Systematic analysis of frequency dependent differential photoacoustic cross-section data for source size estimation

Anuj Kaushik; Avijit Paul; Ratan K. Saha

doi:10.1364/JOSAA.409955

Journal of the Optical Society of America A
Vol. 37,
Issue 12,
pp. 1895-1904
(2020)
•https://doi.org/10.1364/JOSAA.409955

Systematic analysis of frequency dependent differential photoacoustic cross-section data for source size estimation

Anuj Kaushik, Avijit Paul, and Ratan K. Saha

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Anuj Kaushik, Avijit Paul, and Ratan K. Saha, "Systematic analysis of frequency dependent differential photoacoustic cross-section data for source size estimation," J. Opt. Soc. Am. A 37, 1895-1904 (2020)

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Abstract

A frequency dependent differential photoacoustic cross-section (DPACS) over a large frequency band (100–1000 MHz) was computed, and subsequently, morphological parameters of a photoacoustic (PA) source were quantified. The Green’s function approach was utilized for calculating the DPACS for spheroidal droplets with varying aspect ratios, Chebyshev particles with different waviness and deformation parameters, and normal red blood cells and cells affected by hereditary disorders (e.g., spherocytosis, elliptocytosis, and stomatocytosis). The theoretical framework considers that PA waves propagate through an acoustically dispersive and absorbing medium and are detected by a planar detector of finite size. The frequency dependent DPACS profile was fitted with tri-axial ellipsoid, finite cylinder, and toroid form factor models to obtain size and shape information of the PA source. The tri-axial ellipsoid form factor model was found to provide better estimates of the shape parameters compared to other models for a variety of sources. The inverse problem framework may motivate developing PA-based technology to assess single-cell morphology.

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$ρ$	$1005 kg / m^{3}$
$v$	1498 m/s
$μ$	$809.02 m^{- 1}$
$β$	$1.5 \times 10^{- 4} K^{- 1}$
$C_{P}$	$3.23 \times 10^{3} {Jkg}^{- 1} K^{- 1}$
$I_{0}$	$1.51 \times 10^{12} {Jm}^{- 2} s^{- 1}$
$α_{0}$	$5.5 \times 10^{- 10} Np (rad/s)^{- γ} m^{- 1}$
$γ$	1.5
$r$	100 µm
$A_{d}$	$5.03 \times 10^{3} µ m^{2}$
$N_{O}$	200

Objects	Volume	Shape Parameters
Spheroids	523.6	$b : a = 1 : 2$ , 1:4, 1:8, 2:1, 4:1, 8:1
Chebyshev	523.6	$ϵ = \pm 0.25$ , $n = 2$ , 4 and 6
	523.6	$ϵ = \pm 0.05,$ $n = 35$ and 45
RBC	122.4	$D = 7.65$ , $t / 2 = 0.70$ , $h / 2 = 1.42$ , $d = 0.7 D$
ST	112.2	$D = 6.37$ , $t / 2 = 1.36$ , $h / 2 = 1.47$ , $d = 0.7 D$
SC	104.3	$b : a = 1 : 1$
EC	104.6	$b : a = 7 : 11$

Nominal Values (µm)	Estimated Values (µm) Using Method 1	Estimated Values (µm) Using Method 2
$a = 6.28 \pm 0.07, b = 3.14 \pm 0.03$ , $AR = 1 : 2$	$ρ_{1} = 6.18$ , $ρ_{3} = 3.29$ , $VE = 0.60 %$	$ρ_{1} = 6.18$ , $ρ_{3} = 3.29$ , $VE = 0.60 %$
$a = 7.94 \pm 0.08, b = 1.98 \pm 0.02$ , $AR = 1 : 4$	$ρ_{1} = 6.20$ , $ρ_{3} = 2.15$ , $VE = 33.80 %$	$ρ_{1} = 8.25$ , $ρ_{3} = 2.10$ , $VE = 14.47 %$
$a = 10.0 \pm 0.10, b = 1.25 \pm 0.01$ , $AR = 1 : 8$	$ρ_{1} = 5.80$ , $ρ_{3} = 1.40$ , $VE = 62.28 %$	$ρ_{1} = 10.5$ , $ρ_{3} = 1.40$ , $VE = 23.61 %$
$a = 3.96 \pm 0.04, b = 7.94 \pm 0.08$ , $AR = 2 : 1$	$ρ_{1} = 3.80$ , $ρ_{3} = 6.40$ , $VE = 25.98 %$	$ρ_{1} = 3.80$ , $ρ_{3} = 9.05$ , $VE = 4.66 %$
$a = 3.14 \pm 0.03, b = 12.57 \pm 0.13$ , $AR = 4 : 1$	$ρ_{1} = 3.00$ , $ρ_{3} = 8.20$ , $VE = 40.89 %$	$ρ_{1} = 3.00$ , $ρ_{3} = 11.9$ , $VE = 14.22 %$
$a = 2.50 \pm 0.03, b = 20.02 \pm 0.21$ , $AR = 8 : 1$	$ρ_{1} = 2.35$ , $ρ_{3} = 13.40$ , $VE = 40.73 %$	$ρ_{1} = 2.35$ , $ρ_{3} = 16.40$ , $VE = 27.46 %$
$R_{cb} = 5.31 \pm 0.06$ , $n = 2$ , $ϵ = 0.25$	$ρ_{1} = 3.90$ , $ρ_{3} = 6.50$ , $VE = 20.81 %$	$ρ_{1} = 3.85$ , $ρ_{3} = 8.60$ , $VE = 2.09 %$
$R_{cb} = 4.93 \pm 0.05$ , $n = 4$ , $ϵ = 0.25$	$ρ_{1} = 4.30$ , $ρ_{3} = 6.35$ , $VE = 5.96 %$	$ρ_{1} = 4.30$ , $ρ_{3} = 7.10$ , $VE = 5.14 %$
$R_{cb} = 4.89 \pm 0.05$ , $n = 6$ , $ϵ = 0.25$	$ρ_{1} = 5.05$ , $ρ_{3} = 4.25$ , $VE = 1.19 %$	$ρ_{1} = 4.60$ , $ρ_{3} = 6.75$ , $VE = 14.39 %$
$R_{cb} = 5.00 \pm 0.05$ , $n = 35$ , $ϵ = 0.05$	$ρ_{1} = 5.00$ , $ρ_{3} = 4.40$ , $VE = 11.90 %$	$ρ_{1} = 4.70$ , $ρ_{3} = 5.35$ , $VE = 5.34 %$
$R_{cb} = 5.00 \pm 0.05$ , $n = 45$ , $ϵ = 0.05$	$ρ_{1} = 5.00$ , $ρ_{3} = 4.40$ , $VE = 11.90 %$	$ρ_{1} = 4.70$ , $ρ_{3} = 5.35$ , $VE = 5.34 %$
$R_{cb} = 4.53 \pm 0.05$ , $n = 2$ , $ϵ = - 0.25$	$ρ_{1} = 5.50$ , $ρ_{3} = 3.50$ , $VE = 15.20 %$	$ρ_{1} = 6.20$ , $ρ_{3} = 3.50$ , $VE = 7.75 %$
$R_{cb} = 4.78 \pm 0.05$ , $n = 4$ , $ϵ = - 0.25$	$ρ_{1} = 4.25$ , $ρ_{3} = 6.00$ , $VE = 13.20 %$	$ρ_{1} = 4.25$ , $ρ_{3} = 7.40$ , $VE = 7.04 %$
$R_{cb} = 4.82 \pm 0.05$ , $n = 6$ , $ϵ = - 0.25$	$ρ_{1} = 5.20$ , $ρ_{3} = 4.30$ , $VE = 6.87 %$	$ρ_{1} = 5.60$ , $ρ_{3} = 4.50$ , $VE = 13.02 %$
$R_{cb} = 5.00 \pm 0.05$ , $n = 35$ , $ϵ = - 0.05$	$ρ_{1} = 5.00$ , $ρ_{3} = 4.40$ , $VE = 11.90 %$	$ρ_{1} = 4.70$ , $ρ_{3} = 5.35$ , $VE = 5.34 %$
$R_{cb} = 5.00 \pm 0.05$ , $n = 45$ , $ϵ = - 0.05$	$ρ_{1} = 5.00$ , $ρ_{3} = 4.40$ , $VE = 11.90 %$	$ρ_{1} = 4.70$ , $ρ_{3} = 5.35$ , $VE = 5.34 %$

Nominal Values	Estimated Values (µm) Using Method 1
Nominal Values	TAEFF	CFF	TFF
RBC, $D = 7.65 \pm 0.09$	$ρ_{1} = 4.05$ , $ρ_{3} = 3.35$	$Γ = 3.45$ , $L = 1.20$	$R_{t} = 2.90$ , $R_{c} = 0.80$
$t / 2 = 0.7$ , $h / 2 = 1.42$ , $d = 0.7 D$	$VE = 88.04 %$	$VE = 63.34 %$	$VE = 70.06 %$
ST, $D = 6.37 \pm 0.07$	$ρ_{1} = 2.95$ , $ρ_{3} = 1.95$	$Γ = 2.65$ , $L = 3.70$	$R_{t} = 1.50$ , $R_{c} = 1.20$
$t / 2 = 1.36$ , $h / 2 = 1.47 d = 0.7 D$	$VE = 36.64 %$	$VE = 27.24 %$	$VE = 61.99 %$
SC, $a = 2.92 \pm 0.03$ ,	$ρ_{1} = 2.65$ , $ρ_{3} = 3.00$	$Γ = 2.55$ , $L = 4.50$ ,	$R_{t} = 2.20$ , $R_{c} = 0.40$
$b = 2.92 \pm 0.03$ , $AR = 1 : 1$	$VE = 15.40 %$	$VE = 11.86 %$	$VE = 93.33 %$
EC, $a = 3.40 \pm 0.04$	$ρ_{1} = 2.95$ , $ρ_{3} = 1.90$	$Γ = 1.95$ , $L = 4.50$	$R_{t} = 1.65$ , $R_{c} = 0.80$
$b = 2.16 \pm 0.02$ , $AR = 7 : 11$	$VE = 33.78 %$	$VE = 48.60 %$	$VE = 80.07 %$

$ρ$	$1005 kg / m^{3}$
$v$	1498 m/s
$μ$	$809.02 m^{- 1}$
$β$	$1.5 \times 10^{- 4} K^{- 1}$
$C_{P}$	$3.23 \times 10^{3} {Jkg}^{- 1} K^{- 1}$
$I_{0}$	$1.51 \times 10^{12} {Jm}^{- 2} s^{- 1}$
$α_{0}$	$5.5 \times 10^{- 10} Np (rad/s)^{- γ} m^{- 1}$
$γ$	1.5
$r$	100 µm
$A_{d}$	$5.03 \times 10^{3} µ m^{2}$
$N_{O}$	200

Abstract

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Figures (6)

Tables (4)

Equations (24)

Journal of the Optical Society of America A