Analysis of Flow Cytometric Fluorescence Lifetime with Time-Delay Estimation of Pulse Signals
<p>Schematic representation of fluorescence excitation process of the fluorescently labeled microsphere with three different fluorochromes.</p> "> Figure 2
<p>Generation of forward-scattered and fluorescent light pulses while microsphere flows through the excitation volume. (<span class="html-italic">L<sub>fs</sub></span>(<span class="html-italic">t</span>): forward-scattered light pulse; <span class="html-italic">L<sub>fl</sub></span><sub>1</sub>(<span class="html-italic">t</span>), <span class="html-italic">L<sub>fl</sub></span><sub>2</sub>(<span class="html-italic">t</span>) and <span class="html-italic">L<sub>fl</sub></span><sub>3</sub>(<span class="html-italic">t</span>): light pulse of fluorochromes 1, 2 and 3, respectively; <span class="html-italic">L</span><sub>0</sub>: and <span class="html-italic">L</span><sub>1</sub>: the upper and lower limbs of excitation volume, respectively).</p> "> Figure 3
<p>(<b>a</b>) The waveforms of fluorescent pulse signals with different lifetimes; (<b>b</b>) The change of pulse width of fluorescent signals with different lifetimes resulted from the threshold. (The intensity in this figure is used to represent relativeness with no units.)</p> "> Figure 4
<p>Steps of time-delay estimation between <span class="html-italic">fs</span> and <span class="html-italic">fl</span><sub>1</sub>. (<b>a</b>) Pulse signals of <span class="html-italic">fs</span> and <span class="html-italic">fl</span><sub>1</sub> after photovoltaic conversion and electronic systems; (<b>b</b>) Zoom frequency spectrum of <span class="html-italic">fs</span>(<span class="html-italic">n</span>) and <span class="html-italic">fl</span><sub>1</sub>(<span class="html-italic">n</span>) calculated with MCZT, <span class="html-italic">N</span><sub>1</sub><span class="html-italic">/N</span> = 10; (<b>c</b>) Cross-correlation frequency spectrum calculated with <span class="html-italic">FS_Z</span> and <span class="html-italic">FL</span><sub>1</sub><span class="html-italic">_Z</span>; (<b>d</b>) Cross-correlation frequency spectrum period expansion by inserting zero, <span class="html-italic">N</span><sub>2</sub><span class="html-italic">/N</span><sub>1</sub> = 10; (<b>e</b>) Time domain cross-correlation function calculated with FICP. (Δ<span class="html-italic">t</span>: time-delay between <span class="html-italic">fs</span> and <span class="html-italic">fl</span><sub>1</sub>; <span class="html-italic">n</span><sub>1</sub>: the time-delay estimation result).</p> "> Figure 5
<p>Time-delay calibration. The LED1 emission light is blue and the LED2 emission light is red; <span class="html-italic">S_fs</span> is forward-scattered light pulse, <span class="html-italic">S_fl</span><sub>1</sub> is the fluorescence light pulse. (<b>a</b>) Light-pulse time-delay calibration. <span class="html-italic">H</span><sub>0</sub>(<span class="html-italic">ω</span>) is the frequency-domain transfer function of electric system 0; (<b>b</b>) Hardware time-delay calibration. <span class="html-italic">H</span><sub>1</sub>(<span class="html-italic">ω</span>) is the frequency-domain transfer function of electric system <span class="html-italic">1</span>.</p> "> Figure 6
<p>Cytometric pulse signals from single cell stained with three-color reagents simultaneously. Four AD9446-100 (100 MSPS) are used for the analogy-to-digital conversation.</p> "> Figure 7
<p>(<b>a</b>) Cross-correlation function of <span class="html-italic">fs</span>(<span class="html-italic">n</span>) and <span class="html-italic">fl<sub>m</sub></span>(<span class="html-italic">n</span>) in time-domain calculated with FICP (<span class="html-italic">N</span><sub>2</sub>/<span class="html-italic">N</span><sub>1</sub> = 50). The red curves are the cross-correlation functions of <span class="html-italic">fs</span>(<span class="html-italic">n</span>) and <span class="html-italic">fl</span><sub>1</sub>(<span class="html-italic">n</span>); the blue curves are the cross-correlation functions of <span class="html-italic">fs</span>(<span class="html-italic">n</span>) and <span class="html-italic">fl</span><sub>2</sub>(<span class="html-italic">n</span>); the black curves are the cross-correlation functions of <span class="html-italic">fs</span>(<span class="html-italic">n</span>) and <span class="html-italic">fl</span><sub>3</sub>(<span class="html-italic">n</span>); (<b>b</b>) Peak detail of cross-correlation function of <span class="html-italic">fs</span>(<span class="html-italic">n</span>) and <span class="html-italic">fl</span><sub>2</sub>(<span class="html-italic">n</span>) in (<b>a</b>).</p> "> Figure 8
<p>Gauss fitting results of pulse signals (<span class="html-italic">fs</span>, <span class="html-italic">fl</span><sub>1</sub>, <span class="html-italic">fl</span><sub>2</sub> and <span class="html-italic">fl</span><sub>3</sub>). (<b>a</b>) Results of pulse signal <span class="html-italic">fs</span>; (<b>b</b>) Results of pulse signal <span class="html-italic">fl</span><sub>1</sub>; (<b>c</b>) Results of pulse signal <span class="html-italic">fl</span><sub>2</sub>; (<b>d</b>) Results of pulse signal <span class="html-italic">fl</span><sub>3</sub>.</p> "> Figure 9
<p>Fluorescence pulse signals after normalization. The intensity is used to indicate the relative relationship with no units.</p> "> Figure 10
<p>Calculated pulse width variation with different lifetimes. The blank curve marked with “x” represents the results acquired using Equation (2). The red points are the results of proposed method in this work.</p> ">
Abstract
:1. Introduction
2. Theory
2.1. Flow Cytometric Fluorescence Lifetime
2.2. Forward-Scattered and Fluorescent Light Pulses
2.3. Time-Delay Estimation
3. Materials and Method
3.1. Time-Delay Estimation with Microspheres
3.2. Time-Delay Calibration of Photovoltaic Conversion and Electric Systems
4. Results and Discussion
4.1. Time-Delay Estimation
4.2. Curve Fitting
4.3. Verification with Pulse Width Variation
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
FCM | Flow cytometry |
ADC | Analog-to-Digital Converter |
MCZT | Modified Chirp Z-Transform |
FICP | Fine Interpolation of Correlation Peak |
PMT | Photomultiplier tube |
LED | Light-emitting diodes |
MSPS | Mega samples per second |
RMSE | Root Mean Square Error |
SSR | Sum of Squares of the Regression |
SST | Total Sum of Squares |
SD | Standard Deviation |
RSD | Relative standard deviation |
CV | Coefficients of Variation |
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Signals | Conversion Rate (MSPS) | Curves Fitting Results | Evaluation Indexes | |||
---|---|---|---|---|---|---|
K1 | K2 | K3 | RMSE | R-Squared | ||
fs | 500 | 0.7357 | 2065 | 639.3 | 0.0201 | 0.9928 |
100 | 0.7386 | 412.3 | 128.9 | 0.0201 | 0.9928 | |
fl1 | 500 | 1.309 | 2446 | 615.8 | 0.0182 | 0.9981 |
100 | 1.308 | 488.3 | 123 | 0.0181 | 0.9982 | |
fl2 | 500 | 2.901 | 2440 | 611.6 | 0.0290 | 0.9990 |
100 | 2.898 | 486.9 | 122 | 0.0276 | 0.9991 | |
fl3 | 500 | 1.475 | 2453 | 625.9 | 0.0288 | 0.9963 |
100 | 1.475 | 489.5 | 125.2 | 0.0286 | 0.9964 |
Peak Location (ns) | Time-Delay (ns) | |||||||
---|---|---|---|---|---|---|---|---|
fs | fl1 | fl2 | fl3 | Δt1 | Δt2 | Δt3 | ||
FICP | ---- | ---- | ---- | ---- | 765.6 | 748.4 | 772.6 | |
Curve fitting | 500 MSPS | 4130 | 4892 | 4880 | 4906 | 762 | 750 | 776 |
100 MSPS | 4123 | 4883 | 4869 | 4895 | 760 | 746 | 772 |
τ1 | τ2 | τ3 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Mean (ns) | SD (ns) | RSD (%) | Mean (ns) | SD (ns) | RSD (%) | Mean (ns) | SD (ns) | RSD(%) | ||
FICP | 7.36 | 1.58 | 18.90 | 4.85 | 1.16 | 23.92 | 10.33 | 1.65 | 15.97 | |
Curve fitting | 500 MSPS | 7.24 | 1.76 | 21.36 | 4.92 | 1.24 | 25.20 | 10.41 | 1.88 | 18.06 |
100 MSPS | 7.17 | 1.93 | 23.62 | 5.11 | 1.59 | 31.12 | 11.54 | 2.13 | 18.46 |
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Zhu, L.; Zhang, W.; Dong, M.; Lou, X. Analysis of Flow Cytometric Fluorescence Lifetime with Time-Delay Estimation of Pulse Signals. Sensors 2018, 18, 442. https://doi.org/10.3390/s18020442
Zhu L, Zhang W, Dong M, Lou X. Analysis of Flow Cytometric Fluorescence Lifetime with Time-Delay Estimation of Pulse Signals. Sensors. 2018; 18(2):442. https://doi.org/10.3390/s18020442
Chicago/Turabian StyleZhu, Lianqing, Wenchang Zhang, Mingli Dong, and Xiaoping Lou. 2018. "Analysis of Flow Cytometric Fluorescence Lifetime with Time-Delay Estimation of Pulse Signals" Sensors 18, no. 2: 442. https://doi.org/10.3390/s18020442