a focusing element 1204, a chamber alignment feature 1212, a thermal control unit 1220, and a surface modification feature 1230 are integrated into the consumable.

[0118] exist Figure 12 In one embodiment, the consumable component makes acoustic contact with the instrument through the action of the clamping mechanism 1214. In one embodiment, the clamping mechanism is a lead screw actuated by a stepper motor. Other embodiments may include, for example, a mechanically actuated rod or some other mechanical mechanism. Where the coupling agent 1202 is a fairly robust material, the clamping mechanism 1214 may require a significant amount of force to eliminate any air gaps and form a good acoustic contact. In one embodiment, the clamping mechanism 1214 applies a force of approximately 110 Newtons to clamp a single resonant chamber 116. In an alternative embodiment, where a single consumable comprises multiple resonant chambers, a single clamping mechanism may be shared on the channel. In this case, the clamping mechanism may need to apply a force exceeding 110 Newtons. For example, in an embodiment with four chambers, the clamping mechanism may apply a force of approximately 440 Newtons.

[0119] exist Figure 12 In one embodiment, alignment features 1210 and 1212 are associated with transducer assembly 114 and focusing member 1204. Alignment features 1210 and 1212 cooperate to precisely generate and place the sound beam within test chamber 116. In one embodiment, alignment feature 1210 incorporates four different components. Two of these components are pins, each having an axis parallel to the ultrasonic beam. One of these pins can engage in a hole as a component of transducer alignment feature 1212. Another pin can engage in a slit as a component of chamber alignment feature 1212. In addition to the pin / hole and pin / slit alignment features, another embodiment may include at least one hard stop to control the degree of compression of the coupling agent 1202. In one embodiment, the hard stop consists of rails located above and below the coupling agent 1202 and associated with the focusing member 1204, which contacts the transducer assembly 114. These rails together can force the focusing member 1204 parallel to the surface of transducer assembly 114.

[0120] exist Figure 12In one embodiment, the test chamber 116 is in thermal contact with the thermal control unit 1220. Since coagulation is a temperature-dependent process, the use of the thermal control unit improves repeatability and increases the coagulation rate, allowing clinicians to receive results more quickly. In one embodiment, the temperature control unit is an aluminum block with an embedded thermistor and an electric heater. The thermistor acts as the input to a PID controller (Proportional-Integral-Derivative Controller). In another embodiment, the thermal control unit uses a Peltier device to heat and cool the sample relative to its input temperature.

[0121] exist Figure 12 In one implementation, the internal surface of the test chamber 116 is formed or modified to have a surface 1230 that facilitates clot adhesion. This treatment may be necessary so that the clot cannot be pulled away from the chamber wall when the blood clot and platelets contract. This can be advantageous because if the clot is pulled away from the chamber wall, the assumed properties of the computational or analytical models may be incorrect. For example, a chamber with contracting clots would include a serum layer filling the gap between the contracting clot and the resonant chamber wall, rather than a uniform material extending throughout the test chamber 116. This gap would alter the resonant geometry of the resonant chamber, thus biasing modulus measurements under these conditions. Even if clot contraction only opens a tiny gap between the clot and the chamber wall, the boundary conditions upon which our predictive models are based will no longer apply, and therefore estimates of mechanical properties will be compromised. Even if we limit ourselves to characterizing mechanical properties (without calculating absolute properties), the characterization will be compromised due to the altered boundary conditions within the chamber. These errors can be eliminated by forming a chamber with a roughened internal surface to which the clot can adhere firmly. Such a surface can be formed by patterning an injection mold for forming the cavity, or by roughening the internal surface after manufacturing through a bead-spraying mechanism. Alternatively, the internal surface can be treated with plasma or corona to roughen the surface and alter its chemical properties to enhance clot adhesion. In another alternative embodiment, the internal surface can be treated with proteins such as fibronectin that the clot can adhere to.

[0122] exist Figure 13 Another alternative embodiment of this disclosure is illustrated. In this embodiment, transducer assembly 114 includes a focusing element 802 and two separate transducer elements 1302 and 1304. The first transducer element 1302 is connected to the transmitter rather than the data processor and is designed to transmit a force waveform. The second transducer element 1304 is connected to both the transmitter and the data processor and is designed to transmit a sensed waveform and receive its echo. Figure 13This configuration can prove advantageous because, for example, the most desirable ultrasonic beam shape for the applied force waveform may differ from the optimal ultrasonic beam shape for the sensing waveform. Furthermore, since the energy of the applied force waveform is typically higher than that of the sensing waveform, this configuration may reduce the requirements for protection circuitry associated with the data processor and improve sensitivity.

[0123] exist Figure 14 Another alternative embodiment of this disclosure is shown. In this embodiment, transducer assembly 114 includes a focusing element 802 and two separate transducer elements 1402 and 1404. The first transducer element 1402 is connected to the transmitter rather than the data processor and is intended for waveform transmission only. The second transducer element 1404 is connected to the data processor and is intended for echo reception only. Figure 14 This configuration can prove advantageous because it eliminates the need for protection circuitry associated with the data processor.

[0124] One advantage of this disclosure over the prior art is the significant reduction in the blood volume required for testing. For example, at least one prior art method requires a 60 ml blood sample per test. In the various embodiments described herein, only about 330 microliters are required per test chamber. Larger or smaller volumes of blood can also be used, depending on the test conditions. This reduction in test chamber volume allows patients to provide less blood while also benefiting from the ability to perform multiple tests in parallel within a single cartridge. In some embodiments, a single cartridge may comprise multiple test chambers that can be tested in parallel. In an alternative embodiment in which the focusing element is integrated into the transducer assembly, the total blood volume can be further reduced to only tens of microliters per chamber.

[0125] In one embodiment described above, the sensing waveform is designed not to exert a significant acoustic radiation force on the sample. However, in other embodiments, the sensing waveform may exert a small amount of radiation force. In these embodiments, the measured displacement will consist of a superposition of resonant time-displacement curves. The main part of this superposition is the resonant time-displacement curve caused by the applied force waveform. However, smaller delay responses from each of the sensing waveforms will be added to this curve. In cases where the displacement caused by the applied sensing waveform has a significant effect, the ideal response can be reconstructed by deconvolving the input. The effect of a small amount of radiation force from the sensing waveform can also be mitigated by reducing the emission rate of the sensing waveform.

[0126] In addition to measuring coagulation in human blood, this disclosure has numerous applications. For example, it may be useful in veterinary and biomedical research to quantify the process of quantifying blood coagulation samples from non-human animals.

[0127] In the food industry, there is a strong interest in quantifying the mechanical properties of food and food additives. In this field, resonant chambers are filled directly with the food to be tested. One might find it valuable to apply this disclosure to monitor cheese aging or other dynamic processes. In one example, this disclosure can be applied to measuring the aging of cheese blocks. Large cheese blocks can have a diameter exceeding 50 inches. In the context of this disclosure, such a cheese block can be considered a resonant chamber. Given that the size is approximately 300 times larger than the resonant test chamber considered in the detailed example above, it can be advantageous to similarly scale the operating frequency. This suggests that measurements of such large objects may require the use of lower frequency acoustic energy; this could extend to audible conditions. Compared to the fixed boundaries discussed above for blood, the chamber of this application would be formed by the boundaries of the cheese block itself, with the surrounding air forming a free boundary.

[0128] In the field of tissue engineering, there is an unmet need to measure the mechanical changes that occur as cells grow, mature, and construct the extracellular matrix within certain engineered tissue structures. This disclosure can be applied to this problem by growing cells within a resonant chamber. Alternatively, the cell growth matrix can be placed in a nutrient fermentation broth, thus the geometry of the matrix itself forms a resonant geometry. In this case, the analytical or computational model assumes free boundaries, rather than the infinitely rigid boundaries considered elsewhere in this application.

[0129] Example – Finite Difference Time Domain Model

[0130] The exemplary model described below is a derivation of a finite-difference time-domain model of radiation-induced shear waves in a cylindrical geometry. This formula can be used to model time-displacement waves in a resonant cavity.

[0131] The analysis begins with the velocity-stress formula of the shear wave equation. It should be noted that although this formula considers velocity, the results calculated using this method can be numerically integrated to derive displacement, thus agreeing with experimental results. The traditional formula is extended by including terms that account for viscous losses.

[0132]

[0133]

[0134] Equation 1 is expanded by expressing it in cylindrical coordinates, and the vector velocity is expanded into its constituent components.

[0135]

[0136]

[0137]

[0138] Further consideration of our problem allows for significant simplification. First, we recognize that only the physical force is the applied ultrasonic radiation force. Assuming the force is entirely along the z-direction, we can derive F... θ =F r =0. Assuming the test chamber and the applied radiation force are perfectly axisymmetric, all the relationships can be derived based on θ equal to zero. Applying these simplifications to equations 3 to 5, we obtain:

[0139]

[0140] 0 = 0 (7)

[0142]

[0143] We follow a similar strategy to expand equation 2, and obtain:

[0144]

[0145] From aggregation equations 6 to 9, we obtain:

[0146]

[0147]

[0148]

[0149] Equations 10 to 12 form a system of partial differential equations that can be solved together to predict how radiation forces induce shear waves and how these induced shear waves interact. This system is particularly suitable for finite difference decomposition using an alternating grid method similar to the Yee method. The finite difference expression for equations 10 to 12 is as follows:

[0150]

[0151]

[0152]

[0153] Can be used as Figure 15 The staggered mesh method shown numerically implements the above mathematical formula. Each calculation cycle consists of two steps. In the first step, the velocity components are calculated using the finite difference equations described above. In the next step, the shear is calculated using the finite difference equations.

[0154] Example - Analysis and Modeling of Pulse-Induced Resonance

[0155] The exemplary analytical model derived below represents a mechanical model of blood clot displacement in a cylindrical resonant chamber. This model qualitatively captures the behavior observed in real-world experiments.

[0156] Our analysis is based on the well-known Cauchy-Navier equations concerning linear elasticity. We utilize formulas that incorporate the properties of viscoelastic materials.

[0157]

[0158] In our initial experiments, we used a cylindrical test volume, where the radiation force was applied to a cylindrical volume with a smaller radius that shared the same central axis as the test volume. This geometry ensures that the angular parameters remain constant. We also assume an infinite length, which further simplifies the problem by eliminating variations in the range. We apply these simplifications to the components of (16):

[0159]

[0160] Due to the cylindrical shape's symmetry and infinite length, we can assume that all derivatives with respect to φ and z are equal to zero. Therefore, (17) becomes:

[0161]

[0162] We now take the gradient and obtain:

[0163]

[0164] We again recognize that all derivatives with respect to φ and z are equal to zero. Therefore, (19) can be simplified to:

[0165]

[0166] We consider another component of (16):

[0167]

[0168] We again recognize that all derivatives with respect to φ and z are equal to zero. Furthermore, the displacement components with respect to φ are also equal to zero. Therefore, (21) simplifies to:

[0169]

[0170] Expanding the Laplace operator, we obtain:

[0171]

[0172] We recognize once again that the derivatives with respect to φ and z are equal to zero. Therefore, (23) becomes:

[0173]

[0174] The partial differential equation (16) can be divided into three distinct equations; one equation for each direction. We begin by considering the results in the z-direction. Note that the displacement in the z-direction is solely a function of r and t, as the dependence of φ and z is eliminated through the radial symmetry and infinite length of the model:

[0175]

[0176] Substituting (20) and (24) into (25) yields:

[0177]

[0178] Expanding (26) yields:

[0179]

[0180] Further simplification leads to:

[0181]

[0182] It should be noted that (28) does not include dependence on radial displacement. Therefore, the potential set of partial differential equations becomes a single partial differential equation.

[0183] Oscillating force:

[0184] We solve equation 28 by considering the solution of the following formula, where the displacement is oscillating.

[0185] u z (r, t) = S(r)e jωt (29)

[0186] We further assume that the applied force is also oscillating.

[0187] F z (r, t) = F(r)e jωt (30)

[0188] Substituting (29) into (28) yields:

[0189]

[0190] Evaluating the derivative with respect to time yields:

[0191]

[0192] We will run through (32) where e appears jωt Setting aside the terms, we arrive at:

[0193]

[0194] To simplify the notation, we will use (μ+jωη) s Replace (33) with the general complex shear modulus G, so that (33) becomes:

[0195]

[0196] The solution to this equation depends on the exact form of the applied force function. A simple form assumes that at a certain transmit beam radius r... tx There exists a constant force F within the radius r, and a force of zero outside the radius r. The solution to this simple force function has two domains, one within the radius r. tx Inside, and one outside that radius. The solution is:

[0197]

[0198]

[0199] Where J0 is a zero-order Bessel function of the first kind, and Y0 is a zero-order Bessel function of the second kind. Considering our boundary conditions, we can further simplify this solution. The derivative of the solution is 0 when r = 0. Since Y0 has no finite derivative at 0, we know that c2 = 0. Therefore, we obtain the following solution:

[0200]

[0201] S2(r)=c3J0(Ar)+c4Y0(Ar)for r>r tx (36)

[0202] It should be noted that, in order to simplify the symbol representation, we have already... A has been replaced. We will now solve for the arbitrary constant by considering the boundary conditions and continuity conditions of the problem. We assume that the clot is rigidly adhered to the chamber wall and therefore S2(R) = 0, where R is the radius of the test chamber. Furthermore, both solutions must be continuous at their junction such that S1(r) = 0. b )=S2(r b Finally, both solutions must have continuous derivatives at their junction such that S1′(r) b )=S2′(r b We can express these three conditions as follows:

[0203] c3J0(AR)+c4Y0(AR)=0

[0204]

[0205] c1J0′(Ar b)-c3J0′(Ar b )-c4Y0′(Ar b )=0 (37)

[0206] Recognizing that J′0(Ar)=-AJ1(Ar) and Y′0(A)=-AY1(A), and reformulating the above expressions into a single system of linear equations, we obtain:

[0207]

[0208] This system of equations can be solved using Gaussian elimination. We are primarily concerned with the region where the force is applied, where r ≤ r tx Therefore, the coefficient of most interest is c1. Solving for c1 yields:

[0209]

[0210]

[0211]

[0212] The above expression provides a rigorous solution to the analytical formula proposed in this paper. Unfortunately, these rigorous solutions are prone to numerical instability when the operands of the Bessel function become large. In these cases, subtraction is used to amplify the numerical error in the evaluation of the Bessel function, making the evaluations of c1, c3, and c4 potentially invalid.

[0213] The numerical instability of (39), (40), and (41) can be reduced by using simpler expressions for Bessel functions with large operands. We use the following simplification for large operands.

[0214]

[0215]

[0216]

[0217]

[0218] By applying these expressions to equations 39 through 41, and then using trigonometric identities, c1, c3, and c4 can be reformulated to remain numerically stable. Note that this reformulation is only effective for large operands; therefore, empirically determined transformations must be used between the two expressions.

[0219] The received signal is a weighted sum of signals received from each torus within the receiving beam. Formally, the signal can be considered a complex exponent, and the resulting sum is also a complex exponent, which is then analyzed to determine the displacement. Since small displacements make the first term of the Taylor series a reasonable approximation of the complex exponent (cos(x)≈1 and (sin(x)≈x), the complex exponent can be neglected, making the estimated displacement approximate as the sum of displacements on the torus.

[0220] Therefore, the estimated displacement is a weighted sum of the actual displacements over the axisymmetric region. If the effective receiving beam radius is smaller than the transmitting beam radius, then the estimated displacement is:

[0221]

[0222] In the known In this case, the integral of (46) can be easily calculated.

[0223]

[0224] However, if the received beam is larger than the transmitted beam, the solution takes the following form:

[0225]

[0226]

[0227]

[0228] Displacement caused by the oscillating force from the small beam:

[0229] In some cases, it is useful to consider oscillatory displacement within the limits of very small ultrasonic beams. When r tx As we approach zero, we will consider equation 36 in the limit.

[0230]

[0231]

[0232] We recognize that, depending on r b The only term is a constant, c1. Therefore, when r b When it reaches zero, we take the limit of c1.

[0233]

[0234]

[0235] Therefore, the displacement is equal to:

[0236]

[0237] We further simplify this by considering the displacement at the center, i.e., the beam position:

[0238]

[0239] in

[0240] By examining this expression, we realize that the displacement will be at its maximum, i.e., the system is in resonance when J0(AR) = 0. The first zero occurs at J0(2.4048). Therefore, the resonance frequency can be solved as follows:

[0241]

[0242]

[0243] constant force :

[0244] The above analysis is only valid for oscillating forces. In the static case, where the force remains constant over time, we must perform a separate analysis. We begin by reconsidering equation (28), which, for clarity, is copied below.

[0245]

[0246] Since we are particularly interested in static or DC problems, we eliminate all derivatives with respect to t, as they must be equal to zero. We also change the notation to indicate that we are considering the static shear modulus.

[0247]

[0248] Similar to oscillation problems, the solution to this equation depends on the exact form of the applied force function. A simple form assumes that at a certain transmitted beam radius r... tx There exists a constant force F within the radius r, and a force of zero outside the radius r. The solution to this simple force function has two domains, one within the radius r. tx One is inside, and the other is outside the radius. The solution is:

[0249]

[0250] S2(r) = c3 + c4log(r) for r > r tx (61)

[0251] We will now solve for the arbitrary constant by considering the boundary and continuity conditions of the problem. We assume the clot is rigidly adhered to the chamber wall and therefore S2(R) = 0, where R is the radius of the test chamber. Furthermore, both solutions must be continuous at their junction such that S1(r) = 0.b )=S2(r b Finally, both solutions must have continuous derivatives at their junction such that S1′(r) b )=S2′(r b We propose the following solution instead of the analysis used for the repetitive oscillation solution:

[0252]

[0253]

[0254]

[0255] The estimated displacement is the average of the actual displacements on the receiving beam. If the effective receiving beam radius is smaller than the transmitting beam radius, then the estimated displacement is:

[0256]

[0257] The integral of (47) can be easily calculated.

[0258]

[0259] However, if the received beam is larger than the transmitted beam, the solution takes the following form:

[0260]

[0261]

[0262]

[0263] Viscoelastic tissue model :

[0264] Successful application of the proposed model requires the selection of an appropriate viscoelastic model, such as that achieved through the complex frequency-dependent shear modulus G. Figure 17 As shown, we have examined the Kelvin-Voigt model (Example 1) and the Jeffrey model (Example 2). The Kelvin-Voigt model is generally well-suited for modeling clot behavior, but it fails to capture certain porous elastic behaviors that may be observed in blood clots. In this sense, the Jeffrey model is sometimes more ideal.

[0265] Although specific embodiments have been described in detail in the foregoing detailed description and illustrated in the accompanying drawings, those skilled in the art will understand that various modifications and alternatives to these details can be formed based on the overall teachings of this disclosure and its broad inventive concept. Therefore, it should be understood that the scope of this disclosure is not limited to the specific embodiments and implementations disclosed herein, but is intended to cover modifications within the substance and scope defined by the appended claims and any and all their equivalents.

Claims

1. A method for assessing hemostatic function, comprising: - Applying a force waveform to the test sample inside the test chamber; - The applied force waveform applies ultrasonic radiation force, which is used to generate shear waves within the test sample, thereby causing motion. The shear waves are induced to propagate in parallel within the test chamber and are repeatedly reflected from one or more walls of the test chamber, thereby generating resonance. - Ultrasonic sensing pulses are applied to the test sample, and the differences in their echoes provide information about the movement of the test sample, where these differences include phase changes or time shifts, either of which are related to displacement; as well as - The characteristics of these differences are compared with analytical or computational models to estimate the mechanical properties of the specimen based on resonance, thereby assessing the hemostatic function.

2. The method for evaluating hemostasis function according to claim 1, wherein the feature is the oscillation period of sample movement.

3. The method for evaluating hemostasis according to claim 1, wherein the transmitter emits an electrical waveform comprising at least one force waveform, which is received by a transducer assembly and converted into an ultrasonic waveform.

4. The method for evaluating hemostasis according to claim 3, wherein the applied force waveform induces sample movement within the test chamber.

5. The method for evaluating hemostatic function according to claim 4, wherein the returned ultrasonic echo is converted by a transducer assembly into further electrical waveforms, which are analyzed by a data processor to estimate mechanical properties.

6. The method for evaluating hemostasis function according to claim 5, wherein the timing of transmission, reception and data processing is controlled by a controller.

7. The method for evaluating hemostasis according to claim 1, wherein the shear wave is generated by guiding ultrasound waves into the test sample via a force waveform.

8. A method for characterizing the mechanical properties of a test sample, the method comprising: Multiple waveforms are transmitted into the test chamber, including at least one applied force waveform and at least two sense waveforms, wherein at least one applied force waveform is transmitted as one or more acoustic pulses; At least two sensing waveforms corresponding to at least two emitted sensing waveforms are received from the test chamber via at least one transducer; The processor estimates the resonance of the test sample based on at least two received sensing waveforms; and The processor determines the modulus value associated with the stiffness of the agglomerate formed from the test sample based on the estimated resonance. and The processor outputs a first hemostatic parameter derived from the determined modulus value, wherein the output first hemostatic parameter is used to assess or treat hemostatic dysfunction.

9. The method of claim 8, wherein the at least one applied force waveform comprises an ultrasonic wave carrying sufficient energy to generate a radiative force through absorption and reflection within the test sample.

10. The method of claim 9, wherein the generated radiative force is induced along the propagation direction of the at least one applied force waveform.

11. The method of claim 9, wherein the generated radiation force induces a shear wave that travels within the test chamber and is reflected from one or more walls of the test chamber.

12. The method of claim 11, wherein a single reflected shear wave is detected by the transducer and its arrival time is used as the basis for estimating the modulus of the agglomerate formed by the test sample in the test chamber.

13. The method of claim 8, wherein each of the at least two transmitted sensing waveforms has a magnitude sufficient to return at least two received sensing waveforms, but insufficient to induce a shear wave.

14. The method of claim 8, wherein the estimated modulus value includes the shear modulus value of the clot formed by the test sample in the test chamber.

15. The method of claim 8, wherein the estimated modulus value includes a Young's modulus value or a Lamé constant value for the modulus of the agglomerate formed by the test sample in the test chamber.

16. The method of claim 8, wherein a modulus value associated with the stiffness of the clot formed from the test sample is determined by comparing an estimated resonance with a reference model derived from parameters associated with the at least one applied force waveform and parameters associated with the test chamber.

17. The method of claim 16, wherein the reference model comprises a plurality of curves, each curve having a time-displacement curve associated with a given modulus value.

18. The method of claim 8, wherein a modulus value associated with the stiffness of the clot formed from the test sample is determined by comparing an estimated resonance with an experimentally determined model associated with the test sample.

19. The method of claim 8, wherein at least one emitted force waveform is emitted as an ultrasonic beam.

20. The method of claim 8, wherein at least two transmitted sensing waveforms are transmitted as two or more acoustic pulses.

21. The method of claim 8, wherein at least two transmitted sensing waveforms are transmitted as two or more ultrasonic beams.

22. The method of claim 8, further comprising: Repeated transmission, reception, estimation, and determination steps are used to generate a shear modulus curve, wherein parameters associated with the shear modulus curve are extracted as hemostatic parameters.

23. The method of claim 8, further comprising: The second plurality of waveforms are transmitted into the second test chamber of the barrel, including at least one second force waveform and at least two second sensing waveforms, wherein the barrel includes the test chamber and the second test chamber; At least two second sensing waveforms corresponding to at least two emitted second sensing waveforms are received from the second test chamber via at least one second transducer; The processor estimates the resonance of the second test sample based on at least two received second sensing waveforms; and The processor determines a second modulus value associated with the stiffness of the second agglomerate formed from the second test sample based on the estimated resonance of the second test sample; and The processor outputs a second hemostasis parameter derived from the determined second modulus value, wherein the output second hemostasis parameter, together with the first hemostasis parameter, is used to assess or treat the hemostasis dysfunction.

24. The method of claim 22, wherein the four shear modulus curves, including the shear modulus curve, are generated by characterization of at least four test chambers of a barrel, including the test chamber.

25. The method of claim 8, wherein the output hemostatic parameters are used to assess platelet damage, factor and fibrinogen consumption and / or the presence of residual anticoagulant in the test sample.

26. The method of claim 8, wherein the method is used for bedside hemostasis detection.

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