Journal of Medical Ultrasonics
https://doi.org/10.1007/s10396-023-01382-z

ORIGINAL ARTICLE–PHYSICS & ENGINEERING

Optimizing irradiation conditions for low‑intensity pulsed ultrasoundto upregulate endothelial nitric oxide synthase
Daiki Ouchi1 · Shohei Mori1 · Mototaka Arakawa1,2
Satoshi Yasuda3 · Hiroshi Kanai1,2· Tomohiko Shindo3· Hiroaki Shimokawa4,3·Received: 7 April 2023 / Accepted: 18 September 2023
© The Author(s), under exclusive licence to The Japan Society of Ultrasonics in Medicine 2023

Abstract
Purpose Here we aimed to develop a minimally invasive treatment for ischemic heart disease and demonstrate that lowintensity pulsed ultrasound (LIPUS) therapy improves myocardial ischemia by promoting myocardial angiogenesis in a
porcine model of chronic myocardial ischemia. Studies to date determined the optimal treatment conditions within the rangeof settings available with existing ultrasound equipment and did not investigate a wider range of conditions.
Methods We investigated a broad range of five parameters associated with ultrasound irradiation conditions that promote
expression of endothelial nitric oxide synthase (eNOS), a key molecule that promotes angiogenesis in human coronary artery
endothelial cells (HCAEC).
Results Suboptimal irradiation conditions included 1-MHz ultrasound frequency, 500-kPa sound pressure, 20-min total
irradiation time, 32–48-μs pulse duration, and 320-μs pulse repetition time. Furthermore, a proposed index, PN , calculated
as the product of power and the total number of irradiation cycles applied to cells using LIPUS, uniformly revealed theexperimental eNOS expression associated with the various values of five parameters under different irradiation conditions.
Conclusion We determined the suboptimal ultrasound irradiation conditions for promoting eNOS expression in HCAEC.
Keywords Low-intensity pulsed ultrasound therapy · Endothelial nitric oxide synthase · Angiogenesis · Human coronary
artery endothelial cells

Introduction
Ischemic heart disease (IHD) is the leading cause of deathin developed countries [1], and its incidence is increasing indeveloping countries [2]. Therefore, noninvasive treatment
methods for this disorder are needed. Ultrasound has been
* Mototaka Arakawa
arakawa@tohoku.ac.jp* Hiroshi Kanai
hiroshi.kanai.e7@tohoku.ac.jp
1

Graduate School of Engineering, Tohoku University, 6‑6‑05
Aoba, Aramaki, Aoba‑Ku, Sendai, Miyagi 980‑8579, Japan

2

Graduate School of Biomedical Engineering, Tohoku
University, 6‑6‑05 Aoba, Aramaki, Aoba‑Ku, Sendai,
Miyagi 980‑8579, Japan3

Department of Cardiovascular Medicine, Tohoku University
Graduate School of Medicine, Sendai, Japan

4

Graduate School, International University of Healthand Welfare, Narita, Japan

used clinically for diagnosis, bone therapy, tumor resection,and drug delivery enhancement [3]. Low-intensity pulsed
ultrasound (LIPUS) reportedly induced angiogenesis andameliorated myocardial ischemia in a porcine model ofchronic myocardial ischemia [4]. LIPUS has been used totreat various orthopedic, dental, and brain disorders [5–7].
We have been studying noninvasive treatment methods
for microcirculatory disorders such as IHD. We have shownthat LIPUS irradiation of human umbilical vein endothelial
cells with 32 wave cycles significantly increases the mRNA
expression of vascular endothelial growth factor (VEGF),
with subsequent therapeutic angiogenesis [4]. However,
because these irradiation conditions were determined using
existing sector probes, conditions such as the frequency,
sound pressure, and pulse repetition frequency were not
optimized. We found that a signaling pathway mediated bymechanotransduction was involved in the effects of LIPUS[8]. Indeed, LIPUS may induce the distortion of endothelial caveolae [9, 10], which are transmitted into cells, ultimately leading to the upregulation of endothelial nitric oxide

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Journal of Medical Ultrasonics

synthase (eNOS) and VEGF with subsequent therapeutic
angiogenesis.
The present study aimed to explore ultrasound irradiation conditions that promote eNOS expression in humancoronary artery endothelial cells (HCAEC). We varied thetotal irradiation time, sound pressure, frequency, and pulse
repetition frequency, as well as the wave cycle, as discussed
in a previous report [4]. We examined the ultrasound irradiation conditions in HCAEC with LIPUS in vitro and usedthe expression level of eNOS, a key molecule that promotes
angiogenesis, to quantitatively evaluate cell activation under
the suboptimal LIPUS irradiation conditions. Furthermore, aproposed index, PN, calculated as the product between power
and the total number of irradiation cycles applied to cells
using LIPUS, uniformly showed the experimental ultrasoundcontribution to eNOS expression for the various values offive parameters under different irradiation conditions.

Materials and methods
Cell culture
HCAEC (CC-2585; Lonza, Tokyo, Japan) from one donor
were cultured in endothelial cell medium (Lonza). The cells
were passaged to passage 2, resuspended 24 h before LIPUS
irradiation, sown uniformly in 24-well plates (353,047;
Corning, New York, USA) (n = 6) at 4 × ­104 cells/well, andincubated (37°C, 5% ­CO2).

Irradiation experiment
Figure 1a shows a schematic of the experimental setup. The
desired pulse wave was generated using a signal generator(WF1974; NF, Kanagawa, Japan), amplified using a power
amplifier (705,810; Yokogawa, Tokyo, Japan), applied toa disk-shaped ultrasound transducer ( ϕ = 20 mm), andirradiated with ultrasound. Four types of transducers withcenter frequencies of 0.1, 0.3, 1, and 3 MHz were used. The
transducers were glued to circular dishes with a bottom surface thickness of 0.8 mm (150,460; Thermo Fisher Scientific, Waltham, USA). The temperature in the thermostaticchamber was kept at 37°C during the experiment. The cells
were irradiated with ultrasound through agar (010–15815;
Fujifilm Wako Pure Chemicals, Osaka, Japan) (n = 6). The
difference in propagation attenuation between the agar andculture media was neglected.
As illustrated in Fig. 1b, the five parameters that weremonitored under ultrasound irradiation conditions were
ultrasound frequency f0 [Hz], maximum sound pressure P0[Pa], total irradiation time Tttl [s], pulse duration ΔT [s], andpulse repetition time PRT [s].

13

The following three parameters are derived from these
five parameters. The wave cycle wl [cycles] was obtainedby multiplying the pulse duration ΔT by the frequency
f0 , that is, wl = ΔT × f0 . The duty cycle DC [%] was calculated as the ratio of the pulse duration ΔT to the pulse
repetition time PRT , that is, DC = ΔT∕PRT . Since thenumber of irradiations with a pulse repetition time PRT is
Tttl ∕PRT within the total irradiation time Tttl , the effective
irradiation time Tef f [s] is given by

Tef f =

Tttl ×ΔT
,
PRT

(1)

as shown in Fig. 1c. The irradiation conditions were optimized in the following order: total irradiation time Tttl, pulse
duration ΔT , maximum sound pressure P0 , and ultrasoundfrequency f0.
The LIPUS group underwent irradiation with ultrasound, while the control group did not. After irradiation,
RNA was extracted from the LIPUS and control groups
after 6-h incubation.
The maximum sound pressure P0 was measured at depth
d [m] from the transducer using a needle hydrophone(HY05N; Toray, Tokyo, Japan) on the central axis of thetransducer. Ultrasound was irradiated to the hydrophonethrough the agar as well as the irradiation to cells. The
sound field of a disk-type transducer is determined by D[11] and defined as

D = a𝜆2 ⋅ d,(2)

where λ [m] is the wavelength and a [m] the radius of thetransducer. Considering the theoretical sound pressure distribution [11] of a disk-type transducer [11], D = 1.8 waschosen to maintain the sound pressure difference between
the center of the well and the edge of the well approximately
twice as large. For each frequency f0 , the distance d wasdetermined so that D = 1.8. Thus, distance d was set to 17
mm at 0.1 MHz, 35 mm at 0.3 MHz, 117 mm at 1 MHz, and
350 mm at 3 MHz, respectively.
To correctly evaluate pulse duration ΔT and acoustic energy, a polypropylene cylinder whose material isclose to the acoustic impedance of the plate was bonded
to the back of the plate to suppress multiple reflections
within the plate, which was made of polystyrene, whose
acoustic impedance was 2.52 × 106 kg∕(m ⋅ s2 ) , and thepolypropylene cylinder had an acoustic impedance of
1.9 × 106 kg∕(m ⋅ s2 ) [12]. To suppress the reflected waves
from the bottom surfaces of the polypropylene cylinderand constant-temperature bath, the bottom surface of thepolypropylene cylinder was roughened with sandpaper.
The reflection coefficient for a rough surface is generally
known to be lower compared with that for a flat surface[13].

Journal of Medical Ultrasonics
Fig. 1  a Cross-sectional viewof the experimental system
for ultrasonic irradiation. b
Schematic diagram of the transmitted waveform. c Effective
irradiation time Tef f . d A new
index PN , showing the productof power and the total numberof irradiation cycles

13Journal of Medical Ultrasonics

Evaluation of LIPUS‑induced effect
In a previous study, we demonstrated that LIPUS therapy enhances the proliferation of human umbilical vein
endothelial cells (HUVECs) in scratch assays [8]. LIPUS
therapy also upregulates both mRNA expression and protein
enhancement of eNOS [8]. It is well known that nitric oxide(NO) is produced by eNOS [14–16].
In the present study, it was necessary to examine numerous LIPUS irradiation conditions on in vitro HCAEC todetermine the suboptimal LIPUS irradiation conditions.
Therefore, only the mRNA expression of eNOS, a key molecule that promotes angiogenesis, was used as an evaluationindex.

Real‑time polymerase chain reaction

Ultrasound evaluation index
The instantaneous intensity of the ultrasound, I(t), is calculated as follows:
2

13

PRT

(3)

ΔT

1
1
∫ 0 I(t)dt = PRT⋅ 𝜌c1 ∫ 0 p(t)2 dt ≈ 𝜌c1
Ispta = PRT

�

P
√0
2

�2

ΔT
.
PRT

(4)

To examine the action of ultrasound on cells that contributes to eNOS, EX expression, we defined the following
two evaluation indices. First, the total energy per unit area,
Ettl [J∕m2 ], irradiated on the cells can be defined as theaverage intensity Ispta within the pulse repetition time PRT
multiplied by the total irradiation time Tttl ∶1
Ettl = Ispta × Tttl ≈ 𝜌c

The procedures and conditions for the real-time polymerase
chain reaction (PCR) were the same as those used in ourprevious study [8]. We extracted mRNA using the RNeasy
Plus Mini kit (QIAGEN, Hilden, Germany) and QIAcube(QIAGEN, Hilden, Germany). Synthesis of cDNA was carried out using PrimeScript RT Master Mix (Takara Bio Inc.,
Shiga, Japan). The primer sequences (forward, reverse) were
5’-AAA​GAC​AAG​GCA​GCA​GTG​GAAAT-3’ and 5’-TCC​
ACG​ATG​GTG​ACT​TTG​GCTA-3’ for eNOS, and 5’-GCA​
CCGT
​ CAA
​ GGC
​ TGA
​ GAA
​ C-3’ and 5’-TGGT
​ GAA
​ GAC
​ GC​
CAG​TGG​A-3’ for glyceraldehyde 3-phosphate dehydrogenase (GAPDH), all of which were designed by the Perfect
Real Time Support System (Takara Bio, Shiga, Japan). Afterreverse transcription, real-time PCR was performed using
TB Green Premix Ex Taq II (Takara Bio, Shiga, Japan), a
CFX96TM Real-Time system (Bio-Rad Laboratories, California, USA), and a C1000TM Thermal Cycler (Bio-Rad
Laboratories, California, USA).
The amplification efficiency of the PCR reaction greatly
depends on the differences in each sample; therefore, it
was necessary to normalize using the endogenous control gene, GAPDH, for this study. In the present study, themRNA expression of eNOS, EX , was normalized to thatof GAPDH and compared between the control and LIPUS
groups. Parameters were compared between the control and
LIPUS groups using an uncorrelated Student’s t-test, andvalues of P < 0.05 were considered statistically significant.

I(t) = p𝜌c(t) ,()
where p(t) = P0 sin 2𝜋f0 t is the instantaneous sound pressure, ρ is the density of the medium, and c is the soundvelocity. The average intensity within the pulse repetition
time PRT , Ispta [mW∕cm2 ], is a safety standard for diagnostic ultrasound systems [17] and is calculated by

�

P
√0
2

�2

�2
ΔT
1�
× Tttl = 𝜌cPrms ⋅ Tef f ,
PRT

(5)

where Prms is the root-mean-square value of p(t) defined byP(6)Prms = √0 .
2

We defined Ettl by spatially averaging Ettl over the irradiated area as follows:{
0.55 × Ettl , for f = 0.1 or 0.3 MHz
Ettl =(7)
0.51 × Ettl . for f = 1 or 3 MHz

When the total irradiation time Tttl, pulse duration ΔT , maximum sound pressure P0, and pulse repetition time PRT were
kept constant, Ettl did not change at various frequencies of
f0. Although conditions (1), (2), (3), (4), (11), (18), and (19)in Table 1 have nearly the same Ettl value, the eNOS expression EX values were different, as shown in “Results”.
()
Next, we introduced a new index PN [J∕ m2 ⋅ μs ] bycalculating)2 ( Tef f )1(,
PN = Ettl × f0 = Ispta × Tttl × f0 ≈ 𝜌c
Prms
(8)
T
0

where T0 = 1∕f0 is one period of ultrasound irradiation. PN
was defined by spatially averaging PN over the irradiatedarea as follows:{
0.55 × PN , for f = 0.1 or 0.3 MHz
PN =(9)0.51 × PN . for f = 1 or 3 MHz

Ettl corresponds to the energy that changes to heat, anddoes not depend on the irradiation frequency f0 . Alternatively, to evaluate the mechanotransduction caused byultrasonic irradiation, PN shows the power per unit area,()2
Prms ∕𝜌c , multiplied by the total number of irradiation
cycles, Tef f ∕T 0 , during the effective irradiation time Tef f ,as shown in Fig. 1d.

Ultrasoundfrequency
f0 = T1
0
[MHz]

0.1
0.1
0.3
0.3
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3

Number

(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)

500
500
500
500
125
250
500
500
500
500
500
500
500
500
750
1000
1250
500
500

Maximum
soundpressure
P0 [kPa]

20
20
20
20
20
20
5
20
10
20
20
20
30
20
20
20
20
20
20

Total
irradiationtime
Tttl [min]

50
480
46.7
160
48
48
32
16
32
32
48
64
48
128
48
48
48
16
48

Pulse
duration
ΔT [μs]

333
3200
311
1067
320
320
320
320
320
320
320
320
320
320
320
320
320
107
320

Pulse
repetitiontime
PRT [μs]

5
48
14
48
48
48
32
16
32
32
48
64
48
128
48
48
48
48
144

Wave
cycle
wl
= ΔT ⋅ f0[cycles]
15
15
15
15
15
15
10
5
10
10
15
20
15
40
15
15
15
15
15

Duty
cycle
DC
ΔT
= PRT
[%]

Table 1  Irradiation condition of LIPUS, indices, and mRNA of eNOS for each experiment

180
180
180
180
180
180
30
60
60
120
180
240
270
480
180
180
180
180
180

Effective
irradiation
time
Tef f
Tttl ⋅ΔT
= PRT
[s]
1.581
1.581
0.913
0.913
0.125
0.25
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.75
1
1.25
0.289
0.289

Mechanical
index
MI

1231
1231
1231
1231
76.91
307.6
820.4
410.2
820.4
820.4
1231
1641
1231
3282
2769
4922
7691
1231
1231

[mW∕cm2 ]Averageintensity
Ispta

8.1
8.1
8.1
8.1
0.5
1.9
1.3
2.5
2.5
5.0
7.6
10.1
11.3
20.2
17.0
30.2
47.3
7.6
7.6

Ettl
(
)
×106
2
[J∕m ]

0.8
0.8
2.4
2.4
0.5
1.9
1.3
2.5
2.5
5.0
7.6
10.1
11.3
20.2
17.0
30.2
47.3
22.7
22.7

(PN 6 )
×10
[J∕(m2 ⋅ μs)]

1.05 ± 0.08
1.03 ± 0.13
1.14 ± 0.09
1.19 ± 0.10
0.98 ± 0.10
1.01 ± 0.06
1.09 ± 0.15
1.15 ± 0.07
1.10 ± 0.11
1.20 ± 0.07
1.20 ± 0.14
1.19 ± 0.17
1.18 ± 0.22
1.00 ± 0.08
1.13 ± 0.18
1.07 ± 0.09
0.97 ± 0.13
1.05 ± 0.12
1.02 ± 0.13

mRNA ofeNOS (/GAPDH)
EX

1.02
1.02
1.12
1.12
0.97
1.10
1.06
1.13
1.13
1.19
1.18
1.15
1.13
1.06
1.08
1.01
0.96
1.05
1.05

̂ of
EX
Eq. (A10)

Journal of Medical Ultrasonics

13

Journal of Medical Ultrasonics

Using the indices, Ettl and PN , we attempted to uniformly
show the ultrasound contribution to eNOS expression, EX ,for various values of five parameters under different irradiation conditions.

Results
In vitro experimental results
For various values of ultrasound total irradiation time T 𝐭𝐭𝐥
The common irradiation conditions were set as follows:
ultrasound frequency f0 = 1 MHz, maximum soundpressure P0 = 500 kPa, pulse duration ΔT = 32 μs , andpulse repetition time PRT = 320 μs. Figure 2a-1 shows

Fig. 2  Expression of eNOS,
EX , under different experimental conditions. a For various
values of irradiation time Tttl,(a-1) pulse duration ΔT = 32
μs, and (a-2) ΔT = 48 μs. b For
various values of pulse duration
ΔT . c For various values ofmaximum sound pressure P0. d
For various values of ultrasonicfrequency f0, (d-1) wl was fixedat 48 cycles, and (d-2) ΔT was
fixed at 48 µs. The number ineach bar corresponds to thenumber in Table 1. eNOS,
endothelial nitric oxide synthase13

the results when the total irradiation time Tttl was set
to 5, 10, and 20 min, which correspond to (7), (9), and(10) in Table 1, respectively. When Tttl was 20 min, themRNA expression of eNOS, EX , was significantly higher(P < 0.05) than those of the control group.
For the common irradiation conditions of f0 = 1
MHz, P0 = 500 kPa, ΔT = 48 μs , and PRT = 320 μs, Tttl
was set as 20 and 30 min, which correspond to (11) and(13) in Table 1, respectively. As shown in Fig. 2a-2, themRNA expressions of eNOS, EX , increased significantly(P < 0.05) at 20 and 30 min compared to that in the control, while there was no significant difference between 20
and 30 min, and the expression of EX peaked at 20 min.
Thus, a total irradiation time of T̂
ttl = 20 min was selectedbased on the clinical consideration that maintaining afixed posture for more than 20 min places a burden on
the patient.

Journal of Medical Ultrasonics

For various values of pulse duration 1T
Figure 2b shows the results obtained when the pulse duration
ΔT was changed to 16, 32, 48, 64, and 128 μs, corresponding to (8), (10), (11), (12), and (14) in Table 1, respectively.
The other irradiation conditions were identical to thosedescribed above: f0 = 1 MHz, P0 = 500 kPa, Tttl = 20 min,and PRT = 320 μs. The expression EX was significantly(P < 0.05) increased at ΔT = 16, 32, 48, and 64 μs compared to the control group, and there was no significant difference among ΔT = 16, 32, 48, and 64 μs. For ΔT = 48 μs,
the expression EX significantly increased by 15% and thenpeaked. Based on these results, the optimal wave duration
̂ = 48 μs was selected.
ΔT

For various values of maximum sound pressure P0
Figure 2(c) shows the results when the maximum soundpressures P0 were 125, 250, 500, 750, 1000, and 1250
kPa, corresponding to (5), (6), (11), (15), (16), and (17) inTable 1, respectively. The other irradiation conditions wereidentical to those described above: f0 = 1 MHz, Tttl = 20
min, ΔT = 48 μs, and PRT = 320 μs. The maximum soundpressure P0 significantly (P < 0.05) increased the expression
EX at 500 and 750 kPa compared to the control, with nosignificant difference between them, and the expression EX
peaked at 500 kPa. Based on these results, an optimal sound̂0 = 500 kPa was selected.
pressure of P

For various values of ultrasound frequency f0
Figure 2d-1 shows the results obtained when the frequency
f0 was varied as 0.1, 0.3, 1, and 3 MHz, corresponding to(2), (4), (11), and (18) in Table 1, respectively. The otherirradiation conditions were identical to those describedabove: P0 = 500 kPa, Tttl = 20 min, PRT = 320 μs, andwl = 48 cycles. When the wave cycle wl was fixed at 48
cycles, the pulse duration ΔT = wl∕f0 changed according
to the frequency f0 . The expression EX was significantly(P < 0.05) increased when the frequency f0 was 300 kHz or
1 MHz compared with the control.
To change frequency f0 with the same pulse duration ΔT ,ΔT was fixed at 48 µs. The common irradiation conditions
were as follows: P0 = 500 kPa, Tttl = 20 min, ΔT = 48 ± 2
μs, and PRT = 320 μs. Frequency f0 was changed to 0.1,
0.3, 1, and 3 MHz, corresponding to (1), (3), (11), and (19)in Table 1, respectively. The results are shown in Fig. 2d-2.
The expression EX increased significantly (P < 0.05) when f0
was 300 kHz and 1 MHz compared with the control. Basedon these results, the optimal frequency of f̂0 = 1 MHz was
selected.

Fig. 3  a The relationship between energy index Ettl and mRNA
expression of eNOS, EX. b The relationship between the proposed
index PN (product of power and the total number of irradiation
cycles) and EX

For indices E𝐭𝐭𝐥 and P𝐍 contributing to eNOS, EX
expression
To examine the effects of ultrasound on cells that contribute to eNOS, EX expression, based on the above results,
we evaluated the relationship between Ettl , PN , and EX for(1) to (19), as presented in Table 1. The results pertaining
to Ettl and PN are shown in Fig. 3a and b, respectively. For
f0 of 0.1, 0.3, 1, and 3 MHz, the displayed colors were red,
yellow, green, and blue, respectively.
Figure. 3a does not uniformly show the experimental eNOS expression for various values of five parameters under different irradiation conditions. Alternatively,
Fig. 3b shows the eNOS mRNA expression, EX , and theapproximated broken line graph (polyline) determinedby the least squares fitting, which is described in the13

Journal of Medical Ultrasonics

Appendix. The broken( line reachedthe maximum around)PN_max = 6.2 × 106 J∕ m2 ⋅ μs , and the expression EX
decreased as PN moved away from this maximum.

Discussion
Based on these results, the suboptimal ultrasound irradiation conditions were determined as follows: frequency f̂0 = 1
̂0 = 500 kPa, total irradiaMHz, maximum sound pressure P̂ = 32 − 48 μs, and̂tion time Tttl = 20 min, pulse duration ΔT̂pulse repetition rate PRT = 320⋅μs.
As shown in Fig. 3b, the relationship between PN andthe mRNA expressions of eNOS, EX , showed an upward
convex trend. When PN was smaller than PN_max and under
the conditions where EX was maximal, maximum soundpressure P0 and the total number Tef f ∕T0 of irradiation
cycles were underestimated, and EX was not sufficiently
enhanced, because PN is the product of the power per unit(
)2
area, Prms ∕𝜌c, and the total number of irradiation cycles,
Tef f ∕T 0.
However, for a PN larger than PN_max , Ispta or the total
number Tef f ∕T0 of irradiation cycles tended to be larger,
and therefore, cell injury would be induced and EX was notenhanced.
Caveolae in endothelial cells reportedly play an important role in detecting strain and stress on the extracellular
membrane via β1-integrin and contributing to the associatedsignal transduction [18–22]. When cells are irradiated byultrasound, caveolae are displaced and velocity is generated.
The evaluation index PN in Eq. (8) includes the power andtotal number of irradiation cycles, showing that the amplitude and number of actuations on the caveolae are importantfor eNOS, EX expression. Therefore, these results indicatethat LIPUS treatment may be more efficient under conditions
with an extended evaluation index PN within a range that
does not cause cell damage when setting ultrasound irradiation conditions.

Study limitations
The present study had several limitations. First, because thesuboptimum irradiation conditions were determined in theorder of total irradiation time Tttl, pulse duration ΔT , maximum sound pressure P0, and frequency f0 , the optimum isapparent but not real. Thus, it is possible that there were more
efficient conditions than those determined in this study. It
remains to be confirmed whether cellular damage is caused
by ultrasound irradiation under conditions of large Ispta values√
and a mechanical index MI = Pneg ∕ f0 , where Pneg is the
maximum negative pressure, showing an evaluation index of

13

ultrasound effects on a living body [23]. The LIPUS was irradiated under only two conditions for frequencies f0 of 0.1, 0.3,
and 3 MHz. It is necessary to confirm the relationship between
PN and the mRNA expressions of eNOS, EX , with a frequency
f0 other than 1 MHz.
In the present study, the mRNA expressions of eNOS, EX ,decreased for a PN larger than PN_max . This could be attributed
to cell damage caused by irradiating ultrasound. Therefore,in our future studies, the proper maximum sound pressure P0
and the total number Tef f ∕T0 will be determined by evaluating
the cell injury.

Conclusion
The present study determined the suboptimal ultrasoundirradiation conditions that would promote the expression ofeNOS, EX , in HCAEC. The suboptimal irradiation conditions were as follows: ultrasound frequency, f̂0 = 1 MHz;̂0 = 500 kPa; total irradiation
maximum sound pressure, P̂time, T̂
ttl = 20 min; pulse duration, ΔT = 48 μs; and pulsêrepetition time, PRT = 320 µs. An upward convex trend wasobserved between PN and the mRNA expression of eNOS, EX ,suggesting that they may be influenced by the proposed evaluation index PN, calculated as the product of power and the total
number of irradiation cycles applied to cells using LIPUS.

Appendix: Derivation of approximated lines
in Fig. 3b using the least squares method
By introducing new variables x and y as

x = log10 Eq ,(A1)

y = EX,(A2)

let us define an approximated line graph (polyline) in
Fig. 3b as
)
(
)
{ (
a1( x − x0) + y0 , ( x < x0)y=(A3)
a2 x − x0 + y0 , x ≥ x0 ,where a1, a2 , x0 , and y0 are the coefficients of the approximated polyline that should be estimated. For the measured
values {xi , yi } ( xi < x0 ) and {xj , yj } ( xj ≥ x0 ), the weighted
mean squared error 𝛼(a1 , a2 , y0 ; x0 ) between the measured
values and polyline in Eq. (A3) can be obtained as follows:

�
� ∑
� �
�
��2
�
𝛼 a1 , a2 , y0 ; x0 = i wi ⋅ �yi − a1 xi − x0 + y0 ��� � (A4)
� �
�
��2 �
∑
�
+ j wj ⋅ �yj − a2 xj − x0 + y0 � , xi < x0 , xj ≥ x0��

where w is the weight defined by the variance of EX , 𝜎 2 , as

Journal of Medical Ultrasonics

w = 𝜎12 ,(A5)

where the standard deviation 𝜎 of EX is presented in Table 1
and Fig. 3b. By fixing the coefficient x0 to an arbitrary value
and defining x′ as)�(x x0 = x − x0 ,(A6)()
the condition minimizing 𝛼 a1 , a2 , y0 ; x0 is given by∑∑∑� � �2�� ��� �
1 𝜕𝛼 (a1 , a2 , y0 ; x0 )= a1 i wi xi x0 − i wi yi xi x0 + y0 i wi xi x0 = 0,
2
𝜕a1

(A7)

∑
∑
∑
� � �2�� ��� �
1 𝜕𝛼 (a1 , a2 , y0 ; x0 )= a2 j wj xj x0 − j wj yj xj x0 + y0 j wj xj x0 = 0,
2
𝜕a2

(A8)

1 𝜕𝛼 (a1 , a2 , y0 ; x0 )
= y0
2
𝜕y0

+a1

∑

�∑

i wi +

∑

j wj

�

−

�∑

i wi yi +

� �
�
∑
��
i wi xi x0 + a2 j wj xj x0 = 0.
�∑j wj yj�(A9)

By substituting a1 into Eq. (A7),( and a2 in Eq.) (A8) into
Eq. (A9), ŷ0 (x0 ), which minimizes 𝛼 a1 , a2 , y0 ; x0 with fixed
x0 , is estimated by
�∑

∑

�

� � BI EI DJ +BJ EJ DI − i wi yi + j wj yj DI DJ�∑,ŷ0 x0 =∑ �
2
2
BI DJ +BJ DI −i wi +

j wj

DI DJ

(A10)

where

�
�
∑
∑
��
��
BI = i wi xi x0 , BJ = j wj xj x0 ,
�2
�2
∑
∑
��
��
DI = i wi xi x0 , DJ = j wj xj x0 ,
�
�
�
�
∑
∑
�
�
EI = i wi yi xi x0 , EJ = j wj yj xj x0 .

(A11)( ) E −B ŷ (x )â1 x0 = I DI 0 0 ,(A12)( ) E −B ŷ (x )â2 x0 = J DJ 0 0 .

(A13)

( )
( )
S u b s e qu e n t ly, â1 x0 a n d â2 x0 m i n i m i z i n g()
𝛼 a1 , a2 , y0 ; x0 with a fixed x0 are estimated by substituting
Eq. (A10) into Eq. (A7) and (A8), respectively.
I

J

( )
( )
( )
Using
and
â x ,â x ,
ŷ0 x0 ,( ( ) ( ) 1 (0 ) ) 2 0
𝛼 â1 x0 , â2 x0 , ŷ0 x0 ; x0 is calculated for each of the{ }various values x0 . Thus, the coefficient x̂0 that minimizes()
𝛼 a1 , a2 , y0 ; x0 in Eq. (A4) can be obtained as follows:( ( ) ( ) ( ) )x̂0 = argmin𝛼 â1 x0 , â2 x0 , ŷ0 x0 ; x0 .
(A14)
x0Finally, the optimum values of a1, a2, and( y)0 for (the)minimum condition can be determined by â1 x̂0 , â2 x̂0 , and( )ŷ0 x̂0 , respectively.

Acknowledgements We thank Dr. Kazuto Kobayashi and Mr. Nagaya
Okada (Honda Electronics) for their assistance with fabricating thetransducers and calibrating the hydrophone used in this study. This
work was partially supported by Grants-in-Aid for Scientific Research(23H03753) from the Japan Society for the Promotion of Science andGrants-in-Aid for H-24 from the Japan Society for the Promotion ofInterdisciplinary Research and Development.
Data availability The data are available from the corresponding author
upon reasonable request.

Declarations
Conflict of interest Daiki Ouchi, Shohei Mori, Mototaka Arakawa,
Tomohiko Shindo, Hiroaki Shimokawa, Satoshi Yasuda, and Hiroshi
Kanai declare no conflicts of interest.
Ethical approval None.

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