19 research outputs found
Directed networks and self-similar systems
The formula ∂Lᵣ/∂r∣ᵣ₌₁/₂ = 2T in Hata and Yamaguti [1], where Lr is Salem’s singular function and T is the Takagi function, was generalized to the formula ∂ᵏLᵣ/∂rᵏ = k!Tᵣ,ₖ in Sekiguchi and Shiota [17] by using the measure theoretic method, where Tᵣ,ₖ is the k-th order Takagi function. In this paper we reconsider these functions fromthe viewpoint of de Rham’s functional equation, and by investigating such functional equation on a directed network we expand the above formula without the measure theoretic method
An Explicit Formula of Subblock Occurrences for the p-Adic Expansion
Let b(n,w) be the number of occurrences of subblock w in the p-adic expansion of n ∈ N and set B(N,w)=Σn=0Nb(n,w) for N ∈ N. Properties of the value of B(N,w) were investigated by Prodinger [8] (for p=2) and by Kirschenhofer [3] (for a general p). In this paper we give a simple representation of B(N,w) by means of previous result [5] on the explicit formula of generalized power and exponential sums of digital sums
トウイン ニオケル セツジョ フノウ キョクショ シンコウ ショクドウガン ノ チリョウ セイセキ
【背景】遠隔転移のない切除不能局所進行食道癌に対する標準治療は根治的化学放射線療法(CRT)だが,近年Docetaxel/5-FU/ Cisplatin 療法をはじめとした導入化学療法(ICT)からの外科的切除の有用性が報告されている.今回,当院での切除不能局所進行食道癌に対する治療成績について検証した.【対象と方法】2016年から2019年の期間で,当院で治療した切除不能局所進行食道癌9例(リンパ節T4bも含む)を対象とした.【結果】男性:6例,女性:3例.年齢:中央値 64(41-78)歳.腫瘍主占居部位:Ut/Mt/Lt=1/7/1.浸潤臓器:気管/左主気管支/大動脈=2/4/3,cN0/1/2=1/3/5,初回治療: ICT/CRT=7/2であった.初回治療別に検証すると,奏効率:ICT/CRT=5(71.4%)/0(0%)であり,ICTにて奏効が得られた5例は根治切除可能と判断し,4例(80%)でR0切除が得られた.術後合併症は,縫合不全0例,肺炎1例(20%),反回神経麻痺2例(40%)であった.術後在院日数中央値は16日(13-21)であった.R0切除4例は全例1年以上の生存が得られているが,2例で再発(リンパ節再発1例,肺・リンパ節再発1例)を認めた.R1切除例はCRTを追加し,術後2年無再発生存中である.根治切除を施行していない4例の初回治療からの1年生存率は25%と予後不良であった.【結語】切除不能局所進行食道癌であってもICTを組み入れることでconversion surgeryが安全に施行され,高いR0切除率が得られ,予後の延長に寄与する可能性がある.Background:Recently, the usefulness of surgical resection after induction chemotherapy (ICT) including Docetaxel / 5-FU / Cisplatin therapy for locally advanced esophageal cancer has been reported. Methods:Nine patients with locally advanced unresectable esophageal cancer who underwent multidisciplinary treatment in our hospital from 2016 to 2019 were eligible for this study. Results:The patients’ characteristics included a median age of 64 years; the male/female ratio of 6/3; Tumor main occupancy site Ut / Mt / Lt = 1/7/1; Invading adjacent organs: trachea / left main bronchus / aorta; 2/4/3, Lymph node metastasis (0/1/2); 1/3/5, and initial treatment ICT / CRT; 7/2. Response rate of ICT were 71.4% (5 cases) and that of CRT were 0%. Four patients (80%) of 5 patients who responded to ICT were underwent R0 resection. Postoperative complications were anastomotic leakage in 0 cases, pneumonia in 1 case (20%), and recurrent nerve paralysis in 2 cases (40%). The median length of hospital stay after surgery was 16 days. All 4 cases of R0 resection had survived for 1 year or more. The 1-year survival rate from the initial treatment of 4 patients who did not undergo radical resection was 25%. Conclusion:Conversion surgery after ICT for locally advanced unresectable esophageal cancer may contribute to a high R0 resection rate and better clinical outcomes
ショクドウ ソウカン ニヨル フンゴウブ カンゼン リカイ オ カイケッチョウ サイケン デ シュウフクシタ ショクドウ セツジョ ノ 1レイ
症例は60 歳代, 男性. 身長162.6 cm, 体重40.0 kg, Body Mass Index(BMI)15.1 kg / m2であり, 既往歴に慢性閉塞性肺疾患(COPD)を認めた. 胸部上部食道癌 T1b N0 M0 Stage Iに対して食道亜全摘, 3領域リンパ節郭清, 胸骨後胃管再建を施行した.術当日に抜管したが, 術後肺炎に伴う呼吸不全のため, 術後6日目に気管内挿管を試みたが、食道挿管となった.再挿管, 人工呼吸管理の後に軽快し術後13日目に抜管となったが, 術後透視で吻合部周囲に造影剤漏出を認めた. 2ヶ月間の保存的加療で造影剤漏出は消失したが吻合部に長径4 cmの高度狭窄を認めた.内視鏡的拡張術での改善は困難であり, 術後243日目に消化管再建術を施行した. 手術所見として, 第2肋間より頭側の胸骨を切除したところ, 胃管の口側断端は第2肋間の高さの胸骨後面に位置していた.食道断端までは肉芽で置換されていた.胸骨前経路回結腸再建を施行し, 再建術後 8日目に食事を開始し, 合併症なく再建術後30日目に退院となった. 回結腸再建後2年経過後も食道癌の再発は認めず, 通過障害なく経口摂取のみでの生活が可能となっている.A 60s-year-old man underwent endoscopic screening during which a tumor was detected in the upper thoracic esophagus, which was diagnosed as T1bN0M0 Stage I esophageal squamous cell carcinoma. He had a history of chronic obstructive pulmonary disease. He underwent subtotal esophagectomy with 3 field lymph node dissection. Reconstruction was performed by gastric tube through the posterior sternal route. Extubation was performed on the day of surgery. Respiratory failure by postoperative pneumonia occurred, and ventilatory management was performed on the sixth postoperative day. However, the intubation was put into the esophagus. He became well and extubation was performed on the 13th postoperative day. Postoperative fluoroscopy showed contrast leakage around the anastomotic site. After 2 months of conservative treatment, the contrast leak disappeared, but there was a severe stenosis of 4 cm in length at the anastomosis. Endoscopic dilatation was not sufficient to improve the stenosis. Gastrointestinal reconstruction was performed on the 243rd postoperative day. The cephalic sternum was resected, and the gastrointestinal canal opening margin was located on the posterior surface of the sternum, at the level of the second intercostal space. The segment was replaced by a granulation. The patient underwent anterior sternal ileocolic reconstruction. Oral intake started on the 8th day after the reconstruction, and hospital discharge was on the 30 th day after the reconstruction without any complications. Two years after ileocolic reconstruction, there has been no cancer recurrence, and he lives well on oral intake only
トウイン ニオケル キョウクウ キョウカ ショクドウ セツジョ ノ ドウニュウ ト タンキ チリョウ セイセキ ノ ケントウ
【背景】食道癌に対する胸腔鏡手術は本邦で広く行われており、施設ごとに手術手技の定型化がなされている.胸腔鏡下手術の利点として拡大視効果や緻密な手術操作が可能となることが挙げられるが、当院でも2016年より腹臥位胸腔鏡下食道手術を導入し、出血の少ない安全かつ確実な郭清を目指し、定型化に向けてその手技を刷新している.【対象と方法】】2016年4月から2019年4月までに当院で施行した胸腔鏡下食道切除38例につき、その短期成績を検討した.【結果】男:女=32:6、年齢中央値 66歳(41-76)、cStage I / II / III / IVa: 17 / 6 / 13 / 2であった.胸腔内出血量中央値は10ml(0-53)、胸部操作時間中央値は192分(97-478)、胸腔内郭清リンパ節個数中央値は17個(1-42)であった.術後合併症は、縫合不全3例(7.9%)、反回神経麻痺7例(18.4%)、肺炎12例(31.6%)であった.術後在院日数中央値は19日(11-38)であった.導入期からの前半19例では反回神経麻痺を6例(31.6%)に認めたが、後半19例では1例(5.2%)であった(p=0.036).【結語】当院における胸腔鏡下食道切除術は安全に導入、施行可能であった.手術手技が定型化されることで反回神経麻痺を少なくする郭清が可能になると考えられた.Background: Thoracoscopic esophagectomy (TE) is increasingly being used worldwide in patients with esophageal cancer. In this study, we investigated the clinical short-term outcomes of TE performed in patients placed in the prone position. Method: We investigated the surgical and clinical outcomes in 38 patients with esophageal cancer who underwent TE at our hospital between April 2016 and April 2019. Results: Of the 39 patients investigated, 32 were men. Median patient age was 66 (range 41–76) years, the median intraoperative blood loss was 10 (0–53) mL, and the median operation time for thoracoscopy was 192 (97–478) min. The mean operation time for thoracoscopy in the latter group was significantly shorter than that in the former group (188 min vs. 232 min, p=0.013). The following postoperative complications were observed: 7 (18.4%) cases of recurrent nerve palsy, 3 (7.9%) cases of anastomotic leakage, 12 (31.6%) cases of pneumonia, and 0 (0%) cases of chylothorax. The incidence of recurrent nerve palsy was lower in the latter group than in the former group (5.2% vs. 31.6%, p=0.036). Conclusions: TE in the prone position is safe and feasible. As experience performing the procedure increases, the performance of the procedure stabilizes
ノウホウナイ シュッケツ ニ トモナイ シンゴウ キョウド ノ コトナッタ タボウセイ ノウホウ オ テイシタ スイショウエキセイ ノウホウ センシュ ノ 1レイ
症例は33歳,女性.経時的に増大する膵体部嚢胞性病変を認めた.MRIではT1強調画像で低信号を呈する部位とT1強調画像で淡い高信号を呈する,信号強度の異なる大小不同の多房性嚢胞性病変を認め,MRCPおよび超音波内視鏡検査で主膵管拡張および腫瘍と主膵管との交通が疑われた.以上よりmixed typeの膵漿液性嚢胞腺腫を疑ったが粘液性嚢胞腺腫や膵管内乳頭粘液性腫瘍を否定できず,腹腔鏡下脾温存膵体尾部切除術を施行した.病理組織学的検査所見では卵巣様間質は認めず,主膵管交通も認めず,mixed typeの膵漿液性嚢胞腺腫と診断した.膵漿液性嚢胞腺腫は漿液性嚢胞液を有するが,異なった信号強度を呈する多房性嚢胞を有するものはまれである.今回われわれは,信号強度の異なった多房性嚢胞を呈した膵漿液性嚢胞腺腫の1例を経験したので報告する.A 33-year-old woman presented at our hospital with cystic tumor increased over time at pancreatic body. Magnetic resonance image revealed multilocular cysts with different signal intensities, which were mixed to low and slightly high intensities in T1 weighted image. Moreover, the connection of the cyst and main pancreatic duct was suspected by magnetic resonance cholangiopancreatography and endoscopic ultrasonography. We diagnosed as mixed-type serous cystadenoma, yet we could not contradict mucinous cystadenoma and intraductal papillary mucinous neoplasm. Therefore, we performed laparoscopic spleen preserved distal pancreatectomy. Histopathological findings revealed mixed-type serous cystadenoma, and the connection of the cyst and main pancreatic duct was not seen. Serous cystadenoma usually has serous discharge in the cyst and shows uniform signal intensity in the image findings. However, serous cystadenoma with different signal intensities in the multilocular cysts is relatively rare. We described a case of serous cystadenoma of the pancreas with different signal intensities in the multilocular cysts that was treated by laparoscopic surgery
カンサイボウガン ト カンベツ ガ コンナンデアッタ カンケッカンキン シボウシュ ノ 1レイ
肝原発の血管筋脂肪腫(angiomyolipoma; AML)は、肝細胞癌と鑑別が困難な場合がある。今回、単発の肝腫瘍に対して肝細胞癌を否定できず切除を行ったが、病理組織学的検査でAMLと診断した一例を経験したので報告する。症例は50歳代の女性。検診にて外側区域の肝腫瘍を指摘され、加療目的に紹介となった。造影CT検査では肝外側区域、門脈臍部に接して2cm大の腫瘍性病変を認め、動脈相で濃染し平衡相でwashoutしていた。腹部MRI検査では同部位にT2強調像で高信号、T1 out of phaseにて若干の信号低下を認めた。Gadolinium-ethoxybenzyl-diethylene-triaminepentaacetic-acid(Gd-EOB-DTPA; EOB) MRIでは動脈相で濃染、門脈相から平衡相にかけてwashoutし、肝細胞相では低信号であった。画像所見から肝細胞癌を疑い、腹腔鏡下肝左葉切除術を施行した。病理組織学的には好酸性紡錘形細胞や淡明~淡好酸性細胞の上皮様配列がみられ、内部に脂肪組織が島状に介在し、また、平滑筋性の厚い壁を持った血管構造も一部存在しており、肝血管筋脂肪腫と診断した。一般に脂肪成分の少ないAMLは、肝細胞癌との鑑別が困難である。最近では、肝静脈への流出血管の有無が鑑別診断に有用であるとの報告が見られるため、これらを注意深く観察すべきと考えられた。Hepatic angiomyolipoma (AML) may be difficult to distinguish from hepatocellular carcinoma. Here we report a resected case of a hepatic AML mimicking hepatocellular carcinoma. The patient was a woman in her 50s referred for further evaluation of a tumor in the left lateral segment of the liver. Contrast-enhanced computed tomography showed a two cm-sized tumor attached with the umbilical portion in the left lateral segment of the liver, which was enhanced in the arterial phase and washed out in the portal venous phase. Abdominal MRI showed a high-intensity tumor on T2-weighted image and a slight decrease of signal intensity on T1 out of phase. The tumor on Gd-EOB-DTPA enhanced MRI displayed high intensity in the arterial phase and washout in the portal venous phase, and low signal intensity in hepatobiliary phase. Based on these imaging findings, we suspected hepatocellular carcinoma and a laparoscopic left lobectomy was performed. Histopathological examination showed spindle and perivascular epithelioid cells and a few fat cells, and immunohistochemical analysis revealed positive staining of HMB-45 and αSMA. The tumor was diagnosed as a hepatic AML. Hepatic AML with a small fatty component is generally difficult to distinguish from hepatocellular carcinoma. More recently, the presence of outflow blood vessels to the hepatic vein has been reported to be useful in the differential diagnosis for AML. These imaging findings should be carefully observed
ドウニュウ カガク リョウホウ ニテ コンチ セツジョ ガ カノウ トナッタ ケイブ ショクドウガン ノ 1レイ
症例は50歳代,男性.咽頭痛,嚥下障害を主訴に近医受診し,上部消化管内視鏡検査にて頸部食道に1/4周性のtype3病変(squamous cell carcinoma)と食道胃接合部に0-IIa+IIc病変(adenocarcinoma)を指摘され,当院当科紹介となった.造影CT検査にて左頸部に原発巣と一塊となった腫瘤を認め,左総頸動脈及び気管への浸潤を認めた.精査の結果,頸部食道癌cT4bN2M0 cStageIVa,バレット食道腺癌cT1bN0M0 cStageIと診断し,切除不能局所進行食道癌であり導入化学療法の方針とした.DCF(Docetaxel/Cisplatin/5-Fluorouracil) 療法3コースで病変の縮小が得られ,頸部腫瘍は長径37mmから17mmとなり,総頸動脈の浸潤が解除されたため,根治術を行う方針とした.手術は咽頭喉頭食道全摘,頸部縦隔腹部リンパ節郭清,後縦隔経路遊離空腸付加胃管再建,腸瘻造設術を施行した.術中偶発症なく,手術時間846分,出血量670mLであった.病理組織学的検査では,頸部食道癌ypT4aN2M0 ypStegeIII,治療効果Grade 1b,バレット食道癌ypT1b-SM2N0M0 ypStageI,治療効果Grade 1aであった.術後経過は概ね良好で術後9日目より経口摂取を開始し,術後18日目に退院となった. 切除不能局所進行食道癌に対する標準治療は化学放射線療法であるが,近年,DCF療法による導入化学療法後の外科的切除の有用性が報告されている.今回,導入化学療法により根治切除可能であった頸部食道癌,食道腺癌の重複例を経験したため報告する. A 58-year-old man with sore throat and dysphagia revealed type 3 lesion in cervical esophagus and 0-IIa+IIc lesion in esophagogastric junction on upper gastrointestinal endoscopy. Histopathologic examination of biopsy specimens showed squamous cell carcinoma at cervical esophagus and adenocarcinoma at esophagogastric junction. Computed tomography suggested that the large tumor in left neck infiltrated into the common carotid artery and trachea. According to these findings, we diagnosed locally advanced unresectable cervical esophageal cancer (cT4bN2M0, cStageIVa) and Barret’s esophageal adenocarcinoma (cT1bN0M0, cStageI), and decided to perform induction chemotherapy with Docetaxel, Cisplatin, and 5-Fluorouracil (DCF). After 3 courses of that, the primary tumor decreased from 37 mm to 17 mm as major axis and released infiltration into the common carotid artery. Therefore, we performed conversion surgery, pharyngolaryngectomy and total esophagectomy. Histopathological findings showed cervical esophageal cancer (ycT4aN2M0, ycStageIVa) and Barret’s esophageal adenocarcinoma (ycT1b-SM2N0M0, ycStageI). The postoperative course was uneventful, he resumed eating 9 days after surgery and was discharged 18 days after surgery. Conversion surgery after induction chemotherapy for locally advanced unresectable esophageal cancer may contribute to radical resection and better clinical outcome
Digital Sum Problems for the p-adic Expansion of Natural Numbers
Let p be a positive integer greater than 1 and denote the p-adic expansion of n∈N by n=∑_{i≥0}α_{i}(n)p^i, where α_{i}(n)∈{0,1,…,p-1}. We set s(n,l)=∑_{i≥0}1{αi(n)=l} for l=1,2,…,p-1, and s(n)=∑_{l=1}^{p-1}ls(n,l). We define the power sum of sum of digits by Sk(N)=∑_{n=0}^{N-1}s(n)^k, k∈N, and the exponential sum of sum of digits by F(ξ,N)=∑_{n=0}^{N-1}e^{ξs(n)}, ξ∈R for N∈N. Explicit formulas of these sums have been investigated by many authors for a long time. In this paper, developing our previous results, we shall give explicit formulas of F(ξ,N) and S_{k}(N)