simplex

  • adj.
simple

   

WordNet

  1. having only one part or element; "a simplex word has no affixes and is not part of a compound--like `boy compared with `boyish or `house compared with `houseboat"
  2. allowing communication in only one direction at a time, or in telegraphy allowing only one message over a line at a time; "simplex system"
  3. unornamented; "a simple country schoolhouse"; "her black dress--simple to austerity"
  4. any herbaceous plant having medicinal properties
  5. (botany) of leaf shapes; of leaves having no divisions or subdivisions (同)unsubdivided
  6. having few parts; not complex or complicated or involved; "a simple problem"; "simple mechanisms"; "a simple design"; "a simple substance"

PrepTutorEJDIC

  1. 『簡単な』容易な,分かりやすい / (複合に対して)単一の / 『単純な』,込み入っていない / 『純然たる』,全くの / 『飾り気のない』,簡素な,地味な,質素な / 『もったいぶらない』;誠実な,実直な / お人よしの,だまされやすい / 《文》地位のない,普通の,平(ひら)の
  2. 薬草,薬用植物

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア(Wikipedia)』「2016/10/27 20:57:42」(JST)

wiki en

[Wiki en表示]

\<add_contents_exp><m=6 date=20150923>\end{pmatrix}},{\begin{pmatrix}x_{1}\\y_{1}\\z_{1}\end{pmatrix}},{\begin{pmatrix}x_{2}\\y_{2}\\z_{2}\end{pmatrix}},{\begin{pmatrix}x_{3}\\y_{3}\\z_{3}\end{pmatrix}}}</annotation>

 </semantics>

</math>

By the second property the dot product of v0 with all other vectors is -13, so each of their x components must equal this, and the vectors become

Next choose v1 to have all but the first two elements zero. The second element is the only unknown. It can be calculated from the first property using the Pythagorean theorem (choose any of the two square roots), and so the second vector can be completed:

The second property can be used to calculate the remaining y components, by taking the dot product of v1 with each and solving to give

From which the z components can be calculated, using the Pythagorean theorem again to satisfy the first property, the two possible square roots giving the two results

This process can be carried out in any dimension, using n + 1 vectors, applying the first and second properties alternately to determine all the values.

Geometric properties

Volume

The volume of an n-simplex in n-dimensional space with vertices (v0, ..., vn) is

where each column of the n × n determinant is the difference between the vectors representing two vertices.[6] Without the 1/n! it is the formula for the volume of an n-parallelotope. This can be understood as follows: Assume that P is an n-parallelotope constructed on a basis of . Given a permutation of , call a list of vertices a n-path if

(so there are n! n-paths and does not depend on the permutation). The following assertions hold:

If P is the unit n-hypercube, then the union of the n-simplexes formed by the convex hull of each n-path is P, and these simplexes are congruent and pairwise non-overlapping.[7] In particular, the volume of such a simplex is

.

If P is a general parallelotope, the same assertions hold except that it is no more true, in dimension > 2, that the simplexes need to be pairwise congruent; yet their volumes remain equal, because the n-parallelotop is the image of the unit n-hypercube by the linear isomorphism that sends the canonical basis of to . As previously, this implies that the volume of a simplex coming from a n-path is:

Conversely, given a n-simplex of , it can be supposed that the vectors form a basis of . Considering the parallelotope constructed from and , one sees that the previous formula is valid for every simplex.

Finally, the formula at the beginning of this section obtains by observing that

From this formula, it follows immediately that the volume under a standard n-simplex (i.e. between the origin and the simplex in Rn+1) is

The volume of a regular n-simplex with unit side length is

as can be seen by multiplying the previous formula by xn+1, to get the volume under the n-simplex as a function of its vertex distance x from the origin, differentiating with respect to x, at    (where the n-simplex side length is 1), and normalizing by the length of the increment, , along the normal vector.

The dihedral angle of a regular n-dimensional simplex is cos−1(1/n),[8][9] while its central angle is cos−1(-1/n).[10]

Simplexes with an "orthogonal corner"

Orthogonal corner means here, that there is a vertex at which all adjacent facets are pairwise orthogonal. Such simplexes are generalizations of right angle triangles and for them there exists an n-dimensional version of the Pythagorean theorem:

The sum of the squared (n-1)-dimensional volumes of the facets adjacent to the orthogonal corner equals the squared (n-1)-dimensional volume of the facet opposite of the orthogonal corner.

where are facets being pairwise orthogonal to each other but not orthogonal to , which is the facet opposite the orthogonal corner.

For a 2-simplex the theorem is the Pythagorean theorem for triangles with a right angle and for a 3-simplex it is de Gua's theorem for a tetrahedron with a cube corner.

Relation to the (n+1)-hypercube

The Hasse diagram of the face lattice of an n-simplex is isomorphic to the graph of the (n+1)-hypercube's edges, with the hypercube's vertices mapping to each of the n-simplex's elements, including the entire simplex and the null polytope as the extreme points of the lattice (mapped to two opposite vertices on the hypercube). This fact may be used to efficiently enumerate the simplex's face lattice, since more general face lattice enumeration algorithms are more computationally expensive.

The n-simplex is also the vertex figure of the (n+1)-hypercube. It is also the facet of the (n+1)-orthoplex.

Topology

Topologically, an n-simplex is equivalent to an n-ball. Every n-simplex is an n-dimensional manifold with corners.

Probability

Main article: Categorical distribution

In probability theory, the points of the standard n-simplex in -space are the space of possible parameters (probabilities) of the categorical distribution on n+1 possible outcomes.

Algebraic topology

In algebraic topology, simplices are used as building blocks to construct an interesting class of topological spaces called simplicial complexes. These spaces are built from simplices glued together in a combinatorial fashion. Simplicial complexes are used to define a certain kind of homology called simplicial homology.

A finite set of k-simplexes embedded in an open subset of Rn is called an affine k-chain. The simplexes in a chain need not be unique; they may occur with multiplicity. Rather than using standard set notation to denote an affine chain, it is instead the standard practice to use plus signs to separate each member in the set. If some of the simplexes have the opposite orientation, these are prefixed by a minus sign. If some of the simplexes occur in the set more than once, these are prefixed with an integer count. Thus, an affine chain takes the symbolic form of a sum with integer coefficients.

Note that each facet of an n-simplex is an affine n-1-simplex, and thus the boundary of an n-simplex is an affine n-1-chain. Thus, if we denote one positively oriented affine simplex as

with the denoting the vertices, then the boundary of σ is the chain

.

It follows from this expression, and the linearity of the boundary operator, that the boundary of the boundary of a simplex is zero:

Likewise, the boundary of the boundary of a chain is zero: .

More generally, a simplex (and a chain) can be embedded into a manifold by means of smooth, differentiable map . In this case, both the summation convention for denoting the set, and the boundary operation commute with the embedding. That is,

where the are the integers denoting orientation and multiplicity. For the boundary operator , one has:

where ρ is a chain. The boundary operation commutes with the mapping because, in the end, the chain is defined as a set and little more, and the set operation always commutes with the map operation (by definition of a map).

A continuous map to a topological space X is frequently referred to as a singular n-simplex.

Algebraic geometry

Since classical algebraic geometry allows to talk about polynomial equations, but not inequalities, the algebraic standard n-simplex is commonly defined as the subset of affine n+1-dimensional space, where all coordinates sum up to 1 (thus leaving out the inequality part). The algebraic description of this set is

,

which equals the scheme-theoretic description with

the ring of regular functions on the algebraic n-simplex (for any ring ).

By using the same definitions as for the classical n-simplex, the n-simplices for different dimensions n assemble into one simplicial object, while the rings assemble into one cosimplicial object (in the category of schemes resp. rings, since the face and degeneracy maps are all polynomial).

The algebraic n-simplices are used in higher K-Theory and in the definition of higher Chow groups.

Applications

Simplices are used in plotting quantities that sum to 1, such as proportions of subpopulations, as in a ternary plot.

In industrial statistics, simplices arise in problem formulation and in algorithmic solution. In the design of bread, the producer must combine yeast, flour, water, sugar, etc. In such mixtures, only the relative proportions of ingredients matters: For an optimal bread mixture, if the flour is doubled then the yeast should be doubled. Such mixture problem are often formulated with normalized constraints, so that the nonnegative components sum to one, in which case the feasible region forms a simplex. The quality of the bread mixtures can be estimated using response surface methodology, and then a local maximum can be computed using a nonlinear programming method, such as sequential quadratic programming.[11]

In operations research, linear programming problems can be solved by the simplex algorithm of George Dantzig.

In geometric design and computer graphics, many methods first perform simplicial triangulations of the domain and then fit interpolating polynomials to each simplex.[12]

See also

  • Complete graph
  • Causal dynamical triangulation
  • Distance geometry
  • Delaunay triangulation
  • Hill tetrahedron
  • Other regular n-polytopes
    • Hypercube
    • Cross-polytope
    • Tesseract
  • Hypersimplex
  • Polytope
  • Metcalfe's Law
  • List of regular polytopes
  • Schläfli orthoscheme
  • Simplex algorithm - a method for solving optimisation problems with inequalities.
  • Simplicial complex
  • Simplicial homology
  • Simplicial set
  • Ternary plot
  • 3-sphere

Notes

  1. ^ Elte, E. L. (1912), The Semiregular Polytopes of the Hyperspaces, Groningen: University of Groningen  Chapter IV, five dimensional semiregular polytope
  2. ^ "Sloane's A135278 : Pascal's triangle with its left-hand edge removed". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  3. ^ Kozlov, Dimitry, Combinatorial Algebraic Topology, 2008, Springer-Verlag (Series: Algorithms and Computation in Mathematics)
  4. ^ Yunmei Chen, Xiaojing Ye. "Projection Onto A Simplex". arXiv:1101.6081. 
  5. ^ MacUlan, N.; De Paula, G. G. (1989). "A linear-time median-finding algorithm for projecting a vector on the simplex of n". Operations Research Letters. 8 (4): 219. doi:10.1016/0167-6377(89)90064-3. 
  6. ^ A derivation of a very similar formula can be found in Stein, P. (1966). "A Note on the Volume of a Simplex". The American Mathematical Monthly. 73 (3): 299–301. doi:10.2307/2315353. JSTOR 2315353. 
  7. ^ Every n-path corresponding to a permutation is the image of the n-path by the affine isometry that sends to , and whose linear part matches to for all i. hence every two n-paths are isometric, and so is their convex hulls; this explains the congruence of the simplexes. To show the other assertions, it suffices to remark that the interior of the simplex determined by the n-path is the set of points , with and Hence the components of these points with respect to each corresponding permuted basis are strictly ordered in the decreasing order. That explains why the simplexes are non-overlapping. The fact that the union of the simplexes is the whole unit n-hypercube follows as well, replacing the strict inequalities above by "". The same arguments are also valid for a general parallelotope, except the isometry between the simplexes.
  8. ^ Parks, Harold R.; Dean C. Wills (October 2002). "An Elementary Calculation of the Dihedral Angle of the Regular n-Simplex". The American Mathematical Monthly. Mathematical Association of America. 109 (8): 756–758. doi:10.2307/3072403. 
  9. ^ Harold R. Parks; Dean C. Wills (June 2009). Connections between combinatorics of permutations and algorithms and geometry. Oregon State University. 
  10. ^ Salvia, Raffaele (2013), Basic geometric proof of the relation between dimensionality of a regular simplex and its dihedral angle, arXiv:1304.0967 
  11. ^ Cornell, John (2002). Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data (third ed.). Wiley. ISBN 0-471-07916-2. 
  12. ^ Vondran, Gary L. (April 1998). "Radial and Pruned Tetrahedral Interpolation Techniques" (PDF). HP Technical Report. HPL-98-95: 1–32. 

References

  • Walter Rudin, Principles of Mathematical Analysis (Third Edition), (1976) McGraw-Hill, New York, ISBN 0-07-054235-X (See chapter 10 for a simple review of topological properties.).
  • Andrew S. Tanenbaum, Computer Networks (4th Ed), (2003) Prentice Hall, ISBN 0-13-066102-3 (See 2.5.3).
  • Luc Devroye, Non-Uniform Random Variate Generation. (1986) ISBN 0-387-96305-7; Web version freely downloadable.
  • H.S.M. Coxeter, Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8
    • p120-121
    • p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n>=5)
  • Weisstein, Eric W. "Simplex". MathWorld. 
  • Stephen Boyd and Lieven Vandenberghe, Convex Optimization, (2004) Cambridge University Press, New York, NY, USA.

External links

  • Olshevsky, George. "Simplex". Glossary for Hyperspace. Archived from the original on 4 February 2007. 
Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform 4-polytope 5-cell 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds


</raw> </toggledisplay>

English Journal

  • Size-exclusion chromatography (HPLC-SEC) technique optimization by simplex method to estimate molecular weight distribution of agave fructans.
  • Moreno-Vilet L1, Bostyn S2, Flores-Montaño JL3, Camacho-Ruiz RM4.
  • Food chemistry.Food Chem.2017 Dec 15;237:833-840. doi: 10.1016/j.foodchem.2017.06.020. Epub 2017 Jun 7.
  • PMID 28764075
  • Loratadine bioavailability via buccal transferosomal gel: formulation, statistical optimization, in vitro/in vivo characterization, and pharmacokinetics in human volunteers.
  • Elkomy MH1, El Menshawe SF1, Abou-Taleb HA2, Elkarmalawy MH2.
  • Drug delivery.Drug Deliv.2017 Nov;24(1):781-791. doi: 10.1080/10717544.2017.1321061.
  • PMID 28480758
  • Seek and destroy: targeted adeno-associated viruses for gene delivery to hepatocellular carcinoma.
  • Dhungel B1,2,3, Jayachandran A1,2, Layton CJ2,4, Steel JC1,2.
  • Drug delivery.Drug Deliv.2017 Nov;24(1):289-299. doi: 10.1080/10717544.2016.1247926.
  • PMID 28165834
  • Low-molecular weight mannogalactofucans prevent herpes simplex virus type 1 infection via activation of Toll-like receptor 2.
  • Kim WJ1, Choi JW2, Jang WJ3, Kang YS4, Lee CW2, Synytsya A5, Park YI6.
  • International journal of biological macromolecules.Int J Biol Macromol.2017 Oct;103:286-293. doi: 10.1016/j.ijbiomac.2017.05.060. Epub 2017 May 15.
  • PMID 28522392

Japanese Journal

  • 症例報告 髄液オレキシン低値をともない過眠症を合併した単純ヘルペス脳炎の1例
  • 向野 晃弘,木下 郁夫,福島 直美 [他]
  • 臨床神経学 = Clinical neurology 54(3), 207-211, 2014-03
  • NAID 40020006443
  • Axin expression delays herpes simplex virus-induced autophagy and enhances viral replication in L929 cells
  • Choi Eun-Jin,Kee Sun-Ho
  • Microbiology and immunology 58(2), 103-111, 2014-02
  • NAID 40020007912
  • Eight types of stem cells in the life cycle of the moss Physcomitrella patens
  • Kofuji Rumiko,Hasebe Mitsuyasu
  • Current Opinion in Plant Biology 17(1), 13-21, 2014-02
  • … A simplex meristem with a single stem cell was acquired in the sporophyte generation early in land plant evolution. … patens develops at least seven types of simplex meristem in the gametophyte and at least one type in the sporophyte generation and is a good material for regulatory network comparisons. …
  • NAID 120005418471
  • 前頭葉に病変が及んだ非ヘルペス性急性辺縁系脳炎の1例
  • 朱膳寺 圭子,石川 元直,西村 芳子,柴田 興一,大塚 邦明,佐倉 宏,高橋 幸利
  • 東京女子医科大学雑誌 84(E1), E197-E203, 2014-01-31
  • 【症例】45歳男性【主訴】発熱、痙攣発作、意識障害【現病歴】入院2週間前から感冒症状が出現し、入院1週間前から40℃の発熱があり解熱鎮痛剤を内服していた。入院当日、全身性の痙攣発作が出現したため救急搬送された。【入院後経過】入院時、軽度の意識障害と前向性健忘を認め、頭部MRIでは異常はなかったが、第2病日、口からはじまる部分発作が増悪した。第6病日に強直性痙攣が出現し、第7病日のMRIでは両側の海 …
  • NAID 110009752578

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★リンクテーブル★
リンク元100Cases 33」「100Cases 16」「単一性」「単式
拡張検索genital herpes simplex virus infection
関連記事simple

100Cases 33」

  [★]

☆case33 頭痛と混乱
glossary
accompany
vt.
(人)と同行する、(人)に随行する。(もの)に付随する。~と同時に起こる。~に加える(添える、同封する)(with)
slurred n. 不明瞭
強直間代痙攣 tonic-clonic convulsion
 意識消失とともに全身随意筋強直痙攣が生じ(強直痙攣tonic convulsion)、次いで全身の筋の強直弛緩とが律動的に繰り返される時期(間代痙攣clonic convulsion)を経て、発作後もうろう状態を呈する一連発作
症例
28歳、女性 黒人 南アフリカ 手術室看護師 ロンドン住在
主訴頭痛と混乱
現病歴過去3週間で頭痛が続いており、ひどくなってきた。現在頭痛持続しており、頭全体が痛い。友人曰く「過去六ヶ月で体重が10kg減っていて、最近、混乱してきたようだ」。発話不明瞭救急室にいる間に強直間代痙攣を起こした。
診察 examination
やせている。55kg。38.5℃。口腔カンジダ症(oral candidiasis)。リンパ節腫脹無し。心血管呼吸器系、消化器系正常。痙攣前における神経検査では時間場所、人の見当識無し。神経局所症状無し(no focal neurological sign)。眼底両側に乳頭浮腫有り。
検査 investigation
血算:白血球増多
血液生化学ナトリウム低下
CT供覧
キーワード着目するポイント
口腔カンジダ症(oral candidiasis)
頭痛精神症状強直間代痙攣
・眼底両側に乳頭浮腫
CT所見
・低ナトリウム血症は二次的なもの
アプローチ
口腔カンジダ症(oral candidiasis) → 細胞免疫低下状態(DM免疫抑制AIDSなど) or 常在細菌叢の攪乱(長期抗菌薬の使用)
 ・The occurrence of thrush in a young, otherwise healthy-appearing person should prompt an investigation for underlying HIV infection.(HIM.1254)
 ・More commonly, thrush is seen as a nonspecific manifestation of severe debilitating illness.(HIM.1254)
精神症状強直間代痙攣 → 一次的、あるいは二次的な脳の疾患がありそう
頭痛 → 漠然としていて絞れないが、他の症状からして機能性頭痛ではなく症候性頭痛っぽい。
・眼底両側に乳頭浮腫 → 脳圧亢進徴候 → 原因は・・・脳腫瘍、ことにテント下腫瘍側頭葉腫瘍クモ膜下出血、脳水腫など、そのほか、眼窩内病変、低眼圧などの局所的要因、悪性高血圧、血液疾患大量出血肺気腫などの全身的要因 (vindicate本のp342も参考になる)
 ・頭痛脳圧亢進 → 頭蓋内圧占拠性病変脳炎(IMD.274)
CT所見 → ringform病変脳浮腫脳圧亢進
・低ナトリウム血症 → 脳ヘルニア続発して起こることがあるらしい。実際には下垂体トキソプラズマによる病変形成されることにより起こりうる。
・そのほか出身地、体重減少もHIVを疑わせる点
パターン認識HIV + 精神症状 + てんかん発作(強直間代痙攣) + 脳圧亢進 + CT所見 = 一番ありそうなのはToxoplasma gondiiによるトキソプラズマ脳症 cerebral toxoplasosis (トキソプラズマ脳炎 toxoplasmic encephalitis)
Toxoplasma gondii
 原虫 胞子原虫
(感染予防学 080521のプリント、CASES p,92、HIM p.1305-)
疫学:西洋では30-80%の成人トキソプラズマ感染既往がある・・・うぇ(CASES)。日本では10%前後(Wikipedia)。
生活環
 ・終宿主ネコネコ小腸上皮細胞で有性・無性生殖 糞便オーシスト排泄
 ・中間宿主ヒト.ブタを含むほ乳類と鳥類無性生殖増殖シスト形成
   急性期増殖盛んな急増虫体tachyzoiteシスト内の緩増虫体bradyzoite
病原病因 phathogenesis
 ・緩増虫体(bradyzoite)、接合子嚢(oocyst)
感染経路
 1. オーシスト経口摂取
 2. 中間宿主の生肉中のシスト経口摂取
 3. 初感染妊婦からの経胎盤感染。既感染なら胎盤感染しないらしい(HIM.1306)
 (4)移植臓器、輸血確率は低い(at low rate)(HIM.1306)
病態
 1. 先天性トキソプラズマ症 congenital toxoplasmosis
   ①網脈絡膜炎、 ②水頭症、 ③脳内石灰化、 ④精神運動障害
 2. 後天性トキソプラズマ症 acquired toxoplasmosis
  (1) 健常者
   ・多くは不顕性感染発熱リンパ節腫脹、皮疹(rash)
   ・(少数例)筋肉痛、暈疼痛、腹痛、斑状丘疹状皮疹(maculopapular rash)、脳脊髄炎、混乱(HIM.1308)
   ・(まれ)肺炎心筋炎脳症心膜炎多発筋炎
   ・網膜脈絡叢瘢痕や、脳に小さい炎症性病変を残すことあり(CASES)。
   ・急性感染症状は数週間で消失 筋肉中枢神経系緩増虫体残存
  (2)HIV感染者、臓器移植例、がん化学療法例
   シスト緩増虫体急増虫体播種性の多臓器感染
   AIDSでは、トキソプラズマ脳炎が指標疾患 AIDS-defineing illness(CASES)
治療
 (日本)アセチルスピラマイシンファンシダール(感染予防学 080521)
トキソプラズマ脳炎 toxoplasmic encephalitisトキソプラズマ脳症 cerebral toxoplasosis
症状
 発熱頭痛、混乱m、痙攣認知障害、局所神経徴候(不全片麻痺歯垢脳神経損傷視野欠損、感覚喪失)(CASES)
・画像検査
 (CT,MRI)多発性両側性ring-enhancing lesion、特に灰白質-白質境界、大脳基底核脳幹小脳が冒されやすい(CASES)
鑑別診断(臨床症状画像診断所見で)
 リンパ腫、結核、転移性脳腫瘍(CASES)
病歴と画像所見からの鑑別診断
 リンパ腫、結核、転移性腫瘍
このCTcerebral toxoplasmosis特徴的かは不明
最後に残る疑問
 AIDSWBC(leukocyte)の数はどうなるんだろう???AIDSの初診患者ではWBCが低い人が多いらしいし()、HIVCD4+ T cellmacrophage感染して殺すから、これによってB cellは減るだろうし、CD8+ T cellも若干減少するだろうからWBCは減るんじゃないか?!好中球AIDSとは関係ない?好中球は他の感染症に反応性増加している?ちなみに、好酸球寄生虫(原虫)の感染のために増える傾向にあるらしい(HIMのどこか)。
スルファジアジン
sulfadiazine
ピリメタミン
pyrimethamine
葉酸拮抗剤である。
サルファ剤と併用され、抗トキソプラズマ薬、抗ニューモシチス・カリニ薬として相乗的に働く。
ST合剤
SMX-TMP
スルファメトキサゾールトリメトプリム合剤 sulfamethoxazole and trimethoprim mixture
AIDS定義(http://en.wikipedia.org/wiki/CDC_Classification_System_for_HIV_Infection_in_Adults_and_Adolescents)
A CD4+ T-cell count below 200 cells/μl (or a CD4+ T-cell percentage of total lymphocytes of less than 14%).
or he/she has one of the following defining illnesses:
People who are not infected with HIV may also develop these conditions; this does not mean they have AIDS. However, when an individual presents laboratory evidence against HIV infection, a diagnosis of AIDS is ruled out unless the patient has not:
AND
AIDSのステージング
参考文献
HIM = Harrison's Principles of Internal Medicine 17th Edition
CASES = 100 Cases in Clinical Medicine Second edition
IMD = 内科診断学第2版

100Cases 16」

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☆case16 膝の痛み
glossary
indigestion 消化障害消化不良
症例
80歳 男性
主訴:左膝の痛みと腫脹
現病歴:左膝の痛みを2日前から認めた。膝は発熱腫脹しており、動かすと疼痛を生じる。時々胸焼けと消化不良が見られる。6ヶ月前のhealth checkで、高血圧(172/102mmHg)と血中クレアチニンが高い(正常高値)こと以外正常といわれた。その4週間数回血圧測定したが、高値継続したため、2.5mg bendrofluamethizide(UK)/ベンドロフルメチアジドbendroflumethiazide(US)で治療開始した。最近血圧は138/84 mmHgであった。
喫煙歴:なし。
飲酒歴:一週間に平均4unit。
既往歴股関節中程度(mild)の変形性関節症
家族歴:特記なし
服薬歴アセトアミノフェン(股関節疼痛に対して)
身体所見 examination
 血圧 142/86mmHg体温37.5℃。脈拍88/分。grade 2 hypertensive retinopathy(高血圧症性網膜症)。心血管系呼吸器系検査場異常なし。手にDIPにヘバーデン結節なし。
 左膝が発熱腫脹している。関節内に液、patellar tap陽性。90℃以上膝関節屈曲させると痛みを生じる。右の膝関節正常に見える。
検査 investigation
 生化学白血球増多、ESR上昇、尿素高値グルコース高値
 単純X線:関節間隙やや狭小。それ以外に異常は認めない。
problem list
 #1 左膝の痛み
 #2 胸焼け
 #3 消化不良
 #4 高血圧
 #5 クレアチニン正常高値
 #6 股関節変形性リウマチ
 #7 高血圧性網膜症
■考え方
 ・関節痛鑑別診断を考える。
 ・VINDICATEで考えてみてもよいでしょう。
 ・関節痛頻度としては 外傷慢性疾患(OAなど)>膠原病脊椎疾患悪性腫瘍
関節痛の鑑別疾患
DIF 282
V Vascular 血友病 hemophilia, 壊血病 scurvy, 無菌性骨壊死 aseptic bone necrosis (Osgood-Schlatter diseaseとか)
I Inflammatory 淋疾 gonorrhea, ライム病 lyme disease, 黄色ブドウ球菌 Staphylococcus, 連鎖球菌 Streptococcus, 結核 tuberculosis, 梅毒 syphilis, 風疹 rubella, 単純ヘルペス herpes simplex, HIV human immunodeficiency virus, サイトメガロウイルス cytomegalovirus
N Neoplastic disorders 骨原性肉腫 osteogenic sarcoma, 巨細胞腫 giant cell tumors
D Degenerative disorders degenerative joint disease or 変形性関節症 osteoarthritis
I Intoxication 痛風 gout (uric acid), 偽痛風 pseudogout (calcium pyrophosphate), ループス症候群 lupus syndrome of hydralazine (Apresoline) and procainamide, gout syndrome of diuretics
C Congenital and acquired malformations bring to mind the joint deformities of tabes dorsalis and syringomyelia and congenital dislocation of the hip. Alkaptonuria is also considered here.
A Autoimmune indicates (多い)関節リウマチ RA (可能性)血清病 serum sickness, 全身性エリテマトーデス lupus erythematosus, リウマチrheumatic fever, ライター症候群 Reiter syndrome, 潰瘍性大腸炎 ulcerative colitis, クローン病=限局性回腸炎 regional ileitis, 乾癬性関節psoriatic arthritis (老人であり得る)リウマチ性多発筋痛症 polymyalgia rheumatica
T Trauma 外傷性滑膜炎 traumatic synovitis, tear or rupture of the collateral or cruciate ligaments, 亜脱臼 subluxation or laceration of the meniscus (semilunar cartilage), 脱臼 dislocation of the joint or patella, a 捻挫 sprain of the joint, and fracture of the bones of the joint.
E Endcrine 先端肥大症 acromegaly, 閉経 menopause, 糖尿病 diabetes mellitus
■答え
 骨格筋系-関節炎-単関節炎-急性単関節
 痛風 尿酸 → 発熱ESR↑、白血球
 偽痛風 ピロリンカルシウム
 高齢女性でチアジド利尿薬の使用により痛風誘発されやすい。特に腎機能低下糖尿病の人はこのリスクが高まる。
■(BSTからの知識「)循環器領域での利尿薬
心不全治療において、循環血漿量を減らし、心臓前負荷軽減する。
利尿薬は高尿酸血症を起こす。(けど、心不全治療において高尿酸血症になったからといって痛風発症している患者はみたことない)
電解質異常を起こしやすいので、血液生化学検査でモニタして注意する。たとえば低Kで不整脈リスクが高まる。
チアジド系の利尿薬血糖を上げるし、尿酸を上げる
長期の使用で腎機能を低下させる
initial plan
 Dx 1. 関節液の吸引関節液の一般検査生化学検査、培養検査
    ・白血球増加していれば急性炎症性であることを示す。
    ・偏光顕微鏡関節液を検鏡する。
     ・尿酸結晶:針状結晶negatively birefringent
     ・ピロリンカルシウム結晶positively birefringent
 Tx 1. 関節液の吸引炎症が軽度改善
   2. NSAIDによる疼痛管理
   3. PPINSAID潰瘍予防するため
   4. ACE inhibitor導入

単一性」

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simplexsimple
単一単式単純単純性簡素シンプル簡便

単式」

  [★]

simplex
単一性

genital herpes simplex virus infection」

  [★] 外陰部単純ヘルペスウイルス感染症

simple」

  [★]

  • adj.
  • (比較級simpler-最上級simplest)単純な、簡便な、シンプルな、簡素な、単一の、単一性の、単純性の
convenientmonoparsimoniousplainsimplexsimplicitysimplysingleunity