In this paper, we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schrödinger equation
{
−
Δ
u
+
V
(
x
)
u
=
μ
q
u
+
a
|
u
|
q
u
in
ℝ
2
,
∫
ℝ
2
|
u
|
...2
d
x
=
1
,
where
μ
q
is the Lagrange multiplier. We show that for
q
> 2 close to 2, the problem admits two solutions: one is the local minimal solution
u
q
and the other one is the mountain pass solution
υ
q
. Furthermore, we study the limiting behavior of
u
q
and
υ
q
when
q
→ 2
+
. Particularly, we describe precisely the blow-up formation of the excited state
υ
q
.
Objective: the purpose of this study was to demonstrate the potential of thermoacoustic tomography (TAT) to reveal anatomic structures of in vivo human finger joints. Methods: all the participating ...volunteers provided written informed consent. Eight healthy middle and index fingers from five volunteers were imaged in vivo by our TAT imaging system. Axial T1-weighted MR imaging (3.0 T) was used to validate the TAT findings. Comparative analyses between TAT and MRI images were performed in two dimension for all the fingers imaged. Three-dimensional (3-D) images and animations were also obtained for some of the fingers thermoacoustically scanned. Results: various intra- and extra-articular tissues were identified in TAT images in high fidelity. These TAT images matched well with the MRI images. Both the 3-D images and animations effectively displayed the extension and transformation of the entire finger along the axis. Conclusion: TAT can noninvasively visualize anatomic structures of the finger joints based on the electrical properties of the joint tissues. The results obtained indicate that TAT may have the potential to contribute to the detection of joint and bone diseases. Significance: this study represents the first for TAT of in vivo human joints and fingers. This study reveals that TAT can effectively recover both soft and hard tissues of the healthy interphalangeal joints, which provides a foundation for its clinical application to detection and diagnosis of joint and bone diseases.
Photoacoustic computed tomography (PACT) has become a promising imaging modality from laboratory to clinical research. Of many components of PACT system, the ultrasound (US) array transducer is an ...essential device to simultaneously receive photoacoustic (PA) signals from several directions in a parallel manner. Many research groups and companies have developed various types of US array transducers while accounting the properties of the PA waves to achieve better image quality, deeper imaging depth, faster imaging speed, and a wider field of view. In this review, we present the implementation and application of the state-of-the-art PACT systems using several types of curved US arrays: arc-shaped, ring-shaped, and hemispherical array transducers. Furthermore, we discuss the current limitations of PACT and also potential future directions for enhancing them.
In this paper, we are concerned with the uniqueness of multi-bump solutions for the following Schrödinger–Poisson system
0.1
-
ε
2
Δ
u
+
Q
(
x
)
u
+
Ψ
(
x
)
u
=
|
u
|
p
-
1
u
,
in
R
N
,
-
Δ
Ψ
=
(
N
-
...2
)
ω
N
-
1
u
2
,
in
R
N
,
where
ε
is a parameter,
Q
(
x
) is a potential function in
R
N
,
N
∈
3
,
6
,
p
∈
(
1
,
N
+
2
N
-
2
)
and
ω
N
-
1
is the surface area of a unit ball in
R
N
. We prove the uniqueness of positive multi-bump solutions for Schrödinger–Poisson system concentrating at the critical points of
Q
(
x
), whenever
Q
(
x
) is degenerate or non-degenerate, or even not
C
2
.
Photoacoustic computed tomography (PACT) has become a premier preclinical and clinical imaging modality. Although PACT's image quality can be dramatically improved with a large number of ultrasound ...(US) transducer elements and associated multiplexed data acquisition systems, the associated high system cost and/or slow temporal resolution are significant problems. Here, a deep learning‐based approach is demonstrated that qualitatively and quantitively diminishes the limited‐view artifacts that reduce image quality and improves the slow temporal resolution. This deep learning‐enhanced multiparametric dynamic volumetric PACT approach, called DL‐PACT, requires only a clustered subset of many US transducer elements on the conventional multiparametric PACT. Using DL‐PACT, high‐quality static structural and dynamic contrast‐enhanced whole‐body images as well as dynamic functional brain images of live animals and humans are successfully acquired, all in a relatively fast and cost‐effective manner. It is believed that the strategy can significantly advance the use of PACT technology for preclinical and clinical applications such as neurology, cardiology, pharmacology, endocrinology, and oncology.
The deep learning‐enhanced multiparametric dynamic volumetric PACT approach (DL‐PACT) improves the slow temporal resolution and at the same time qualitatively and quantitively diminishes the limited‐view artifacts that degrade image quality. DL‐PACT successfully performs high‐quality static structural and dynamic contrast‐enhanced whole‐body images as well as dynamic functional images of live animals and humans, all in a relatively fast and cost‐effective manner.
Liver function reserve (LFR) is the sum of remnant functional hepatic cells after liver injury. In the pathologic process of liver fibrosis (LF), LFR is impaired. LFR assessment can help determine ...the safe scope of liver resection or drug regimen and predict prognosis of patients with liver disease. Here, we used a photoacoustic imaging (PAI) system to assess LF and LFR in rabbit models. We performed PAI, ultrasound elastography and biopsy for 21 rabbits developing none (n = 6) and LF (n = 15). In vivo indocyanine green (ICG) measurements by PAI showed that LF group presented a significantly attenuated ICG clearance compared to control group, indicating LFR impairment of LF. Another finding was a significantly higher collagen photoacoustic signal intensity value was observed in LF both in vivo and in vitro. Our findings demonstrated that PAI was potentially effective to evaluate LFR and collagen accumulation of LF.
This paper deals with a semilinear parabolic equation with variable source under the case that the initial energy is less than the potential well depth. We deduce a sharp threshold for blow-up and ...global existence of solutions. Furthermore, we conclude that the global solution decays as the time goes to infinity.
Liver function reserve (LFR) plays an extensive and important role in patients with liver disease. Indocyanine green (ICG) clearance test is the standard diagnostic approach for LFR evaluation which ...was performed by spectrophotometry or pulse dye densitometry (PDD). Spectrophotometry is the gold standard, it's invasive and not real-time. PDD is non-invasive, but accuracy of PDD is controversial. Taken spectrophotometry as the reference standard, this study investigated the accuracy of photoacoustic imaging (PAI) method for LFR assessment and compared to PDD in healthy volunteers. The results demonstrated a strong correlation between PAI method and spectrophotometry (r = 0.9649, p < 0.0001). No significant difference was shown in ICG clearance between PAI and spectrophotometry method (rate constant k1 vs. k2, 0.001158 +−0.00042 vs. 0.001491 +- 0.00045, p = 0.0727; half-life t1 vs. t2, 601.2 s vs. 474.4 s, p = 0.1450). These results indicated that PAI may be valuable as a noninvasive, accurate diagnostic tool for LFR assessment in human.
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