• Title/Summary/Keyword: proportional distribution

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Principles of Stone Elevation Formation for Walls and Wells in the Silla Dynasty from 5th to 7th Centuries (5~7세기 신라시대 성곽과 우물에 대한 석축입면조형원리)

  • Kang, Seong-Bin;Seo, Seong-Hyeok;Jung, Tae-Yeol
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.41 no.1
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    • pp.47-55
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    • 2023
  • In this study, the following conclusions were drawn by analyzing the size, proportion, shape, angle, distribution, etc. of stones in order to identify the principles of facade molding of stonework of the 5th to 7th centuries of the Silla Dynasty. First, the uniformity of the size of the stones of the stone foundations of the Silla Dynasty was low at -0.8 to 4.1. This means that stones of various sizes were used, from small stones to large stones. In addition, the distribution of large stones in stonework of the Silla Dynasty appeared evenly regardless of height. This was common in the stonework of the Silla Dynasty, regardless of structural classification such as wells and mountain fortresses. It is thought that the Silla people did not only pursue practicality and efficiency in stone construction, but also considered design elements. Second, the proportional deviation of the stones of the stone walls of the Silla Dynasty was high, ranging from 0.861 to 1.515. This means that the stonework of the Silla Dynasty did not use only long flagstone-shaped stones, but used a mixture of long and short stones. Third, the shape average of the stones of the stonework of the Silla Dynasty was low at 0.45, and the shape deviation was high at the maximum of 0.15. This means that the stones as a whole have irregular shapes, and each stone has a high difference in shape. Fourth, the angle deviation of the stones of the Silla Dynasty was 4.3 to 16.2, and the average angle was 2. This means that the angle of each stone on the stone axis of the Silla Dynasty is tilted to the left and right. Fifth, there was no correlation between stone size, slenderness ratio, shape, and angle in the stone axes of the Silla Dynasty. In the case of stone axes in the Joseon Dynasty, there was a positive correlation between stone size and slenderness, and a negative correlation between stone size and shape. It can be said that the stones of the Joseon Dynasty were relatively standardized, but the Silla Dynasty showed the beauty of moderation by keeping the nature of the material and becoming one with the material.

Surgery Alone or Postoperative Adjuvant Radiotherapy in Rectal Cancer - With Respect to Survival, Pelvic Control, Prognostic Factor - (직장암에서 수술단독 또는 수술후 방사선치료 -생존율, 골반종양제어율, 예후인자를 중심으로-)

  • Nam, Taek-Keun;Ahn, Sung-Ja;Nah, Byung-Sik
    • Radiation Oncology Journal
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    • v.19 no.4
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    • pp.327-334
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    • 2001
  • Purpose : To find out the role of postoperative adjuvant radiotherapy in the treatment of rectal cancer by comparing survival, pelvic control, complication rate, and any prognostic factor between surgery alone and postoperative radiotherapy group. Materials and methods : From Feb. 1982 to Dec. 1996 total 212 patients were treated by radical surgery with or without postoperative radiotherapy due to rectal carcinoma of modified Astler-Coiler stage $B2\~C3$. Of them, 18 patients had incomplete radiotherapy and so the remaining 194 patients were the database analyzed in this study. One hundred four patients received postoperative radiotherapy and the other 90 patients had surgery only. Radiotherapy was peformed in the range of $39.6\~55.8\;Gy$ (mean: 49.9 Gy) to the whole pelvis and if necessary, tumor bed was boosted by $5.4\~10\;Gy$. Both survival and pelvic control rates were calculated by Kaplan-Meier method and their statistical significance was tested by Log-rank test. Multivariate analysis was peformed by Cox proportional hazards model. Results : 5-year actuarial survival rate (5YSR) and 5-year disease-free survival rate (5YDFSR) of entire patients were $53\%\;and\;49\%$, respectively. 5YSRs of surgery alone group and adjuvant radiotherapy group were $63\%\;vs\;45\%$, respectively (p=0.03). This difference is thought to reflect uneven distribution of stages between two treatment groups (p<0.05 by $\chi^2-test$) with more advanced disease patients in adjuvant radiotherapy group. 5YSRs of surgery alone vs adjuvant radiotherapy group in MAC B2+3, C1, C2+3 were $68\%\;vs\;55\%$ (p=0.09), $100\%\;vs\;100\%$, $40\%\;vs\;33\%$ (p=0.71), respectively. 5YDFSRs of surgery alone vs adjuvant radiotherapy group in above three stages were $65\%\;vs\;49\%$ (p=0.14), $100\%\;vs\;100\%$, $33\%\;vs\;31\%$ (p=0.46), respectively. 5-year pelvic control rate (5YPCR) of entire patients was $72.5\%$. 5YPCRs of surgery alone and adjuvant radiotherapy group were $71\%\;vs\;74\%$, respectively (p=0.41). 5YPCRs of surgery alone vs adjuvant radiotherapy group in B2+3, C1, C2+3 were $79\%\;vs\;75\%$ (p=0.88), $100\%\;vs\;100\%$, $44\%\;vs\;68\%$ (p=0.01), respectively. Multivariate analysis showed that only stage was significant factor affecting overall and disease-free survival in entire patients and also in both treatment groups. In view of pelvic control, stage and operation type were significant in entire patients and only stage in surgery alone group but in adjuvant radiotherapy group, operation type instead of stage was the only significant factor in multivariate analysis as a negative prognostic factor in abdominoperineal resection cases. Conclusion : Our retrospective study showed that postoperative adjuvant radiotherapy could improve the pelvic control in MAC C2+3 group. To improve both pelvic control and survival in all patients with MAC B2 or more, other treatment modality such as concurrent continuous infusion of 5-FU, which is the most standard agent, with radiotherapy should be considered.

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Community Characteristics and Biological Quality Assessment on Benthic Macroinvertebrates of Bongseonsa Stream in Gwangneung Forest, South Korea (광릉숲 내 봉선사천의 저서성 대형무척추동물의 군집 특성 및 생물학적 하천평가)

  • Jung, Sang-Woo;Cho, Yong-Chan;Lee, Hwang-Goo
    • Korean Journal of Environment and Ecology
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    • v.31 no.6
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    • pp.508-519
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    • 2017
  • There have been many studies on monitoring of biodiversity changes and preservation of Gwangneung Forest Biosphere Reserve (GFBR) in South Korea in recognition of the rare ecosystem that has been preserved for a long period. However, there are few studies on diversity and community characteristics of benthic macroinvertebrates as an indicator of stream health of GFBR. The purpose of this study was to assess the water quality of Bongseonsa Stream that penetrated through Gwangneung Forest and the nearby torrents by analyzing the benthic macroinvertebrates community during April to September 2016. The investigation collected a total of 114 species of benthic macroinvertebrates belonging to 56 families, 17 orders, 8 classes, and 5 phyla from the Bongseonsa Stream and Kwangneung Stream. Ephemeroptera and Trichoptera were the largest groups in species diversity with 30 species (32.3%) and 16 species (17.2%), respectively, and Tubificidae sp., Baetis fuscatus, Antocha KUa, and Cheumatopsyche brevilineata, which usually habit in contaminated streams, appeared frequently. Among the feeding function groups, the gatherers and hunters appeared relatively frequently, and the shredders and scrapers appeared frequently in the torrents. Among the habitat oriented groups, the clingers and burrower appeared more frequently and represented the microhabitats in the shallow areas. The result of the analysis of benthic macroinvertebrates community showed that the dominant index was $0.48{\pm}0.10$ in average while it was lowest with 0.33 in GS 8 of the Gwangneung Forest torrent and highest in BS 1 of Bongseonsa Stream. The diversity and richness indices were inversely proportional to the dominant index and were 2.53 and 4.22, respectively, in GS 8 where the dominant index was low. The result of the analysis of community stability showed that area I, which had high resistance and restoration, was high in Bongseonsa Stream while the area III, which had low resistance and restoration, was high in Gwangneung Forest, indicating that the water system in Gwangneung Forest had a wider distribution of specifies sensitive to agitation. The biological water quality assessment showed ESB of $50.88{\pm}17.69$, KSI of $1.11{\pm}0.57$, and BMI of $78.55{\pm}11.05$. GS 8 of Gwangneung Forest torrent was judged to be the highest priority protective water area with the best water environment and I class water quality with ESB of 63, KSI of 0.55, and BMI of 89.9. On the contrary, BS 1 of Bongseonsa Stream was judged to be the high priority improvement area that had the lowest water quality rating of III with ESB of 25, KSI of 2.13, and BMI of 62.7. Although the diversity of water beetle was higher in the water system of nearby Bongseonsa Stream than the water system inside the Gwangneung Forest, the annual community structure appeared to have distinct differences.

Development and Performance Evaluation of an Animal SPECT System Using Philips ARGUS Gamma Camera and Pinhole Collimator (Philips ARGUS 감마카메라와 바늘구멍조준기를 이용한 소동물 SPECT 시스템의 개발 및 성능 평가)

  • Kim, Joong-Hyun;Lee, Jae-Sung;Kim, Jin-Su;Lee, Byeong-Il;Kim, Soo-Mee;Choung, In-Soon;Kim, Yu-Kyeong;Lee, Won-Woo;Kim, Sang-Eun;Chung, June-Key;Lee, Myung-Chul;Lee, Dong-Soo
    • The Korean Journal of Nuclear Medicine
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    • v.39 no.6
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    • pp.445-455
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    • 2005
  • Purpose: We developed an animal SPECT system using clinical Philips ARGUS scintillation camera and pinhole collimator with specially manufactured small apertures. In this study, we evaluated the physical characteristics of this system and biological feasibility for animal experiments. Materials and Methods: Rotating station for small animals using a step motor and operating software were developed. Pinhole inserts with small apertures (diameter of 0.5, 1.0, and 2.0 mm) were manufactured and physical parameters including planar spatial resolution and sensitivity and reconstructed resolution were measured for some apertures. In order to measure the size of the usable field of view according to the distance from the focal point, manufactured multiple line sources separated with the same distance were scanned and numbers of lines within the field of view were counted. Using a Tc-99m line source with 0.5 mm diameter and 12 mm length placed in the exact center of field of view, planar spatial resolution according to the distance was measured. Calibration factor to obtain FWHM values in 'mm' unit was calculated from the planar image of two separated line sources. Te-99m point source with i mm diameter was used for the measurement of system sensitivity. In addition, SPECT data of micro phantom with cold and hot line inserts and rat brain after intravenous injection of [I-123]FP-CIT were acquired and reconstructed using filtered back protection reconstruction algorithm for pinhole collimator. Results: Size of usable field of view was proportional to the distance from the focal point and their relationship could be fitted into a linear equation (y=1.4x+0.5, x: distance). System sensitivity and planar spatial resolution at 3 cm measured using 1.0 mm aperture was 71 cps/MBq and 1.24 mm, respectively. In the SPECT image of rat brain with [I-123]FP-CIT acquired using 1.0 mm aperture, the distribution of dopamine transporter in the striatum was well identified in each hemisphere. Conclusion: We verified that this new animal SPECT system with the Phlilps ARGUS scanner and small apertures had sufficient performance for small animal imaging.

A Study on the Mechanical and Physical Properties of Sawdustboard combined with Plastic Chip (플라스틱칩 결체(結締) 톱밥보드의 기계적(機械的) 및 물리적(物理的) 성질(性質)에 관(關)한 연구(硏究))

  • Lee, Phil-Woo;Suh, Jin-Suk
    • Journal of the Korean Wood Science and Technology
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    • v.15 no.3
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    • pp.44-55
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    • 1987
  • In order to study the effect of sawdustboard combined with plastic chips, 0.5mm($T_1$), 1mm($T_2$), 1.4mm($T_3$) thick nylon fiber. polypropylene rope fiber(RP), and 0.23mm thick moth-proof polypropylene net fiber(NP) were cut into 0.5, 1, 2cm long plastic chips. Thereafter, sawdustboard combined with plastic chips prepared as the above and plastic non-combined sawdustboard(control) were manufactured into 3 types of one-, two-, and three layer with 5 or 10% combination level. By the discussions and results at this study, the significant conclusions of mechanical and physical properties were summarized as follows: 1. The MORs were shown in the order of 3 layer> 2 layer> 1 layer among plastic non-combined boards, and $T_3$ < $T_2$ < $T_1$ < RP (NP(5%) < NP(l0%) among plastic combined boards. In 2cm long plastic chip in 1 layer board, the highest strength through all the composition was recognized. 1 layer board showing the lower strength with 0.5cm plastic chip rendered to the bending strength improvement by 2 or 3 layer board composition. On the other hand, 2 or 3 layer combined with 1, 2cm long polypropylene net fiber chips incurred MOR's conspicuous decrease requiring optimum plastic chip combined level and consideration to combined type. 2. MOE in plastic non-combined 3 layer board exhibited sandwich construction effect by higher resin content application to surface layer in the order of 3layer>1layer>2layer with the highest stiffness of the board combined with polypropylene chip, while nylon chip-combined board had little difference from plastic non-combined board. In relevant to length and layer effect, 3 layer board combined with the 0.5cm long polypropylene net fiber chip in 5% and 10% combined level presented 34-43% and 44-76% stiffness increase against plastic non-combined board(control), respectively. Moreover, in 1 layer board, 30% stiffness increase with 10% against 5% combined level in the 1 and 2cm long polypropylene net fiber chip was obtained. 3. Stress at proportional limit(Spl) showing the fiber relationship (r: 0.81-0.97) between MOR presented in the order of 1 layer<2 layer<3 layer in plastic non-combined board. Correspondingly, combined effect by layer and plastic chip length was similar to MOR's. 4. Differently from previous properties(MOR, MOE, Spl). work to maximum load(Wml) of 2 layer board approached to that of 3 layer board. Conforming the above phenomenon. 2 layer combined with 0.5cm long polypropylene net fiber chip kept the greater work than 1 layer. The polypropylene combined board superior to nylon -and plastic non - combined board seemed to have greater anti - failing capacity. 5. Internal bond strength(IB), in contrast to MOR's tendency. showed in the order of T1

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An Analysis on the Episodes of Large-scale Transport of Natural Airborne Particles and Anthropogenically Affected Particles from Different Sources in the East Asian Continent in 2008 (2008년 동아시아 대륙으로부터 기원이 다른 먼지와 인위적 오염 입자의 광역적 이동 사례에 대한 분석)

  • Kim, Hak-Sung;Yoon, Ma-Byong;Sohn, Jung-Joo
    • Journal of the Korean earth science society
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    • v.31 no.6
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    • pp.600-607
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    • 2010
  • In 2008, multiple episodes of large-scale transport of natural airborne particles and anthropogenically affected particles from different sources in the East Asian continent were identified in the National Oceanic and Atmospheric Administration (NOAA) satellite RGB-composite images and the mass concentrations of ground level particulate matters. To analyze the aerosol size distribution during the large-scale transport of atmospheric aerosols, both aerosol optical depth (AOD; proportional to the aerosol total loading in the vertical column) and fine aerosol weighting (FW; fractional contribution of fine aerosol to the total AOD) of Moderate resolution Imaging Spectroradiometer (MODIS) aerosol products were used over the East Asian region. The six episodes of massive natural airborne particles were observed at Cheongwon, originating from sandstorms in northern China, Mongolia and the loess plateau of China. The $PM_{10}$ and $PM_{2.5}$ stood at 70% and 16% of the total mass concentration of TSP, respectively. However, the mass concentration of $PM_{2.5}$ among TSP increased as high as 23% in the episode in which they were flowing in by way f the industrial area in east China. In the other five episodes of anthropogenically affected particles that flowed into the Korean Peninsula from east China, the mass concentrations of $PM_{10}$ and $PM_{2.5}$ among TSP reached 82% and 65%, respectively. The average AOD for the large-scale transport of anthropogenically affected particle episodes in the East Asian region was measured at $0.42{\pm}0.17$ compared with AOD ($0.36{\pm}0.13$) for the natural airborne particle episodes. Particularly, the regions covering east China, the Yellow Sea, the Korean Peninsula, and the east Korean sea were characterized by high levels of AOD. The average FW values observed during the event of anthropogenically affected aerosols ($0.63{\pm}0.16$) were moderately higher than those of natural airborne particles ($0.52{\pm}0.13$). This observation suggests that anthropogenically affected particles contribute greatly to the atmospheric aerosols in East Asia.

Manufacturing Location and Linkages in the Suburb of Metropolitan Pusan (부산시 근교의 공업입지와 지역적 연계)

  • Lim, Yeong-Dae
    • Journal of the Korean association of regional geographers
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    • v.6 no.1
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    • pp.1-28
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    • 2000
  • The purpose of this study is to clarify the suburbanization of manufacturing, and location and linkages of decentralized manufacturing from Metropolitan Pusan by means of case study on manufacturing location and linkages in the suburb of Metropolitan Pusan. Kimhae city and Yangsan-Gun toward which heavy decentralization of manufacturing from the Metropolitan Pusan has been done. Both hard data and soft data were used as the basic data. Hard data are the statistical data in statistical yearbooks and firm list in directories. The former consists of the number of establishments and employees classified by product type, firm size and unit area. The latter consists of owner's names, addresses, employee number, products and headquarters of firms. Soft data are the results of the interviews with the 242 owners of firms in the four case study areas selected by Proportional Stratified Sampling Method. The major findings are as follows: 1. The spatial variations of manufacturing in the suburb was regularized in the latter half of 1970's. The primary processes to decentralize manufacturing from Metropolitan Pusan were the birth, relocation and establishment of branches of the firms. Among them the relocation of small outer-oriented single-location firms from Pusan was the most important. 2. The spatial variations undergoing spatial expansion of manufacturing distribution and increase of agglomeration degree of manufacturing, proceeded from the adjacents of Metropolitan Pusan to the outer areas along the main transportation route. 3. The main factors which caused manufacturing to decentralize from the Metropolitan Pusan were firm policy and land for this policy. The main locational factors which induced the decentralizing manufacturing into the suburb were land, market and transportation. 4. The strength of linkages with the outside of the study area is stronger than that of linkages with the inside. There is distance-decay-function in the strength of linkages with the outside, and linkages with short distant areas are stronger than those with long distant areas. 5. The ranges of spatial linkages in procurement of materials, in subcontraction and in marketing are wider than those in ordering. 6. The main factors which cause the formation of linkages are different by types of linkages: monopolistic and oligopolistic supply are important in procurement linkages; characteristics of products and the subsequent marketing difficulties, in subcontraction linkages; fluctuation, cost reduction, insufficient facility and characteristics of products, in ordering linkages; subcontract, characteristics of product and the subsequent marketing difficulties, in marketing linkages. 7. The changes of linkages owing to locational changes of firms were great, and were greater in long distant areas than in short distant areas. 8. The main factor influencing on the changes of linkages was the easiness in the transportation of goods, movement of labour and contacts with customers. In conclusion, some facts described above were proved to be consistent with the results of proceeding studies in the other areas: influence of relocation of decentralizing firms on the suburbanization; the factors of manufacturing decentralization; spatial characteristics of linkages; linkage changes owing to relocation of firms. Some were proved to be partly consistent: locational factors inducing decentralized manufacturing into the suburb were proved to be inconsistent. I think that the results of previous studies on the other areas can be applicable to the explanation on the decentralization of Metropolitan manufacturing from the viewpoint of the suburb. For the better explanation on the decentralization of Metropolitan manufacturing, more empirical case studies on the suburbanization of manufacturing are necessary.

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Preliminary Study on the MR Temperature Mapping using Center Array-Sequencing Phase Unwrapping Algorithm (Center Array-Sequencing 위상펼침 기법의 MR 온도영상 적용에 관한 기초연구)

  • Tan, Kee Chin;Kim, Tae-Hyung;Chun, Song-I;Han, Yong-Hee;Choi, Ki-Seung;Lee, Kwang-Sig;Jun, Jae-Ryang;Eun, Choong-Ki;Mun, Chi-Woong
    • Investigative Magnetic Resonance Imaging
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    • v.12 no.2
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    • pp.131-141
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    • 2008
  • Purpose : To investigate the feasibility and accuracy of Proton Resonance Frequency (PRF) shift based magnetic resonance (MR) temperature mapping utilizing the self-developed center array-sequencing phase unwrapping (PU) method for non-invasive temperature monitoring. Materials and Methods : The computer simulation was done on the PU algorithm for performance evaluation before further application to MR thermometry. The MR experiments were conducted in two approaches namely PU experiment, and temperature mapping experiment based on the PU technique with all the image postprocessing implemented in MATLAB. A 1.5T MR scanner employing a knee coil with $T2^*$ GRE (Gradient Recalled Echo) pulse sequence were used throughout the experiments. Various subjects such as water phantom, orange, and agarose gel phantom were used for the assessment of the self-developed PU algorithm. The MR temperature mapping experiment was initially attempted on the agarose gel phantom only with the application of a custom-made thermoregulating water pump as the heating source. Heat was generated to the phantom via hot water circulation whilst temperature variation was observed with T-type thermocouple. The PU program was implemented on the reconstructed wrapped phase images prior to map the temperature distribution of subjects. As the temperature change is directly proportional to the phase difference map, the absolute temperature could be estimated from the summation of the computed temperature difference with the measured ambient temperature of subjects. Results : The PU technique successfully recovered and removed the phase wrapping artifacts on MR phase images with various subjects by producing a smooth and continuous phase map thus producing a more reliable temperature map. Conclusion : This work presented a rapid, and robust self-developed center array-sequencing PU algorithm feasible for the application of MR temperature mapping according to the PRF phase shift property.

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Prediction of Seabed Topography Change Due to Construction of Offshore Wind Power Structures in the West-Southern Sea of Korea (서남해에서 해상풍력구조물의 건설에 의한 해저지형의 변화예측)

  • Jeong, Seung Myung;Kwon, Kyung Hwan;Lee, Jong Sup;Park, Il Heum
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.31 no.6
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    • pp.423-433
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    • 2019
  • In order to predict the seabed topography change due to the construction of offshore wind power structures in the west-southern sea of Korea, field observations for tides, tidal currents, suspended sediment concentrations and seabed sediments were carried out at the same time. These data could be used for numerical simulation. In numerical experiments, the empirical constants for the suspended sediment flux were determined by the trial and error method. When a concentration distribution factor was 0.1 and a proportional constant was 0.05 in the suspended sediment equilibrium concentration formulae, the calculated suspended sediment concentrations were reasonably similar with the observed ones. Also, it was appropriate for the open boundary conditions of the suspended sediment when the south-east boundary corner was 11.0 times, the south-west was 0.5 times, the westnorth 1.0 times, the north-west was 1.0 times and the north-east was 1.0 times, respectively, using the time series of the observed suspended sediment concentrations. In this case, the depth change was smooth and not intermittent around the open boundaries. From these calibrations, the annual water depth change before and after construction of the offshore wind power structures was shown under 1 cm. The reason was that the used numerical model for the large scale grid could not reproduce a local scour phenomenon and they showed almost no significant velocity change over ± 2 cm/s because the jacket structures with small size diameter, about 1 m, were a water-permeable. Therefore, it was natural that there was a slight change on seabed topography in the study area.

Quantitative Conductivity Estimation Error due to Statistical Noise in Complex $B_1{^+}$ Map (정량적 도전율측정의 오차와 $B_1{^+}$ map의 노이즈에 관한 분석)

  • Shin, Jaewook;Lee, Joonsung;Kim, Min-Oh;Choi, Narae;Seo, Jin Keun;Kim, Dong-Hyun
    • Investigative Magnetic Resonance Imaging
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    • v.18 no.4
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    • pp.303-313
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    • 2014
  • Purpose : In-vivo conductivity reconstruction using transmit field ($B_1{^+}$) information of MRI was proposed. We assessed the accuracy of conductivity reconstruction in the presence of statistical noise in complex $B_1{^+}$ map and provided a parametric model of the conductivity-to-noise ratio value. Materials and Methods: The $B_1{^+}$ distribution was simulated for a cylindrical phantom model. By adding complex Gaussian noise to the simulated $B_1{^+}$ map, quantitative conductivity estimation error was evaluated. The quantitative evaluation process was repeated over several different parameters such as Larmor frequency, object radius and SNR of $B_1{^+}$ map. A parametric model for the conductivity-to-noise ratio was developed according to these various parameters. Results: According to the simulation results, conductivity estimation is more sensitive to statistical noise in $B_1{^+}$ phase than to noise in $B_1{^+}$ magnitude. The conductivity estimate of the object of interest does not depend on the external object surrounding it. The conductivity-to-noise ratio is proportional to the signal-to-noise ratio of the $B_1{^+}$ map, Larmor frequency, the conductivity value itself and the number of averaged pixels. To estimate accurate conductivity value of the targeted tissue, SNR of $B_1{^+}$ map and adequate filtering size have to be taken into account for conductivity reconstruction process. In addition, the simulation result was verified at 3T conventional MRI scanner. Conclusion: Through all these relationships, quantitative conductivity estimation error due to statistical noise in $B_1{^+}$ map is modeled. By using this model, further issues regarding filtering and reconstruction algorithms can be investigated for MREPT.