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Effect of a Deep Learning Framework-Based Computer-Aided Diagnosis System on the Diagnostic Performance of Radiologists in Differentiating between Malignant and Benign Masses on Breast Ultrasonography

  • Ji Soo Choi;Boo-Kyung Han;Eun Sook Ko;Jung Min Bae;Eun Young Ko;So Hee Song;Mi-ri Kwon;Jung Hee Shin;Soo Yeon Hahn
    • Korean Journal of Radiology
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    • 제20권5호
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    • pp.749-758
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    • 2019
  • Objective: To investigate whether a computer-aided diagnosis (CAD) system based on a deep learning framework (deep learning-based CAD) improves the diagnostic performance of radiologists in differentiating between malignant and benign masses on breast ultrasound (US). Materials and Methods: B-mode US images were prospectively obtained for 253 breast masses (173 benign, 80 malignant) in 226 consecutive patients. Breast mass US findings were retrospectively analyzed by deep learning-based CAD and four radiologists. In predicting malignancy, the CAD results were dichotomized (possibly benign vs. possibly malignant). The radiologists independently assessed Breast Imaging Reporting and Data System final assessments for two datasets (US images alone or with CAD). For each dataset, the radiologists' final assessments were classified as positive (category 4a or higher) and negative (category 3 or lower). The diagnostic performances of the radiologists for the two datasets (US alone vs. US with CAD) were compared Results: When the CAD results were added to the US images, the radiologists showed significant improvement in specificity (range of all radiologists for US alone vs. US with CAD: 72.8-92.5% vs. 82.1-93.1%; p < 0.001), accuracy (77.9-88.9% vs. 86.2-90.9%; p = 0.038), and positive predictive value (PPV) (60.2-83.3% vs. 70.4-85.2%; p = 0.001). However, there were no significant changes in sensitivity (81.3-88.8% vs. 86.3-95.0%; p = 0.120) and negative predictive value (91.4-93.5% vs. 92.9-97.3%; p = 0.259). Conclusion: Deep learning-based CAD could improve radiologists' diagnostic performance by increasing their specificity, accuracy, and PPV in differentiating between malignant and benign masses on breast US.

Experimental and numerical study on the structural behavior of Multi-Cell Beams reinforced with metallic and non-metallic materials

  • Yousry B.I. Shaheen;Ghada M. Hekal;Ahmed K. Fadel;Ashraf M. Mahmoud
    • Structural Engineering and Mechanics
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    • 제90권6호
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    • pp.611-633
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    • 2024
  • This study intends to investigate the response of multi-cell (MC) beams to flexural loads in which the primary reinforcement is composed of both metallic and non-metallic materials. "Multi-cell" describes beam sections with multiple longitudinal voids separated by thin webs. Seven reinforced concrete MC beams measuring 300×200×1800 mm were tested under flexural loadings until failure. Two series of beams are formed, depending on the type of main reinforcement that is being used. A control RC beam with no openings and six MC beams are found in these two series. Series one and two are reinforced with metallic and non-metallic main reinforcement, respectively, in order to maintain a constant reinforcement ratio. The first crack, ultimate load, deflection, ductility index, energy absorption, strain characteristics, crack pattern, and failure mode were among the structural parameters of the beams under investigation that were documented. The primary variables that vary are the kind of reinforcing materials that are utilized, as well as the kind and quantity of mesh layers. The outcomes of this study that looked at the experimental and numerical performance of ferrocement reinforced concrete MC beams are presented in this article. Nonlinear finite element analysis (NLFEA) was performed with ANSYS-16.0 software to demonstrate the behavior of composite MC beams with holes. A parametric study is also carried out to investigate the factors, such as opening size, that can most strongly affect the mechanical behavior of the suggested model. The experimental and numerical results obtained demonstrate that the FE simulations generated an acceptable degree of experimental value estimation. It's also important to demonstrate that, when compared to the control beam, the MC beam reinforced with geogrid mesh (MCGB) decreases its strength capacity by a maximum of 73.33%. In contrast, the minimum strength reduction value of 16.71% is observed in the MC beams reinforced with carbon reinforcing bars (MCCR). The findings of the experiments on MC beams with openings demonstrate that the presence of openings has a significant impact on the behavior of the beams, as there is a decrease in both the ultimate load and maximum deflection.

68Ga 표지 PET/CT 검사의 최적화된 매개변수에 대한 연구 (Study of 68Ga Labelled PET/CT Scan Parameters Optimization)

  • 곽인석;이혁;김시활;문승철
    • 핵의학기술
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    • 제27권2호
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    • pp.111-127
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    • 2023
  • Purpose: Gallium-68 (68Ga) is increasingly used in nuclear medicine imaging for various conditions such as lymphoma and neuroendocrine tumors by labeling tracers like Prostate Specific Membrane Antigen (PSMA) and DOTA-TOC. However, compared to Fluorine-18 (18F) used in conventional nuclear medicine imaging, 68Ga has lower spatial resolution and relatively higher Signal to Background Ratio (SBR). Therefore, this study aimed to investigate the optimized parameters and reconstruction methods for PET/CT imaging using the 68Ga radiotracer through model-based image evaluation. Materials and Methods: Based on clinical images of 68Ga-PSMA PET/CT, a NEMA/IEC 2008 PET phantom model was prepared with a Hot vs Background (H/B) ratio of 10:1. Images were acquired for 9 minutes in list mode using DMIDR (GE, Milwaukee WI, USA). Subsequently, reconstructions were performed for 1 to 8 minutes using OS-EM (Ordered Subset Expectation Maximization) + TOF (Time of Flight) + Sharp IR (VPFX-S), and BSREM (Block Sequential Regularized Expectation Maximization) + TOF + Sharp IR (QCFX-S-400), followed by comparative evaluation. Based on the previous experimental results, images were reconstructed for BSREM + TOF + Sharp IR / 2 minutes (QCFX-S-2min) with varying β-strength values from 100 to 700. The image quality was evaluated using AMIDE (freeware, Ver.1.0.1) and Advanced Workstation (GE, USA). Results: Images reconstructed with QCFX-S-400 showed relatively higher values for SNR (Signal to Noise Ratio), CNR (Contrast to Noise Ratio), count, RC (Recovery Coefficient), and SUV (Standardized Uptake Value) compared to VPFX-S. SNR, CNR, and SUV exhibited the highest values at 2 minutes/bed acquisition time. RC showed the highest values for a 10 mm sphere at 2 minutes/bed acquisition time. For small spheres of 10 mm and 13 mm, an inverse relationship between β-strength increase and count was observed. SNR and CNR peaked at β-strength 400 and then decreased, while SUV and RC exhibited a normal distribution based on sphere size for β-strength values of 400 and above. Conclusion: Based on the experiments, PET/CT imaging using the 68Ga radiotracer yielded the most favorable quantitative and qualitative results with a 2 minutes/bed acquisition time and BSREM reconstruction, particularly when applying β-strength 400. The application of BSREM can enhance accurate quantification and image quality in 68Ga PET/CT imaging, and an optimization process tailored to each institution's imaging objectives appears necessary.

Hot Wall Epitaxy(HWE)법에 의한 MgGa2Se4 단결정 박막 성장과 가전자대 갈라짐에 대한 광전류 연구 (Photocurrent study on the splitting of the valence band and growth of MgGa2Se4 single crystal thin film by hot wall epitaxy)

  • 김혜정;박향숙;방진주;강종욱;홍광준
    • 한국결정성장학회지
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    • 제23권6호
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    • pp.283-290
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    • 2013
  • 수평 전기로에서 $MgGa_2Se_4$ 다결정을 합성하여 HWE(Hot Wall Epitaxy)방법으로 $MgGa_2Se_4$ 단결정 박막을 반절연성 GaAs(100)기판에 성장시켰다. $MgGa_2Se_4$단결정 박막의 성장 조건은 증발원의 온도 $610^{\circ}C$, 기판의 온도 $400^{\circ}C$였고 성장 속도는 $0.5{\mu}m/hr$였다. 이때 이중결정 X-선 요동곡선(DCRC)의 반폭치(FWHM)도 212 arcsec로 가장 작아 최적 성장 조건임을 알 수 있었다. $MgGa_2Se_4$/SI(Semi-Insulated) GaAs(100) 단결정 박막의 광흡수와 광전류 spectra를 293 K에서 10 K까지 측정하였다. 광흡수 스펙트럼으로부터 band gap Eg(T)는 varshni공식에 따라 계산한 결과 $E_g(T)=2.34 eV-(8.81{\times}10^{-4}eV/K)T^2/(T+251K)$이었으며 광전류 스펙트럼으로부터 Hamilton matrix(Hopfield quasicubic mode)법으로 계산한 결과 crystal field splitting energy ${\Delta}cr$값이 190.6 meV이며 spin-orbit energy ${\Delta}so$값은 118.8 meV임을 확인하였다. 10 K일 때 광전류 봉우리들은 n = 1, 27일때 $A_{1^-}$, $B_{1^-}$$C_{27}-exciton$ 봉우리임을 알았다.

Hot wall epitaxy(HWE)법에 의한 $ZnIn_{2}Se_{4}$ 단결정 박막 성장과 가전자대 갈라짐에 대한 광전류 연구 (Photocurrent study on the splitting of the valence band and growth of $ZnIn_{2}Se_{4}$ single crystal thin film by hot wall epitaxy)

  • 홍광준
    • 한국결정성장학회지
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    • 제18권5호
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    • pp.217-224
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    • 2008
  • 수평 전기로에서 $ZnIn_2Se_4$ 단결정을 합성하여 HWE(Hot Wall Epitaxy)방법으로 $ZnIn_2Se_4$ 단결정 박막을 반절연성 GaAs(100) 기판에 성장시켰다. $ZnIn_2Se_4$ 단결정 박막의 성장 조건을 증발원의 온도 $630^{\circ}C$, 기판의 온도 $400^{\circ}C$였고 성장 속도는 0.5 $\mu m/hr$였다. $ZnIn_2Se_4$ 단결정 박막의 결정성의 조사에서 10K에서 광발광(photoluminescence) 스펙트럼이 682.7nm ($1.816{\underline{1}}eV$)에서 exciton emission 스펙트럼이 가장 강하게 나타났으며, 또한 이중결정 X-선 요통곡선(DCRC)의 반폭치(FWHM)도 128 arcsec로 가장 작아 최적 성장 조건임을 알 수 있었다. Hall 효과는 van der Pauw 방법에 의해 측정되었으며, 온도에 의존하는 운반자 농노와 이동도는 293 K에서 각각 $9.41\times10^{16}/cm^{-3}$, $292cm^2/V{\cdot}s$였다. $ZnIn_2Se_4$/SI(Semi-Insulated) GaAs(100) 단결정 박막의 광흡수와 광전류 spectra를 293 K에서 10K까지 측정하였다. 광흡수 스펙트럼으로부터 band gap $E_g(T)$는 varshni공식에 따라 계산한 결과 $E_g(T)=1.8622\;eV-(5.23\times10^{-4}eV/K)T^2/(T+775.5K)$ 이었으며 광전류 스펙트럼으로부터 Hamilton matrix(Hopfield quasicubic mode)법으로 계산한 결과 crystal field splitting energy ${\Delta}cr$값이 182.7meV이며 spin-orbit energy ${\Delta} so$값은 42.6meV임을 확인하였다. 10 K일 때 광전류 봉우리들은 n= 1, 27일때 $A_{1}-$, $B_{1}-$$C_{27}-exciton$ 봉우리임을 알았다.

Hot Wall Epitaxy 법에 의한 CdIn2S4 단결정 박막의 성장과 광전류 특성 (Growth and Photocurrent Properties of CdIn2S4/GaAs Single Crystal Thin Film by Hot Wall Epitaxy)

  • 이상열;홍광준;박진성
    • 센서학회지
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    • 제11권5호
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    • pp.309-318
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    • 2002
  • 수평 전기로에서 $CdIn_2S_4$ 다결정을 합성하여 HWE(Hot Wall Epitaxy)방법으로 $CdIn_2S_4$ 단결정 박막을 반절연성 GaAs (100)기판에 성장시켰다. $CdIn_2S_4$ 단결정 박막의 성장 조건은 증발원의 온도 $630^{\circ}C$, 기판의 온도 $420^{\circ}C$였고 성장 속도는 $0.5\;{\mu}m/hr$였다. $CdIn_2S_4$ 단결정 박막의 결정성의 조사에서 10 K에서 광발광(photoluminescence) 스펙트럼이 463.9 nm (2.6726 eV)에서 exciton emission 스펙트럼이 가장 강하게 나타났으며, 또한 이중 결정 X-선 요동 곡선(DCRC)의 반폭치(FWHM)도 127 arcsec로 가장 작아 최적 성장 조건임을 알 수 있었다. Hall 효과는 van der Pauw 방법에 의해 측정되었으며, 온도에 의존하는 운반자 농도와 이동도는 293K에서 각각 $9.01{\times}10^{16}/cm^3$, $219\;cm^2/V{\cdot}s$였다. $CdIn_2S_4$/SI(Semi-Insulated) GaAs(100) 단결정 박막의 광흡수와 광전류 spectra를 293K에서 10K까지 측정하였다. 광흡수 스펙트럼으로부터 band gap $E_g(T)$는 Varshni 공식에 따라 계산한 결과 $2.7116eV-(7.74{\times}10^{-4}eV/K)T^2$/(T+434K)이었으며 광전류 스펙트럼으로부터 Hamilton matrix(Hopfield quasicubic mode)법으로 계산한 결과 crystal field splitting ${\Delta}cr$값이 0.1291 eV이며 spin-orbit ${\Delta}so$값은 0.0248 eV임을 확인하였다. 10K일 때 광전류 봉우리들은 n = 1일때 $A_1$-, $B_1$-와 $C_1$-exciton 봉우리임을 알았다.

치과용 접착제를 사용한 접착 아말감의 결합 강도 (BOND STRENGTH OF BONDED AMALGAM USING DENIAL ADHESIVES)

  • 감동훈;이상대;한세현
    • 대한소아치과학회지
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    • 제26권2호
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    • pp.284-295
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    • 1999
  • 아말감의 단점인 건전 치질 삭제와 미세 누출을 줄이기 위한 접착 아말감(bonded amalgam)에 사용되는 치과용 접착제의 접착 강도를 측정하고 파절면을 관찰하여 콤포지트 레진과 비교 평가하였다. 발거한 우전치의 순면을 직경 8mm의 원형으로 천공하여 얻은 부분을 순면이 바깥쪽으로 향하도록 아크릴릭 레진 블록에 매몰하여 상아질과 법랑질군을 각각 55개씩 준비하였다. 1군:Superbond C&B, 2군:Panavia 21, 3군:All-Bond 2, 4군:Fuji I Glass Ionomer Luting Cement, 5군:Scotchbond Multi-Purpose(Restorative Z-100)의 5개 군으로 나누어 지름 6.3mm, 깊이 1.5mm의 구멍이 뚫린 충전용 틀(mold)을 위치시키고 표면을 접착제로 처리한 후 아말감 충전을 하였다. 5군은 레진 충전 후 40초간 광중합하였다. 각 시편은 아말감 충전 24시간 후 접착 강도 측정용 기구에 장착하고 만능 시험기에서 0.2mm/min의 cross-head 속도로 하중을 가하여 시편이 탈락할 때까지의 하중값(kg)을 측정하고, 파절면을 검사하여 다음과 같은 결론을 얻었다. 1. 상아질군에서 1, 2, 4군은 5군에 비하여 통계학적으로 유의성 있게 낮은 접착 강도를 보였다(P<0.05). 2. 법랑질군에서 4군은 5군에 비하여 통계학적으로 유의성 있게 낮은 접착 강도를 보였다(P<0.05). 3. 2군에서는 상아질군에서 법랑질군에 비하여 통계학적으로 유의성 있게 낮은 접착 강도를 보였으나(P<0.05), 다른 접착제에서는 상아질군과 법랑질군에서의 접착 강도가 유의성 있는 차이를 보이지 않았다(P>0.05). 4. Cohesive failure는 1E군과 5D군에서 관찰되었고, mixed failure는 1, 5군에서 관찰되었으며, 2, 3, 4군에서는 adhesive failure만 관찰되었다.

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LC/ESI-MS/MS를 이용한 식품 중 불법적으로 첨가된 비스테로이드성 소염진통제 및 스테로이드 의약품 동시분석 (Simultaneous Determination of Non-steroidal Anti-inflammatory Drugs and Corticosteroids Added to Foods as Adulterants using LC-ESI-tandem Mass Spectrometry)

  • 이용철;박주성;김성단;양혜란;김은희;이윤정;조성자;조한빈;김정헌;채영주
    • 한국식품위생안전성학회지
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    • 제28권3호
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    • pp.247-251
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    • 2013
  • 소염 진통 의약품 성분인 beclomethasone, dexamethasone, prednisolone, ketoprofen, phenylbutazone 5종에 대한 동시분석을 위해 LC-MS/MS 분석 조건 중 MRM 방식으로 각 성분의 MS 분석 최적조건을 결정하고, 정량이온으로 beclomethasone 409.1/391.0, dexamethasone은 393.1/372.9, prednisolone은 361.0/343.1, ketoprofen은 255.0/209.0, phenylbutazone은 309.1/160.1을 분석하였다. 혼합표준용액을 기울기용매 조건으로 이동상 A(0.1% 개미산), B(0.1% 개미산을 함유한 아세토니트릴)를 이용하여 17분 동안 분석한 결과, prednisolone ($t_R$: 7.34 min), dexamethasone ($t_R$: 7.73 min), beclomethasone ($t_R$: 7.82 min), phenylbutazone($t_R$: 8.31 min), ketoprofen ($t_R$: 9.24 min) 순서로 검출되었다. 5종 성분 모두 약 2-100 ng/mL 농도 수준의 검정곡선에서 $R^2$ 값이 0.999 이상의 우수한 직선성을 나타내었고, prednisolone을 제외한 4종 성분의 검출한계는 0.4-0.9 ng/mL, 정량한계는 0.81-2.22 ng/mL 였으며, prednisolone은 그보다 다소 높은 4.60, 11.46 ng/mL 이었다. 환제품의 기타가공품 공시료에 5종 성분 혼합표준용액을 최종농도가 5, 20, 50 ng/mL이 되도록 직접 첨가하여 분석한 결과, 모든 농도에서 80% 이상의 우수한 회수율을 얻을 수 있었고, 일내 일간 반복 분석의 상대표준편차(%)를 통해 모든 성분에서 비교적 재현성 있는 결과가 나타났다. 실제 인터넷 상에서 유통중인 식품에 이 분석법을 적용한 결과 모든 제품에서 검출되진 않았으나, 소비자들의 건강상 위해를 끼칠 수 있는 이들 성분의 동시분석법을 활용한 지속적인 모니터링이 필요한 실정이다.

신안군(新安郡) 낙도(落島)에서 발생(發生)한 괴질(怪疾)의 원인(原因)에 관한 역학적(疫學的) 조사(調査)(I) (Epidemiologic Investigation for the Etiology of an Epidemic Ocurred among Animals and Humans in an Isolated Island, Korea(I))

  • 김정순;허용;윤형렬;이원영
    • Journal of Preventive Medicine and Public Health
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    • 제22권2호
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    • pp.290-301
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    • 1989
  • This is preliminary report on anthrax epidemic occurred in an island with about 100 residents. Since 1982 there had been sudden deaths among all kinds of domestic animals including cattle, dogs, ducks, chicken and goat but only a few among cats in an isolated island about three hours distance away by ferry boat from Mokpo city. From 1986 through 1988 nine human deaths and four patients occurred, which made the government intervene for investigation on June 25 1988. The epidemiological investigation consisted of interview survey and medical examination, medical record analysis, laboratory work to isolate the pathogens under the direction of hypothesis derived from the study and further confirmation of the pathogens by international institute. The summarized results are as followings: 1. According to the interview survey there were many deaths among domestic animals usually in cold and dry season such as January through March and September through November; 36 heads of cattle leaving one head, more than 40 hogs(all), hundreds of chicken leaving few alive, goats that had taken home from mountain and two or three cats out of around 40 had sudden deaths from 1982 till 1985, when the residents stopped to purchase and take them into the island anymore. Also there were eleven persons who had experienced the similar syndrome complex to those of admitted and expired patients and four of them revealed typical chest X-ray findings; from one of these four patients(Rho) B. anthracis is isolated. 2. Medical record on patients who had been admitted, showed common characteristics of the disease course. On admission they had either gastrointestinal or upper respiratory infection symptoms which invariably progressed to septicemic nature with pulmonary interstitial infiltration and mediastinal widening/bulging, and then to deadly acute respiratory distress syndrome. At the end stage chest X-ray revealed multiple bullous emphysema. One of another characteristics was oral ulceration with bleeding occurred in about 50% of the patients. Laboratory test results in common were leukocytosis with left shift and abnormal liver and kidney functions, particularly at the later stage of the illness. 3. Epidemiological characteristics was striking in that both mortality and incidence rates were high: the mortality rate was 8.7% average, male being three times higher than females but there was no distictive clustering by age group. The incidence rate for both sexes was 28.2% and there was no sex difference although a tendency of higher incidence among older ages was noticed. The highest mortality and incidence were observed in Won village where the first death of animal occurred and with the highest frequency among three villages of the island. 4. Among twelve bacilli species isolated from various specimens, two strains, one from patient and the other from soil where the recently died cow is hurried, were confirmed as B. anthracis by Pasteur Institute and CDC of USA(strain from soil). CDC reported that the strain did not produce capsule in bicarbonate media but reacted with the bacteriophage and one of five sera taken from the patients. Mode of transmission as well as incubation period of the agent has not been established yet, which needs further investigation in relation to the antigenic structure of the variant when it is confirmed.

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가리질비료(加里質肥料) 연용(連用) 고추재배(栽培) 밭토양(土壤)의 치환성가리함량(置換性加里含量) 변동양상(變動樣相) 예측방법(豫測方法) (Prediction Model for Accumulation and Decline of Exchangeable Potassium in Upland Soil with Long-Term Application of Fertilizer Potassium)

  • 정병간;윤정희;황기성
    • 한국토양비료학회지
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    • 제29권4호
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    • pp.342-346
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    • 1996
  • 가리비료(加里肥料)의 시비(施肥)수준이나 퇴비(堆肥) 및 퇴비 계분병용여부(鷄糞倂用與否)에 따른 밭토양(土壤) 치환성가리함량(置換性加里含量)의 장기변동양상(長期變動樣相)을 구명(究明)하기 위하여 고평통(高坪統) 토양(土壤)에서 치환성가리함량(置換性加里含量)이 각각(各各) 1.68, $1.13cmol^+/kg$인 두 필지(筆地)를 선정하여 포장에서 고추를 연작(連作)으로 3년간 재배(栽培)한 시험결과(試驗結果)에서 갈이흙중의 치환성가리함량(置換性加里含量) 변동양상(變動樣相)을 조사연구(調査硏究)한 결과(結果)는 다음과 같다. 1. 고추재배후(裁培後) 토양중(土壤中) 치환성가리함량(置換性加里含量)은 시험전(試驗前) 토양(土壤)의 가리함량(加里含量)이 $1.68cmol^+/kg$이었던 토양(土壤)은 가리기준(加里基準) + 퇴비(堆肥) > 가리기준(加里基準) + 계분(鷄糞) > 가리기준량(加里基準量) > 퇴비(堆肥) > 가리기준량(加里基準量) > 무가리(無加里) 순으로 많았고, 시험전(試驗前)과 토양(土壤)의 가리함량(加里含量)이 전국 고추재배(栽培) 토양(土壤)의 평균함량(平均含量) $1.07cmol^+/kg$과 유사한 $1.13cmol^+/kg$ 이었던 토양(土壤)은 가리기준(加里基準)+퇴비(堆肥) > 가리기준(加里基準)+계분(鷄糞) > 가리기준량(加里基準量) > 가리기준반량(加里基準半量) > 퇴비(堆肥) > 무가리(無加里) 순으로 많았다. 2. 가리(加里) 시용량(施用量)에 따른 시험후(試驗後) 토양중(土壤中) 치환성가리함량(置換性加里含量)의 변화율은 시험전(試驗前) 토양(土壤)의 가리함량(加里含量)이 고저(高低)에 관계없이 무가리(無加里), 가리기준반량(加里基準半量), 퇴비시용(堆肥施用) 처리구(處理區)는 현저히 감소한 반면, 가리기준(加里基準) + 퇴비(堆肥), 가리기준(加里基準) + 계분처리구(鷄糞處理區)에서는 현저히 증가하는 경향이었다. 3. 식질계 고평통(高坪統) 토양(土壤)에서 고추연작재배전(連作栽培前) 갈이흙중(中) 치환성가리합량(置換性加里含量) ($K_0$)일 때에 일정재배년차후(一定栽培年次後) 처리별(處理別) 갈이흙중 치환성가리함량(置換性加里含量)($K_t$)은 다음과 같은 모형식(模型式)에서 추정(推定)할 수 있다. $$Kt=K_0A^t+B\sum^{t-1}_{n=0}A^n$$ 단, Kt : t년후 토양(土壤)의 치환성가리함량(置換性加里含量)($K_0$) : 고추재배전(栽培前) 가리흙의 치환성가리함량(置換性加里含量), A와 B : 작물(作物) 및 시용(施用)하는 가리함유물질(加里含有物質) 및 토양특성(土壤特性) 등에 따라 달라질 수 있는 상수 또는 계수).

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