A RELATIONSHIP OF COMPONENTS IN THE OPTIMAL ARRANGEMENT PROBLEMS FOR THE MULTI-STATE CONSECUTIVE-k-OUT-OF-n:F SYSTEM IN CASE OF max{kj}=2

In a multi-state consecutive-k-out-of-n:F system, both the components and the system are allowed to be M+1 possible states for o,1,...,M. State M represents the perfectly working state, 0 represents the completely failed state, and the others represent the degraded states. k is an M-dimensional vector as a parameter k_j (j=1,2,...,M) which decides the system states. A multi-state system reliability model provides more flexibility for the modeling of equipment conditions. One of the most important problems in the multi-state consecutive-k-out-of-n:F system is the optimal arrangement problem. The optimal arrangement problem is defined to obtain the arrangement as minimizing the system state probabilities for any j. The previous researches have been studied the characteristic of optimal arrangements. Malon showed that the characteristic of invariable optimal arrangements depended on the magnitude relation of the failure probability of each component in a binary-state consecutive-k-out-of-n:F system. However, in the multi-state consecutive-k-out-of-n:F system, previous studies have shown that the optimal arrangement cannot be specified only by the magnitude relation of failure probability of each component. In this study, we discuss a layout of the optimal arrangement for a multi-state consecutive-k-out-of-n:F system by the distribution of a system state probabilities when max{k_j}=2. The purpose of this paper is to investigate the hypothesis of optimal arrangement in a multi-state consecutive-k-out-of-n:F system as similar layout of Malon's proved characteristic optimal arrangement of the binary-state consecutive-k-out-of-n:F system

A Low-Level Carbon Dioxide Laser Promotes Fibroblast Proliferation and Migration through Activation of Akt, ERK, and JNK.

Low-level laser therapy (LLLT) with various types of lasers promotes fibroblast proliferation and migration during the process of wound healing. Although LLLT with a carbon dioxide (CO2) laser was also reported to promote wound healing, the underlying mechanisms at the cellular level have not been previously described. Herein, we investigated the effect of LLLT with a CO2 laser on fibroblast proliferation and migration.Cultured human dermal fibroblasts were prepared. MTS and cell migration assays were performed with fibroblasts after LLLT with a CO2 laser at various doses (0.1, 0.5, 1.0, 2.0, or 5.0 J/cm2) to observe the effects of LLLT with a CO2 laser on the proliferation and migration of fibroblasts. The non-irradiated group served as the control. Moreover, western blot analysis was performed using fibroblasts after LLLT with a CO2 laser to analyze changes in the activities of Akt, extracellular signal-regulated kinase (ERK), and Jun N-terminal kinase (JNK), which are signaling molecules associated with cell proliferation and migration. Finally, the MTS assay, a cell migration assay, and western blot analysis were performed using fibroblasts treated with inhibitors of Akt, ERK, or JNK before LLLT with a CO2 laser.In MTS and cell migration assays, fibroblast proliferation and migration were promoted after LLLT with a CO2 laser at 1.0 J/cm2. Western blot analysis revealed that Akt, ERK, and JNK activities were promoted in fibroblasts after LLLT with a CO2 laser at 1.0 J/cm2. Moreover, inhibition of Akt, ERK, or JNK significantly blocked fibroblast proliferation and migration.These findings suggested that LLLT with a CO2 laser would accelerate wound healing by promoting the proliferation and migration of fibroblasts. Activation of Akt, ERK, and JNK was essential for CO2 laser-induced proliferation and migration of fibroblasts

Effect of inhibition of Akt, ERK, or JNK on LLLT-induced HDF migration.

<p>(A) Cell migration assay of HDFs with or without LLLT irradiation (1.0 J/cm²) in the presence or absence of the inhibitor of Akt. The migration rate is expressed as migration distance/time (μm/h). (B) Cell migration assay of HDFs with or without LLLT irradiation (1.0 J/cm²) in the presence or absence of the inhibitor of ERK. (C) Cell migration assay of HDFs with or without LLLT irradiation (1.0 J/cm²) in the presence or absence of the inhibitor of JNK. Results are expressed as the mean ± SD of three independent experiments. *p<0.05, **p<0.01, ****p<0.0001 (Tukey-Kramer test).</p

Effect of inhibition of Akt, ERK, or JNK on LLLT-induced activation of signaling molecules in HDFs.

<p>(A) Akt activity in HDFs treated with or without the inhibitor of Akt was analyzed by immunoblotting at 15 min after LLLT (1.0 J/cm²). Densitometric measurement of p-Akt was normalized to the amount of total Akt. (B) ERK activity in HDFs treated with or without the inhibitor of ERK was analyzed by immunoblotting at 15 min after LLLT (1.0 J/cm²). Densitometric measurement of p-ERK was normalized to the amount of total ERK. (C) JNK activity in HDFs treated with or without the inhibitor of JNK was analyzed by immunoblotting at 15 min after LLLT (1.0 J/cm²). Densitometric measurement of p-JNK was normalized to the amount of total JNK. The results are presented as fold change compared with the non-inhibited group. Results are expressed as the mean ± SD of three independent experiments. ***p<0.001, ****p<0.0001 (Tukey-Kramer test).</p

Effects of LLLT with a CO₂ laser on HDF proliferation.

<p>HDF proliferation was determined by the MTS assay after irradiation with LLLT (0.1, 0.5, 1.0, 2.0, or 5.0 J/cm²). The non-irradiated group served as the control. Results are expressed as the mean ± SD of three independent experiments. **p<0.01, ***p<0.001 compared with the non-irradiated group (Tukey-Kramer test).</p

Effect of inhibition of Akt, ERK, or JNK on LLLT-induced HDF proliferation.

<p>(A) HDF proliferation was measured by the MTS assay after pretreatment with the inhibitor of Akt and subsequent LLLT irradiation (1.0 J/cm²). (B) HDF proliferation assay after pretreatment with the inhibitor of ERK and subsequent LLLT irradiation (1.0 J/cm²). (C) HDF proliferation assay after pretreatment with the inhibitor of JNK and subsequent LLLT irradiation (1.0 J/cm²). Results are expressed as the mean ± SD of three independent experiments. *p<0.05, **p<0.01, ***p<0.001, ****p<0.0001 (Tukey-Kramer test).</p

Effects of LLLT with a CO₂ laser on HDF migration.

<p>A cell migration assay of HDFs treated with LLLT under several irradiation powers (0.1, 0.5, 1.0, 2.0, or 5.0 J/cm²). The non-irradiated group served as the control. (A) Migration rates (0.1, 0.5, 1.0, 2.0, or 5.0 J/cm²) are expressed as migration distance/time (μm/h). The non-irradiated group served as the control. Results are expressed as the mean ± SD of three independent experiments. *p<0.05, ***p<0.001 compared with the non-irradiated group (Tukey-Kramer test). (B) Images show the wounded cell monolayers at 0, 12, and 24 h after wounding with non-irradiated or irradiated (1.0 J/cm²) HDFs. The line indicates the wound edge at the start of the experiment (0 h). Bar = 300 nm. The migration of irradiated HDFs was promoted compared with the control.</p