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Abstract
In this work, we present a method to discriminate between different microparticle sizes in mixed flowing media based on laser feedback interferometry, which could ultimately form the basis for a small, low-cost, real-time microembolus detector. We experimentally evaluated the performance of the system using microparticle phantoms, and the system achieved approximately 45% positive predictive value and better than 98% negative predictive value in the detection and classification of abnormally large particles.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Thromboembolism is a known, harmful complication of intravascular implants such as blood pumps and stents [1–3]. Assessment of the thrombogenic tendency of implant materials and physical forms currently requires time consuming assays and direct microscopy. The cause of this is not well understood due to the difficulty of monitoring the temporal evolution of blood coagulation over a short time scale. Current detection schemes have limitations, including cost, time taken to assay, physical bulk, require stationary samples or the presence of large (> 1 mm) emboli [4, 5]. A system capable of early realtime detection and characterisation of small emboli (approximately 10–100 µm in diameter) in flowing blood circuits would greatly assist in the refinement of the design of intravascular implants and blood pumps. Ultimately, extension of the role of such a system to a bedside or an implanted device would broaden the applicability immensely.
One potential approach is to develop such a system using Laser Feedback Interferometry (LFI) [6]. This technique allows non-contact measurement of a target by using a laser as both a transmitter and a receiver through a phenomenon known as the self-mixing effect. The output of the laser is reflected off the target of interest, whereby the reflected light is modulated by some property of the target. If the reflected light is directed back into the laser cavity, the returning field will disturb the electromagnetic wave inside the cavity and ultimately force the laser into a disturbed state. By monitoring the photocurrent of an internal photodiode, or by monitoring changes in the laser terminal voltage, this disturbance can be precisely measured and transformed into information about the target.
The major advantage of an LFI sensor is the overall simplicity; in most cases, they can be constructed using a small number of low cost components which are relatively simple to align. In the most minimal configuration, a sensor may only require a single laser diode and associated processing electronics. LFI sensors also have high sensitivity; they are able to perform meaningful measurements with optical power attenuation in the external cavity of more than 70 dB [7]. For these reasons, LFI presents an interesting basis for many novel sensors [8–12], and in this case, for small particle detectors which could be used for the detection of microemboli. LFI sensors have been widely demonstrated as a suitable basis for biomedical sensors and can be constructed using biocompatible materials such as glass fibre [7, 13–15]. For the characterisation of particles in blood, a sensor based on LFI would be particularly useful as it could be used not only in a mock blood-circulation loop at the design stage, but also in an implanted device due to its small size. The low component count means that sensors can also have a low enough cost to be disposable, which is important to reduce cross-contamination and cross-infection risk when measurement sensors must come into contact with bodily fluids.
Previous works in this area have examined a multitude of scenarios in which information about suspended particles can be determined using LFI. It was previously found that for polystyrene nanoparticles in a liquid flow, the spectrum of the LFI signal is morphologically different for different particle size distributions [16, 17]. Similar work has also been presented in which particle size measurement was performed for particles moving only under Brownian motion [18]. Reconstruction techniques for nanoparticle size distributions have been developed which are based on the fitting of a mathematical model of the phenomenon to measured results [19]. Additionally, non-linear optical filters have been used to increase the sensitivity of the LFI sensor [20]. Most recently, a system to detect and count individual nanoparticles based on their time domain signature has been developed and evaluated [21].
In this article, we present an evaluation of LFI as a method for detecting and characterising microembolus-like particles under flow. Most works in the area of LFI which present particle detection techniques are specific to nanoparticles (particles less than 1 µm). However, for the detection of microemboli we are primarily interested in particles which have a diameter greater than 5 µm. This is approximately the size of a single red blood cell, and the emboli generated by intravascular implants are expected to be primarily composed of agglomerated red blood cells. We also only consider the case that a single particle passes through the beam at any one time, as this can be managed through other means (dilution, microfluidic circuits, etc); the LFI signal of high particle concentrations is markedly different due to multiple scattering phenomena [22]. The sensor only uses techniques which do not rely on averaging or repeated measurements; in a flowing stream of particles, a beam obstruction event for a specific particle would only ever occur once.
This article is organised as follows: first, the underlying theory of LFI in the context of single particle detection is presented. Next, we examine a simulation of the LFI signal for a particle passing through the beam, and then consider some of the features of the synthetic signal in the context of experimental results. Finally, a classification algorithm is described which can distinguish between smaller and larger particles using the LFI signal, and its effectiveness is quantified.
2. Theory
When an object passes through the beam of an LFI sensor, one can expect the average reflectivity of the target (with respect to the power re-injected into the lasing cavity) to be a function of the angle between the beam axis and the surface normal. For a structured sphere-like particle which generates a partially diffuse reflection, the amount of reflection will peak when the centre of the particle is on the beam axis. This is shown in Fig. 1(a).
Fig. 1 (a) Qualitative diagram of reflected power for a particle travelling from left to right, assuming that the reflection is a mixture of specular and diffuse reflection. (b) Two different sized particles with a partially specular surface, and the angular spread of reflected power at the position of maximum reflection. In both diagrams, the beam axis is shown shown as a broken line, and reflected rays are shown as solid.
One can also expect that the total amount of light returning to the laser cavity will be greater for a larger particle, as the total reflected power will be distributed over a smaller angular range. This effect is diagrammatically represented in Fig. 1(b) in that the divergence angle for the smaller particle, θ1 (green) is greater than for the larger particle, θ2 (red) due to the larger curvature of the smaller particle owing to its smaller diameter.
To understand the effect of changing reflectivity on the LFI signal, we begin with the excess phase equation for the steady-state response of a laser diode under optical feedback [6, 23]
where ϕFB is the external round-trip phase at the perturbed laser wavelength, ϕ0 is the external round-trip phase of the free-running laser, C is the feedback parameter, and α is the linewidth enhancement factor, a quantity which describes the dependence of the free-running phase of the laser on the cavity optical gain. As with most works of this nature, we consider α to remain constant [24]. In this simple reflection scenario, ϕ0 in Eq. (1) can be substituted with the phase shift experienced by the re-injected wave at the free-running wavelength λ0 over the physical distance d (assuming the medium is air with a refractive index of 1), The term of interest in the excess phase equation is ϕFB, but this quantity is difficult to observe in practice. Instead, it is simpler to monitor the output power of the laser, P which is a function of ϕFB, where P0 is the power of the free-running laser, and β is a power modulation coefficient which describes the properties of the laser and the amount of feedback [25]. The output power can be measured using the internal photodetector at the rear of the laser, and this is what we refer to in this article as the LFI signal.The dependence of C and β on the reflectivity of the target is encompassed in the rate of coupling,
where τin is the roundtrip time inside the laser cavity, R2 is the reflectivity of the front mirror of the laser, and Rext is the effective reflectivity of the external target (including losses). Both C and β are linearly proportional to κ [23, 25]. Due to the homodyning nature of LFI sensors, the reflection quantity of interest is the amplitude reflection coefficient of the target, .Using Eq. (4), we can therefore conclude that the amplitude of P will be proportional, through β, to the amplitude reflection coefficient of the target, rext. However, the relationship between P and rext through ϕFB and C is more complex, owing to the nature of Eq. (2). When C > 1, multiple solutions will exist for ϕFB, meaning that the phase of the laser can wrap before reaching the bounds. This effect will be discussed in further detail in the next section.
3. Simulation implementation
A simulation of the excess phase equation was developed in order to examine in depth the dependency of the LFI signal on the amplitude reflection coefficient. The simulation first solves the right hand side of Eq. (2) for ϕFB at each timestep for a particle moving at a constant velocity, and the output power of the laser is then calculated using Eq. (3). This method of solving the excess phase equation has been evaluated in a previous article [23].
The external cavity length, d, was determined using a 2D ray-tracing routine which calculates the minimum intersection distance between a single ray and a circle, where the circle represents a particle. The incident angle of any rays which miss completely was considered to be equal to the grazing angle.
The target materials of interest were expected to generate a mixture of both specular and diffuse reflection, and so rext was calculated as a function of the incident angle using an enhanced backscattering reflection superimposed on Lambertian scattering profile [26]. The backscattering function is shown in Fig. 2.
Selecting the values of C and β to be used in the simulation normally requires knowledge about the target material and the characteristics of the laser. However, changes in β will linearly modulate the amplitude of the signal as β ∝ rext, and thus the qualitative behaviour of varying rext is captured. It is also important to note that the non-linear dependence of the LFI signal on C results in two qualitatively different regimes: C ≤ 1 (lack of hysteresis) and C > 1 (hysteresis present). As such, we consider these cases separately [6, 23].
4. Simulation results and discussion
The first scenario we will examine is shown in Fig. 3. In this configuration, we consider a particle travelling at a constant velocity perpendicular to the beam axis. For this simulation, we also assume that C ≤ 1; the C > 1 case will be discussed later.
Fig. 3 Initial simulation scenario. A circular particle moves through the beam axis from a laser diode (LD).
Figure 4 shows the results of this simulation for three different particle diameters at a velocity of 2 mm/s. Figure 4(a) shows that the minimum in the cavity length occurs when the particle is exactly half-way through the beam, and according to Fig. 4(b), this position also corresponds to normal incidence. Figure 4(c), where C and β are fixed at 1, shows the characteristic LFI phase wrapping, with a greater rate of change of external cavity length corresponding to shorter oscillation cycles. At 15 ms, the rate of change of the external cavity length reverses, and this results in the direction of phase accumulation also reversing. Finally, Fig. 4(d) shows the result of the simulation with C and β being calculated as a normalised function of the incident angle. The higher frequency oscillations of the LFI signal are attenuated by the relatively low β as a result of the larger incident angle.
Fig. 4 Simulation results for a 50 µm (blue), 20 µm (green), and 5 µm (red) particle travelling perpendicular to the beam. (a) External cavity length calculation results. (b) Incident angle calculation results. (c) Laser output power deviation with C and β fixed at 1 at all positions. (d) Laser output power with C and β as a normalised function of incident angle.
In a practical sense, the attenuation of high frequency components presents two problems for developing an LFI-based microparticle detector. Most LFI sensors require the use of AC-coupled amplifiers in order to remove thermal drift and other relatively slow sources of noise. As a result, detection of a slowly changing signal is difficult, as it may be unavoidably attenuated by these front-end filters. Additionally, the shape which is preserved after the amplitude modulation by β is very simple and has few features, compared to those in Fig. 4(c), which could be used for pattern matching algorithms. To solve these problems, the geometry of the optical system can be modified so that the maximum β value does not occur at the same time as the phase reversal.
We now consider a scenario in which the particle velocity vector is at a 45 degree angle to the beam axis (see Fig. 5). In this case, the velocity has a component in the direction of the beam axis, and as such will contribute a time-dependent, monotonically increasing displacement to the external cavity length.
Fig. 5 Diagram showing the configuration of the second simulation scenario, with the particle moving at a 45 degree angle to the beam axis of the laser diode (LD).
Figure 6 shows the results from the simulation of this second scenario. In Fig. 6(a), the shape of the external cavity length vs time curve is now skewed by the addition of the displacement from the particle velocity. However, Fig. 6(b) is almost identical to the previous simulation, as the temporal evolution of the incident angle of the beam only depends on the component of velocity perpendicular to the beam axis. This means that the point of inflection in both Fig. 6(a) and Fig. 6(b) no longer occurs at the same time.
Fig. 6 Simulation results for a 50 µm (blue), 20 µm (green) and 5 µm (red) particle travelling at a 45 degree angle to the beam. (a) External cavity length calculation results. (b) Incident angle calculation results. (c) Laser output power deviation with C and β fixed at 1 at all positions. (d) Laser output power with C and β as a normalised function of incident angle.
Figure 6(c) shows the LFI signal with C and β fixed to 1. The point of phase reversal occurs at the same time as the minimum in the external cavity length, and as such occurs before the particle passes through the centre of the beam. The result of this is shown in Fig. 6(d); as opposed to Fig. 4(d), the amplitude modulation envelope from β instead captures a region of high frequency oscillation. The resulting burst would pass unimpeded through any AC-coupled system and would be much simpler to detect amongst noise due to its frequency rich content.
Finally, we turn to examine the results of increasing C above 1, where multiple phase solutions to the excess phase equation exist. Figure 7 shows the results of this in simulation where the normalised function C ≡ C(Cmax) is multiplied by a scaling factor Cmax. To better illustrate the effect of increasing C, the modulation is removed by fixing β to 1.
Fig. 7 Simulation results for a 50 µm diameter particle moving at 45 degrees to be beam, with the maximum C value scaled by Cmax, and β held constant. The simulation geometry is otherwise identical to that used in Fig. 6.
The resulting waveforms demonstrate that as C increases above 1, the LFI signal begins to wrap over a smaller phase interval. In this scenario, the reduced interval effectively results in an offset in the LFI signal which is proportional to C. These simulations have been repeated in Fig. 8, but without keeping β constant and instead scaling the normalised value of β ≡ β(βmax) by βmax.
Fig. 8 Simulation results for a 50 µm diameter particle moving at 45 degrees to be beam, but with the maximum C and β value scaled by Cmax and βmax respectively.
As is to be expected, the amplitude modulation in Fig. 8 is most significant in the βmax = 4 case. Most notably, the offset in Fig. 7 (most visible in the Cmax = 4 case) combines with the envelope caused by β to not only increase the amplitude of the oscillations, but also to shift the signal vertically. Given that larger particles are expected to have larger maximum value of C in experiments (due to higher rext), this shift is an additional feature that could be used for particle size discrimination.
5. Displacement and Doppler shift
A number of the previously referenced articles on LFI sensors use Fast Fourier Transform (FFT) methods to detect the Doppler shift of light caused by the particle motion, and this information is used for particle characterisation [6]. For the specific application of single particle detection, this can be problematic as the relative timing information of signal features is inherently obscured by the Fourier transform [27]. Without careful data collection and processing, performing analysis only in the frequency domain increases the risk that the temporal information from two separate particles is subtly merged into a single frequency domain representation. It is also important to note that all of the information present in the frequency domain is present in the time domain; in fact, the result shown in Fig. 6(d), when transformed to the frequency domain, is equivalent to the Doppler shift of light caused by an object moving through the beam.
As mentioned previously, this is because the high frequency content of the particle signal is generated by changing the synchronisation between the location of the phase reversal and the amplitude modulation envelope. The LFI signal increases in frequency as the particle moves further from point of phase reversal, so an increase desynchronisation causes the envelope to be applied to a region with higher frequency content in the underlying phase wrapping. To show that this is consistent with previously developed theory, a simulation of different velocity angles was performed and the results transformed into the frequency domain. The corresponding frequency information is shown in Fig. 9, both of which show a comparison between the frequency with the highest magnitude and the theoretically expected frequency shift for each angle. The theoretical Doppler frequency shift, fD is calculated using the formula [28]
where |v| is the magnitude of the velocity vector, θ is the angle of the velocity with respect to the beam axis and λ0 is the unperturbed laser wavelength.Fig. 9 FFT of the LFI signal over the range of angles from the closed interval of 10 to 85 degrees with a step size of 5 degrees. The blue line corresponds to the theoretically predicted frequency from Eq. (5). Data was computed from a simulated 50 µm diameter particle moving at 2mm/s through the beam at various angles. Both C and β were normalised.
6. Experimental method
After completing the simulations, an experiment was performed using several different sized plastic particles to compare between these simulated signals and their real-world equivalents.
Microporous polyamide particles (Dantec Dynamics PSP Series) were used as a phantom for microemboli, due to their availability, safety, lack of ethical constraints, and robust chemical properties. These particles are available from the vendor in three size distributions, with the means of these distributions being 5 µm, 20 µm, and 50 µm. Initial experiments showed that the particles behaved in a hydrophobic manner, and as a result all experiments were performed with the particles suspended in 99% isopropyl alcohol. No repelling forces were observed in the alcohol. The particles were also examined under an optical microscope, and were found to be round but not perfectly spherical. The particles were also expected to have rough surface geometries due to their microporous nature. The flow profile is expected to be laminar based on similar experiments in flow channels with similar mixtures [8].
A syringe pump (New Era NE-1000) was used to drive the suspension from a syringe through polytetrafluoroethylene tubing into a transparent rectangular hollow glass capillary (ProSciTech G346-030-50) with the inner hollow cross section specified as 0.3 mm × 3 mm. The capillary was glued to an acrylic mount using Norland 63 adhesive. The capillary assembly was mounted on a three axis micrometer stage and was oriented such that the direction of flow was the same direction as gravity. A generic USB microscope and an Olympus LG-PS2 light source were used to monitor the region of interest inside the channel from the rear face to confirm that particles were not agglomerating in the capillary, and that particles were indeed passing through the beam. Throughout the acquisition, the syringe pump was driven at 180 µL/min, which corresponds to a maximum particle velocity of approximately 3.3 mm/s inside the capillary. This velocity was chosen based on the expected particle velocity in the body, as well as based on the bandwidth of the available amplifiers.
An Eagleyard 850 nm DFB laser was collimated and focussed using two Thorlabs C240-TME-B lenses into the glass capillary. Based on the experimental setup, we estimate that the spot size is close to the diffraction limit of ∼10 µm, resulting in a corresponding Rayleigh range of ~350 µm which is similar to the lateral depth of the channel. The wavelength of 850 nm was selected as it is often used in optical experiments with blood cells, and wavelengths around 800 nm are considered to be optimal in this application [29]. The temperature of the laser was regulated using an Arroyo 214 thermoelectric laser mount and an Arroyo thermoelectric controller. The laser and lens assembly was mounted on a rotation stage which controlled the elevation angle of the beam with respect to the flow axis inside the capillary. The elevation angle was adjusted to approximately 45 degrees. To assist in the alignment of the beam spot inside the capillary, a suspension of highly reflective 10 µm glass particles (Dantec Dynamics HGS series) was pumped into the channel, and the laser position was adjusted until the signal was maximised.
The mismatch in density between the dispersion medium and the dispersed phase (0.8 g/cm−3 for isopropyl alcohol, 1.1 g/cm−3 for the polyamide particles) resulted in the particles settling to the bottom of the syringe after 3–4 minutes. To counteract this, the syringe pump was mounted vertically with the direction of infusion being the same direction as gravity, and a magnetic stirrer mounted below the syringe. Three spherical magnets were added to the syringe as a stirrer bar. As the stirrer generated too much vibration to perform useful measurements, the stirrer was intermittently switched on and off via a relay, and measurements were only performed while the stirrer was off. A diagram of the experimental setup is shown in Fig. 10.
Fig. 10 Experimental setup. The syringe pump (red) is held in the vertical direction by an angle bracket (brown), while the laser diode (LD) is fixed at a specific elevation angle using a manual rotary stage (not shown).
The internal photodiode was used to sense the output power of the laser. The signal was extracted using a transimpedance amplifier (TIA) with a gain of approximately 9600. Acquisition was performed using a Digilent Analog Discovery at a resolution of 14 bits and a sample rate of 160 kHz. Stirrer activation and data acquisition was controlled using Python.
7. Experimental results and discussion
Figure 11 shows some typical measured photodiode LFI signals for different sized particles passing through the beam. The amplitude of the signal increases with particle size, and the larger two particles exhibit the offset which appeared in simulation at higher levels of C and β (see Fig. 8). Additionally, the offset is greater for the 50 µm particle than the 20 µm particle, which is also consistent with the argument that larger particles will have a greater magnitude of change in C and β. However, for the 5 µm particle this lift is not evident due to the smaller C and β resulting from the fact that the particle is smaller than the beam spot, resulting in less light reinjected into the laser.
Fig. 11 Measured LFI signal for three different sized particles passing through the beam independently.
Although the envelope behaviour is similar between the simulation results in Fig. 8 and the experiment, there appears to be significantly more high frequency information in the experimental results. This is likely because experimental particles are not perfect spheres, and have a much rougher surface than the simulated sphere. However, closer examination shows that there are still similarities between the behaviour of the simulation and the experimentally recorded signals. Figure 12 shows a zoomed in section of the 20 µm particle signal, with some regions of interest highlighted.
Fig. 12 LFI signal showing highlighted regions of the 20 µm signal from Fig. 11. The black region shows the phase wrapping as the particle moves out of the beam, while the red and green regions likely correspond to surface features of the particle. Features similar to these can be found in earlier simulations. Visualization 1 shows examples of particles passing through the beam.
The black rectangle in Fig. 12 shows the region in which the center of the particle is moving out of the axis of the beam; it is likely that κ is large due to the small amplitude of the phase wrapping (caused by large C) and the significant offset (caused by large β). After the black rectangle, the increased wrapping amplitude and offset decrease both suggest a lower value of κ. This behaviour is to be expected, based on the round shape of the particle and the geometric explanation in Fig. 1. The red rectangle shows one of the locations in which the direction of phase accumulation reverses, as shown in Figs. 4c and 6c, likely indicating a change in surface gradient. Finally, the green rectangle shows a region which is very similar to the simulation results in Fig. 6d of a single particle moving through the beam at an angle. This suggests that a feature with a spherical-like cross section appeared on the edge of the particle topography visible to the laser. Particles under flow can be seen in Visualization 1 (recorded at a slow flow rate); the particles have complex shapes, and are seen to tumble and rotate independently. In some cases, only a small portion of the particle is illuminated by the beam.
A fundamental limitation of a comparison between the simulations and experiment is that the simulations were performed using an ideal pencil beam, whilst the beam in the experiment was focussed (as mentioned previously, with spot size ∼10 µm and Rayleigh range of ~350 µm).
Despite these complexities, the behaviour of the signal envelope can still be used to discern smaller particles from larger ones.
In the broader context of intravascular implants, a smaller mismatch than the one present in the experiment is expected between the refractive index of the embolus and the surrounding medium; approximately 0.13 for the experiment, and 0.08 for normal blood [30, 31]. However, given that LFI sensors are known to be extremely sensitive to changes in refractive index, this is unlikely to be an issue [6].
8. Classifier implementation
In order to detect and provide a embolus-likelihood metric for particle detection events, a simple binary classifier was developed based on the hypothesis that the LFI signal for larger particles will have a higher peak and a greater area under the curve than smaller particles. Although the results for this work were executed offline, there is no reason why a simple variation of this algorithm could not be computed in an online fashion after training. The classifier was designed to distinguish between the 20 µm and 50 µm particles, where the former was considered to be a reference for a natural or minor level of clotting which is not necessarily indicative of a pathology, and the latter a cause for concern and thus the detection of interest. The 5 µm particle signal was used as the background noise level reference because the particles are roughly the same size as normal red blood cells and therefore are also non-pathological.
For the three separate suspensions (each containing only one size of particle), the photodiode voltage was measured for approximately 90 seconds at the full sample rate of 160 kHz. The sensing configuration was identical to that described in the experimental method. The measured data was then passed through a lowpass filter and all of the maxima in the signal were determined by searching for the zero-crossings of the numerically calculated derivative, and the list of maxima was sorted by the photodiode signal amplitude at that point in descending order. All maxima with the voltage below a threshold were discarded at this step to remove those generated by unwanted noise from the measurement system. The threshold was determined by manually examining the data in the regions where no beam obstruction event occurred.
Starting from the largest maxima, all other maxima within a fixed temporal keepout window were then discarded. The keepout window length was manually determined as the approximate duration of a single 50 µm beam obstruction event. This process was repeated in-order until all maxima were either processed or discarded. Finally, integration windows around the remaining maxima were determined by moving in both the positive and negative direction on the time axis until the voltage signal fell below the 99th percentile of the amplitude of the 5 µm beam obstruction events. The integral of these windows were recorded against the value of the maxima.
The measurements of the different particle sizes were processed in the same manner, with the same filters and thresholds used. No anomalies were manually removed.
To classify the particles as either 20 µm or not, the 20 µm dataset was shuffled and 66% of the data taken for training. A classification boundary was then determined by computing the 99th percentile of a two dimensional half-normal distribution fit of the training set; this computation was based on the sklearn.covariance.EllipticEnvelope routine in the Python scikit learn machine learning library. To improve the quality of the fit, the fit to the distribution of training data was performed after subtracting the global offset caused by the previous thresholding operations. The remaining data in the 20 µm dataset as well as the entire 50 µm was then used to test the classifier. Cross-validation was performed by repeating this shuffle and split method 1000 times, and the results of this are shown in Table 2.
Table 1. Classification results for the data in Fig. 13.
Table 2. Classification effectiveness after 1000 cross-validations.
9. Classifier results
Figure 13 contains the results of this algorithm, with the integral of the event plotted against the peak signal amplitude of the event.
Fig. 13 Typical results of the classification algorithm. The black line is the classification boundary, and the coloured gradient shows the shape of the underlying Gaussian fit. Blue crosses are part of the training set, and the other markers are described in Table 1. The total number of measurements in the 20 µm dataset was 243, with 162 being used for training, and remaining 81 being used for classification. The 50 µm dataset contained 153 measurements which were all used for classification.
10. Classifier discussion
Figure 13 and Table 1 show that a number of the 50 µm beam obstruction events in the experiment are classified as 20 µm events (false positive, ). This is because the particles do not necessarily have the perfect trajectory across the beam axis as they did in the simulation, and as a result may only clip an edge of the beam (as also seen in Visualization 1). In any case, the LFI signal is only sensitive to the cross section of the particle which passes through the beam, and so when this is unconstrained, larger particles may appear to have a signature similar to smaller particles. However, there is no flow configuration for spherical particles which can cause a smaller particle to appear as a larger one (false negative, ); Table 1 shows that none of these false negative classifications occurred in this experiment. Therefore, although there may be a non-zero probability of the classification of large particles as small ones (false positive, ), the classification of large particles as large particles (true negative, ) remains unaffected by this problem.
Having a high false positive rate may be problematic for some applications, but for the detection of artificially generated emboli it is only a minor concern. The artificial cardiovascular organs previously mentioned are used to augment or replace the heart, and so if a device of this nature causes thrombosis it will occur within a large volume of blood and likely cause the generation of many large particles. Additionally, the onset of thrombosis is regulated by a strong positive feedback loop, meaning that only small amounts of cell damage need to occur to trigger a significant thrombolytic reaction [3233]. Nonetheless, the false positive rate could be reduced by using a narrower sensing capillary which would reduce the probability of a particle flowing in a suboptimal path, or using multiple sensors in parallel and using the largest particle measurement between them as the most representative one [34, 35].
Table 2 presents two measures of classification effectiveness. Although the positive predictive value of the classifier is close to the worst case of 50%, the negative predictive value is better than 98%. This means that while a classification of a particle as 20 µm is not useful, a classification as not 20 µm is likely to be correct.
In Fig. 13, two anomalous 20 µm false negative events fall outside of the ellipse (in the training set). These can reasonably be explained by the same factors discussed in the experimental results section, and in particular the fact that the particles used in the test were only close to spherical, and thus may have had unusually planar features which increased the reflectivity.
11. Conclusion
We have demonstrated a platform based on LFI showing promising discriminatory power between different microparticle sizes in mixed flowing media. Mathematical analysis, simulations, experimental, and statistical results are provided as evidence to support this conclusion. The system performs effectively with only a single measurement of the particle signature, and as such would be suitable for use in a real-time sensor. This provides a significant step towards the basis for a small, low-cost, real-time microembolus detector, which could eventually be used for evaluation the clotting tendency in blood pumps and associated intravascular implants.
Funding
Australian Research Council (ARC) DP160103910; The Trevor and Judith St Baker Family Foundation.
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