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Radiation Oncology/Bile duct/Unresectable Disease

Patients are typically managed with bile duct stent placement to resolve/prevent malignant obstruction and jaundice. Role of radiotherapy is palliative, and involves both EBRT as well as brachytherapy. There are no prospective randomized studies to show benefit, but a number of single institution retrospective studies suggest palliative advantage. Similarly, the role of combined modality therapy is still under investigation. Photodynamic therapy appears to offer survival advantage over supportive care. Some long-term survival (20% at 4-years) with chemoradiotherapy (intraarterial 5-FU).

External Beam RT
The role of external beam RT in this setting is not clear. There are no randomized studies; most reports are single institution retrospective analyses. Some studies show some benefit (symptom relief and survival), while other do not. Some studies also show benefit for higher dose (>45 Gy).

For EBRT literature review, please see the Unresectable Disease/EBRT page.

3D-CRT / IMRT

 * U Chicago PMID 15145161 -- Intensity-modulated radiotherapy in treatment of pancreatic and bile duct malignancies: toxicity and clinical outcome. (2004 Milano MT, Int J Radiat Oncol Biol Phys. 2004 Jun 1;59(2):445-53.)
 * 25 patients (21 pancreas, 3 bile duct, 1 pancreatic neuroectodermal); median follow-up 10.2 months
 * Conclusion : "In this hypothesis-generating analysis, the acute and chronic toxicity profile with IMRT in the treatment of pancreatic and bile duct cancer was encouraging. Local control was not compromised, despite efforts to increase conformality and avoid doses to normal structures. Distant failure remains a major obstacle in pancreatic cancer."

 * Sikoku Japan PMID 15553012 -- Impact of pretreatment cholinesterase level on survival of inoperable intrahepatic or hepatic-hilar carcinomas treated with three-dimensional conformal radiotherapy (2004 Hamamoto Y, Radiat Med. 2004 Sep-Oct;22(5):316-23.)
 * Retrospective. 35 patients with HCC, intrahepatic cholangio and hilar cholangio treated with 3D-CRT (mean 51.5 Gy); mean follow-up 11 months
 * 2-year OS: HCC 19% vs. intrahepatic 26% vs. hilar 39%
 * Pre-treatment cholinesterase value only multivariate prognostic variable (p<0.01)
 * Conclusion : "Pre-3DCRT cholinesterase value was a significant independent prognostic indicator for survival. Benefit of dose escalation above 60 Gy could not be demonstrated."

 * MD Anderson 2000-03 PMID 15234062 -- Daily ultrasound-based image-guided targeting for radiotherapy of upper abdominal malignancies. (2004 Fuss M, Int J Radiat Oncol Biol Phys. 2004 Jul 15;59(4):1245-56.)
 * Retrospective. 62 patients with upper abdominal CA treated with IMRT (10 cholangio/GB)
 * Daily BAT U/S measurements in 1337 patient setups, mean setup time 4.6 min
 * Mean shift from skin mark position: 4.9, 6.0, and 6.0 mm (x, y, z)
 * Proportion alignments corrected by >10, >15, >20 mm: 49%, 25%, 13%
 * Conclusion : "Daily US-guided BAT targeting for patients with upper abdominal tumors was feasible in the vast majority of attempted setups. This method of US-based image-guided tumor targeting has been successfully implemented in clinical routine. The observed improved daily repositioning accuracy might allow for individualized reduction of safety margins and optional dose escalation. Compared with the established application of the BAT device for prostate radiotherapy, in which the target can be directly visualized, the TV in the present study was predominantly positioned relative to guidance vascular structures in close anatomic relation. We perceived an enormous potential in improved and individualized patient positioning for fractionated radiotherapy and also for stereotactic extracranial radiotherapy and radiosurgery, especially for tumors of the liver and pancreas."

 * Erlangen Germany PMID 15592694 -- Chemoradiation May Prolong Survival of Patients with Non-Bulky Unresectable Extrahepatic Biliary CarcinomaA Retrospective Analysis. (2004 Brunner TB, Strahlenther Onkol. 2004 Dec;180(12):751-757.)
 * Retrospective. 98 pts treated with stenting alone or chemoradiation (3D-CRT 50.8 Gy + 5-FU/Gemcitabine)
 * Median survival: overall 11.8 months, stenting alone 9.3 months, chemoradiation 16.5 months (p=NS)
 * Chemoradiation median survival: <40mm tumor 21.4 months vs. >40mm tumor 8.7 months (p=0.01). Toxicity reasonable.
 * Conclusion: "Inclusion criteria for future CRT trials should be based on tumor size at diagnosis: patients otherwise eligible for CRT should only be included with an inoperable tumor </= 40 mm, while patients with larger tumors may only benefit from palliation by stenting."

 * MD Anderson Cancer Center PMID 30152073 -- Dose escalation of radiotherapy in unresectable extrahepatic cholangiocarcinoma. (2018 Elganainy D, Cancer Med. 2018;00:1–13.)
 * Retrospective. 80 patients treated with standard doses or escalated doses of radiation therapy.
 * Median overall survival for all patients was 18.7 months. No significant difference in overall survival between patients who received standard doses vs patients who received escalated doses.
 * Toxicity: Generally treatment was well tolerated. Rate of Grade 3+ acute GI toxicities was 11%.
 * Conclusion: RT dose escalation does not appear to benefit patients with unresectable non-metastatic extrahepatic cholangiocarcinoma probably due to anatomic constraints.

 * Guangzhou China PMID 14625193 -- [Therapeutic effect of three-dimensional conformal radiotherapy on hilar cholangiocarcinoma] - [Article in Chinese] (2003 Wu DH, Di Yi Jun Yi Da Xue Xue Bao. 2003 Nov;23(11):1217-8.)
 * Retrospective. 21 patients treated with 3D-CRT
 * 52% achieved CR or PR, 3-year OS: 14%
 * Complications: 8 (38%) duodenal ulcer, 4 (19%) died of GI bleeding
 * Conclusion : "3D-CRT can be considered as a valuable palliative approach for unresectabe hilar cholangiocarcinoma, and effective management of the late complications of radiotherapy play a key role in increasing survival rates of the patients."

 * Bordeaux France PMID 11899677 -- [Conformal therapy of locally advanced cholangiocarcinoma of the main bile ducts] - [Article in French] (2002 Bouras N, Cancer Radiother. 2002 Feb;6(1):22-9.)
 * Retrospective. 23 patients, 8 after radical resection (R0 but LN+), 7 after microscopic margins (R1), 7 not resected. Dose 45-50 Gy, followed by boost up to 60 Gy; concomittant chemo in 15 cases
 * Late toxicity: stenosis of duodenum, stenosis of biliary anastamosis, 2 cholangitis deaths
 * Median survival (5-year OS): 16.5 months (7%); similar among subgroups
 * Conclusion : "Conformal radiochemotherapy delivering 60 Gy represents a valuable palliative approach in locally advanced biliary carcinoma."

 * Hokkaido Japan PMID 10974464 -- High-speed magnetic resonance imaging for four-dimensional treatment planning of conformal radiotherapy of moving body tumors. (2000 Shimizu S, Int J Radiat Oncol Biol Phys. 2000 Sep 1;48(2):471-4.)
 * High speed MRI to look at movement of implanted fiduciary markers during normal breathing
 * Movement: average 10.6mm CC, 5.2 mm lateral, 4.6 mm AP
 * If PTV determined during exhalation +10mm margin, CTV not covered in 19% of images
 * If PTV determined during inhalation +10mm margin, CTV not covered in 36% of images
 * Conclusion : "Four-dimensional treatment planning using high speed MRI, and integrating time and spatial information, has the potential to determine the planning target volume of moving body tumors more precisely than does conventional CT planning."

 * Review PMID 10436827 -- Conformal irradiation for hepatobiliary malignancies. (1999 Gunderson LL, Ann Oncol. 1999;10 Suppl 4:221-5.)
 * Data presented from U Michigan. Conformal high dose EBRT (48-72.6 Gy) for (HCC) and intrahepatic cholangiocarcinoma (IHCC) to potentially increase local control and survival, over what would be expected with lower dose EBRT.

 * U Michigan PMID 9392548 -- A phase I trial of hepatic arterial bromodeoxyuridine and conformal radiation therapy for patients with primary hepatobiliary cancers or colorectal liver metastases. (1997 Robertson JM, Int J Radiat Oncol Biol Phys. 1997 Dec 1;39(5):1087-92.)
 * Phase I conformal EBRT with dose escalation of BrDU. Unresectable primary hepatobiliary CA or liver mets. RT dose (24, 48, 66) determined by fractionated volume of liver irradiated. 41 patients (18 CRC liver mets, 16 cholangiocarcinoma and 7 hepatoma)
 * Response rates were not improved compared to our previous experience.
 * Conclusion : "The appropriate dose of HA BrdU for Phase II evaluation is 25 mg/kg/day. Neither the hepatic parenchyma nor the gastrointestinal mucosa appeared to be sensitized by this method of BrdU administration. It is anticipated that these, or still newer methods of therapy, can improve treatment results in the near future."

 * U Michigan PMID 8742902 -- 3-D conformal radiation therapy in upper gastrointestinal cancer. The University of Michigan experience. (1996 Lawrence TS, Front Radiat Ther Oncol. 1996;29:221-8.)
 * No Abstract

 * U Michigan PMID 8391066 -- Treatment of primary hepatobiliary cancers with conformal radiation therapy and regional chemotherapy. (1993 Robertson JM, J Clin Oncol. 1993 Jul;11(7):1286-93.)
 * Retrospective. 26 patients treated with concurrent intraarterial FdUrd and conformal RT (1.5-1.65 Gy/fx bid, dose 48-72.6 Gy), 6 diffuse HCC, 11 localized HCC, 9 cholangiocarcinoma
 * Median survival for localized disease: 19 months
 * Conclusion : "These findings suggest that three-dimensional planned focal liver radiation and IAH FdUrd can produce a high, durable response rate and an encouraging median survival duration in patients with nondiffuse, unresectable primary hepatobiliary cancer."

Stereotactic radiosurgery

 * Stanford ASTRO Abstract Phase I Dose Escalation Study of CyberKnife Stereotactic Radiosurgery for Liver Malignancies (2005 Lieskovsky YC, ASTRO 2005 #2089)
 * Phase I. 6 patients/7 tumors (1 IH-CCA, 7 mets). Tumors <5cm. Treatment delivered with motion tracking of implanted fiducials
 * Dose escalation: 3 tumors with 18 Gy, 4 tumors with 22 Gy. MTD not reached. Toxicity: 1 GI Grade 1
 * Response: 4 PR
 * Conclusion : "Results thus far indicate that single fractions of 18 and 22 Gy are safe to administer to liver tumors with the CyberKnife. We have not yet reached the MTD at 22 Gy. We plan to dose-escalate to 30 Gy."

 * Freiburg Germany PMID 16097074 -- Klatskin tumor treated by inter-disciplinary therapies including stereotactic radiotherapy: a case report. (2005 Becker G, World J Gastroenterol. 2005 Aug 21;11(31):4923-6.)
 * Case report. 1 patient with Stage III unresectable Klatskin tumor
 * Total dose 48 Gy (3X4 Gy/wk), therapy was well tolerated.
 * Conclusion : "In the context of inter-disciplinary treatment concepts, this radiotherapy technique is a promising choice of treatment for patients with hilar CCC."

Brachytherapy
Literature review is available at the Unresectable Disease/Brachytherapy page. There are several dozen retrospective single-institution studies. Overall, the trend is toward BT having some benefit in terms of obstruction, and even survival. Howerver, randomized trials are lacking.

Please also see the Malignant Biliary Obstruction section.

Intraoperative RT

 * Mayo PMID 1341262 -- Intraoperative radiotherapy for unresectable cholangiocarcinoma--the Mayo Clinic experience. (1992 Monson JR, Surg Oncol. 1992 Aug;1(4):283-90.)
 * Retrospective. 13 patients treated with EBRT + IORT + stenting
 * Local failure in 50%; morbidity related to biliary sepsis and GI complications
 * Median survival: 16.5 months
 * Conclusion : "Although the median survival of 16.5 months seemed to be an improvement over our previous results for ERT alone or ERT with 5-fluorouracil, the survival data are still discouraging."

 * Tsukuba Japan PMID 2830731 -- The role of intraoperative radiation therapy in the treatment of bile duct cancer. (1988 Iwasaki, World J Surg. 1988 Feb;12(1):91-8.)
 * 81 patients. 50 resected (33 surgery, 14 +IORT, 3 +PORT). 31 not resected (6 +IORT, 4 +EBRT)
 * IORT (20 Gy) not used in curative resection (1 pt), only with incomplete resection (13 pts) or PTCD (6 pts)
 * 2-year OS: Non-curative resection + IORT 17.1% vs. resection alone 9.0%

 * Tsukuba Japan PMID 7427860 -- Intraoperative radiotherapy for advanced carcinoma of the biliary system. (1980 Todoroki T, Cancer. 1980 Nov 15;46(10):2179-84.)
 * Case report 5 pts. IORT (25-30 Gy) for unresectable patients
 * Mean survival: 10.9 months (2 patients living 16+ and 18+ months)
 * Conclusion : "Intraoperative radiotherapy increased the effectiveness and length of palliation for the unresectable lesion."

Proton therapy

 * PSI; 2000 PMID 10924999 -- "The role of proton therapy in the treatment of large irradiation volumes: a comparative planning study of pancreatic and biliary tumors." (Zurlo A, Int J Radiat Oncol Biol Phys. 2000 Aug 1;48(1):277-88.)
 * Treatment planning. 4 patients (2 pancreatic, 2 biliary). IMRT vs PT vs IMPT. RT 50 Gy + 20 Gy boost
 * Outcome: Protons better dose conformality to PTV and better dose homogeneity, except in post-op case
 * Conclusion: Proton therapy superior dose distribution compared to IMRT

Combined Modality

 * Italy 1991-97
 * PMID 16242254 -- Chemoradiation and brachytherapy in biliary tract carcinoma: long-term results. (2005 Deodato F, Int J Radiat Oncol Biol Phys. 2005 Oct 18; [Epub ahead of print])
 * 22 patients (17 unresectable, 5 residual; 13 perihilar, 8 distal, 1 GB) treated with EBRT (39.6-50.4 Gy) + 5-FU; 12 also BT (30-50 Gy @ 1cm)
 * 45% Grade I/II GI toxicity; 2 with EBRT + BT developed duodenal ulceration
 * Median survival: unresectable tumors 13.0 months (EBRT+BT) or 22.0 (EBRT alone), p=NS
 * Conclusion : "This study confirmed the role of concurrent chemoradiation in advanced biliary carcinoma; the role of intraluminal brachytherapy boost remains to be further analyzed in larger clinical trials."
 * PMID 10705013 -- Combined modality treatment in unresectable extrahepatic biliary carcinoma. (2000 Morganti AG, Int J Radiat Oncol Biol Phys 2000; 46:913-9.)
 * 20 patients with noncurative, nonmetastatic disease treated with EBRT (39.6-50.4 Gy), 19 also received 5-FU. 12 (60%) received ILRT (30-50 Gy) boost
 * Median survival: 21.2 months; distant mets in 50% of patients
 * 2 patients with EBRT + ILRT developed late duodenal ulceration
 * Conclusion : "Our data suggest that chemoradiation plus intraluminal brachytherapy was relatively well-tolerated, and resulted in reasonable local control and median survival."

 * Feldkirch Austria PMID 16101189 -- Radiotherapy and razoxane in advanced bile duct carcinomas. (2005 Rhomberg W, Anticancer Res. 2005 Sep-Oct;25(5):3613-8.
 * Prospective. 23 patients EBRT (median 48 Gy) + radiosensitization with razoxane
 * Overall response rate 64%, local control 75%.
 * Side effects: N/V Grade I/II in 61%, leukopenia Grade III/IV 9%
 * Conclusion : "Combined radiotherapy and razoxane led to local response rates which are superior to data from the literature when radiotherapy alone is used. Obstacles to the treatment were complications of the disease and frequent metastasis."

 * Washington University 1999-2002 PMID 15923794 -- A phase II study of alternating cycles of split course radiation therapy and gemcitabine chemotherapy for inoperable pancreatic or biliary tract carcinoma. (2005 Lin LL, Am J Clin Oncol. 2005 Jun;28(3):234-41.)
 * Phase II. 42 patients (40 pancreas, 1 GB, 1 CCA) treated with 3 6-wk courses: (gemcitabine x 2 weeks, 1 week break, RT 50.4 Gy x2 weeks, 1 week break) x 3 courses; followed by resection if response
 * Toxicity: 4 patients Grade 3/4 toxicity
 * 10 PRs, 6 underwent resection; Median survival: 9.5 months (2-32.5)
 * Conclusion : "Alternating cycles of split-course radiotherapy and gemcitabine chemotherapy permits the delivery of full doses of both modalities with acceptable tolerance."

 * Tokyo Japan PMID 16015690 -- Thermo-chemo-radiotherapy for advanced bile duct carcinoma. (2005 Kamisawa T, World J Gastroenterol. 2005 Jul 21;11(27):4206-9.)
 * Retrospective. 8 patients advanced disease and obstructive jaundice, treated with RT + RF heating to 42C + 5-FU+Cisplatin/MTX
 * Mean survival: 13.2 months, 4 patients >20 months. 3CR / 2PR / 3 no change
 * Conclusion : "Although the number of cases is rather small, TCRT in the treatment of locally advanced bile duct carcinoma is promising in raising local control and thus, long-term survival."

 * Erlangen Germany PMID 15592694 -- Chemoradiation May Prolong Survival of Patients with Non-Bulky Unresectable Extrahepatic Biliary CarcinomaA Retrospective Analysis. (2004 Brunner TB, Strahlenther Onkol. 2004 Dec;180(12):751-757.)
 * Retrospective. 98 pts treated with stenting alone or chemoradiation (3D-CRT 50.8 Gy + 5-FU/Gemcitabine)
 * Median survival: overall 11.8 months, stenting alone 9.3 months, chemoradiation 16.5 months (p=NS)
 * Chemoradiation median survival: <40mm tumor 21.4 months vs. >40mm tumor 8.7 months (p=0.01). Toxicity reasonable.
 * Conclusion : "Inclusion criteria for future CRT trials should be based on tumor size at diagnosis: patients otherwise eligible for CRT should only be included with an inoperable tumor </= 40 mm, while patients with larger tumors may only benefit from palliation by stenting."

 * Oita Japan 1993-2002 PMID 15160347 -- Radiotherapy combined with transarterial infusion chemotherapy and concurrent infusion of a vasoconstrictor agent for nonresectable advanced hepatic hilar duct carcinoma. (2004 Matsumoto S, Cancer. 2004 Jun 1;100(11):2422-9.)
 * Retrospective. 23 patients treated with EBRT (mean 41.4 Gy) + transarterial infusion of epirubicin/mitomycin C/5-FU
 * Response rate 41%. OS 1 year (59%), 2 years (36%), and 3 years (18%)
 * Conclusion : "The combination of radiotherapy, transarterial infusion chemotherapy, and concurrent infusion of a vasoconstrictor can be delivered safely with good efficacy for patients with advanced hilar duct carcinoma."

 * Italy PMID 12972696 -- Concomitant gemcitabine (Gemzar) and extended nodes irradiation in the treatment of pancreatic and biliary carcinoma: a phase I study. (2003 Morganti AG, Onkologie. 2003 Aug;26(4):325-9.)
 * Phase I dose escalation. 15 patients (5 after radical resection). EBRT using 3F technique + gemcitabine short infusion once/week
 * No dose-limiting toxicity at gemcitabine 100-250mg/m2. 3 DLTs at 300 mg/m2
 * 6 patients stable disease, 4 patients progressive disease
 * Conclusion : "Based on this study, the recommended dose for weekly short infusional gemcitabine combined with radiation therapy to the tumor and lymph nodes is 250 mg/m(2). This value is suggestive of a correlation between acute toxicity and inclusion of lymph nodes in the irradiated volume."

 * MD Anderson 1957-2000 PMID 12095564 -- Limitations of conventional doses of chemoradiation for unresectable biliary cancer. (2002 Crane CH, Int J Radiat Oncol Biol Phys. 2002 Jul 15;53(4):969-74.
 * Retrospective. 52 patients treated with RT +/- chemo. Pts grouped by dose: 30 Gy (52%) vs. 36-50.4 Gy (27%) vs. 54-85 Gy (21%). Additionally, 73% received protracted venous 5-FU infusion
 * Median time to radiographic progression: 9 months vs. 11 months vs. 15 months (p=NS)
 * Median survival: 10 months
 * No variables (RT dose, chemo, grade, size) had influence on progression or OS
 * Conclusion : "The primary limitation of definitive chemoradiation was local progression. Although the small patient numbers limited the statistical power of this study, a suggestion of improved local control was found with the use of higher RT doses."

 * Mie Japan PMID 11788896 -- Clinical efficacy of brachytherapy combined with external-beam radiotherapy and repeated arterial infusion chemotherapy in patients with unresectable extrahepatic bile duct cancer. (2002 Nomura M, Int J Oncol. 2002 Feb;20(2):325-31.)
 * Retrospective. 17 patients treated with BT alone (5), BT+EBRT (12), HA infusion (1), or HA infusion+BT+EBRT (6)
 * Mean survival: BT alone 4.6 months vs. HA infusion+BT 16.2 months (p<0.01)
 * RT >50 Gy resulted in radiation gastritis
 * Conclusion : "Brachytherapy combined with external-beam radiotherapy and repeated hepatic arterial infusion chemotherapy increases survival compared with brachytherapy alone in patients with unresectable bile duct cancer."

 * Michigan PMID 9069303 -- Long-term results of hepatic artery fluorodeoxyuridine and conformal radiation therapy for primary hepatobiliary cancers. (1997 Robertson JM, Int J Radiat Oncol Biol Phys. 1997 Jan 15;37(2):325-30.)
 * Retrospective. 22 patients (11 HCC and 11 cholangio) with unresectable tumors, treated with concurrent HA FdUrd + conformal EBRT (48-66 Gy)
 * Median survival (4-year OS): 16 months (20%)
 * Conclusion : "Combined conformal RT and HA FdUrd can produce long-term freedom from hepatic progression and survival in patients with unresectable, nondiffuse primary hepatobiliary malignancies. There were no long-term liver complications observed."

 * Princess Margaret PMID 8567347 -- A phase I study of combined radiation therapy with 5-fluorouracil and low dose folinic acid in patients with locally advanced pancreatic or biliary carcinoma. (1996 Hsue V, Int J Radiat Oncol Biol Phys. 1996 Jan 15;34(2):445-50.)
 * Phase I. 27 patients (pancreas 19, BD 7, GB 1). EBRT split course 40 Gy (20 Gy in 10 fxs, 2 weeks, 20 Gy in 10 fxs) + 5-FU (300-375) + folinic acid.
 * Toxicity: 8 patients Grade 3/4, 4 did not complete treatment, 2 treatment deaths to septic neutropenia
 * Conclusion : "This protocol is poorly tolerated by elderly patients or those with poor performance status, and 350 mg/m2/day is our recommended dose for 5FU as given in this protocol."

 * Jefferson 1984-90 PMID 8138448 -- The impact of radiation dose in combined external beam and intraluminal Ir-192 brachytherapy for bile duct cancer. (1994 Alden ME, Int J Radiat Oncol Biol Phys. 1994 Mar 1;28(4):945-51)
 * Retrospective. 48 patients treated, 24 received RT (EBRT mean 46Gy + ILRT 192Ir mean 25 Gy) + CT (5FU +/- Adriamycin/Mitomycin)
 * Mean survival (2-year OS): no RT 5.5 mo (17%) vs. CMT 12 mo (30%) p=0.01
 * Mean survival (2-year OS): RT <55 Gy 6 mo (0%) vs. RT >55 Gy 24 mo (48%) p=0.003. Dose response suggested
 * Conclusion : "A dose response is shown with more than double the 2-year and median survival for doses > 55 Gy. A brachytherapy dose of 25 Gy, plus 44-46 Gy external beam is well tolerated. High dose combined brachytherapy and external beam radiation (60-75 Gy) appears to be the most effective modality for extrahepatic bile duct cancer."

 * Med Col Ohio PMID 3756765 -- 125I interstitial implant, precision high-dose external beam therapy, and 5-FU for unresectable adenocarcinoma of pancreas and extrahepatic biliary tree. (1986 Dobelbower RR, Cancer. 1986 Nov 15;58(10):2185-95.)
 * 14 patients (2 EHBD, 12 pancreas) treated with EBRT (48.6-63 Gy) + BT (median 140 Gy) + 5FU
 * Acute morbidity: 2 pancreatic fistula, 1 GIB, 1 PE, 1 cholangitis
 * Case presentation of 2 EHBD patients

 * PMID 4186452 -- Combined 5-fluorouracil and supervoltage radiation therapy of locally unresectable gastrointestinal cancer. (1969 Moertel CG, Lancet. 1969 Oct 25;2(7626):865-7.)

Targeted therapy

 * MSKCC PMID 16138120 -- Treatment of cholangiocarcinoma with oncolytic herpes simplex virus combined with external beam radiation therapy. (2005 Jarnagin WR, Cancer Gene Ther. 2005 Sep 2; [Epub ahead of print])
 * Cell lines.
 * Conclusion : "Combined XRT and oncolytic viral therapy is a potentially important treatment strategy that may enhance the therapeutic ratios of both individual therapies.)

 * Hopkins PMID 1657845 -- Variable low dose rate irradiation (131I-anti-CEA) and integrated low dose chemotherapy in the treatment of nonresectable primary intrahepatic cholangiocarcinoma. (1991 Stillwagon GB, Int J Radiat Oncol Biol Phys. 1991 Nov;21(6):1601-5.)
 * 24 patients prospectively treated with induction (RT 21 Gy @ 3 Gy/fx + doxorubicin + 5-FU), followed one month later by doxorubicin + cisplatin + 131I anti-CEA), repeated q 2 months
 * Toxicity: Grade 4 thrombocytopenia (17%) and leukopenia (4%)
 * Median survival: 10.1 months (compared with prior protocol 6.5 months)

 * RTOG PMID 6085756 -- Comparative tumor dose from 131I-labeled polyclonal anti-ferritin, anti-AFP, and anti-CEA in primary liver cancers. (1984 Leichner PK, Cancer Drug Deliv. 1984 Fall;1(4):321-8.)
 * Dosimetric studies for 30 patients with HCC and 5 patients with hepatic CCA.
 * Hepatoma (30 mCi day 0, 20 mCi day 5): mean dose anti-ferritin 11 Gy, anti-AFP 3.5 Gy, combination anti-ferritin/anti-AFP 9.6 Gy
 * CCA (20 mCi day 0, 10 mCi day 5): mean dose 6.2 Gy
 * Total-body irradiation for these injection schedules ranged from 0.3 to 0.50 Gy

Chemotherapy

 * Yonsei Korea PMID 16294346 -- Capecitabine combined with gemcitabine (CapGem) as first-line treatment in patients with advanced/metastatic biliary tract carcinoma. (2005 Cho JY, Cancer. 2005 Nov 17; [Epub ahead of print])
 * Phase II. 44 patients. Oral capecitabine + gemcitabine (CapGem) as first line therapy.
 * Response: 32% PR, 34% SD. Median OS 14 months
 * Toxicity: No Grade 4, transient Grade 3 heme
 * Conclusion : "CapGem is an active and well tolerated first-line combination chemotherapy regimen for patients with advanced/metastatic biliary tract carcinoma that offers a convenient home-based therapy."

 * NCC Japan PMID 16142487 -- Phase II study of single-agent gemcitabine in patients with advanced biliary tract cancer. (2005 Okusaka T, Cancer Chemother Pharmacol. 2005 Sep 2;:1-7 [Epub ahead of print])
 * Phase II. 40 patients. Gemcitabine 1000mg/m2 over 30 min qw
 * Response: 7% PR, 37% SD, 42% PD. Median survival 7.6 months
 * Toxicity: Grade 3/4 30% neutropenia, 12% leukopenia, 10% anemia, 15% liver
 * Conclusion : "In single-agent therapy, gemcitabine demonstrated moderate efficacy with manageable toxicity in patients with advanced or metastatic biliary tract cancer. Further evaluations are warranted, including the exact impact of gemcitabine on the management of advanced or metastatic biliary tract cancer."

 * Munich Germany PMID 15949047 -- Phase II trial of weekly 24-hour infusion of gemcitabine in patients with advanced gallbladder and biliary tract carcinoma. (2005 von Delius S, BMC Cancer. 2005 Jun 12;5(1):61.)
 * Phase I. 19 patients. Gemcitabine 100mg/m2 24 hour infusion on day 1, 8, 15 q28 days until progression
 * Response: 6% PR, 61% SD. Median OS 7.5 months
 * Toxicity: moderate myelosuppression
 * Conclusion : "Weekly 24-hour gemcitabine at a dose of 100 mg/m2 is well tolerated. There was a relatively high rate of disease control for a median duration of 5.3 months (range 2.8-18.8 months). However, the objective response rate of this regimen in gallbladder and biliary tract carcinomas was limited."

Malignant Biliary Obstruction
Please see the Malignant Biliary Obstruction section.

Photodynamic Therapy

 * CHUV Switzerland PMID 14598251 -- Successful photodynamic therapy for nonresectable cholangiocarcinoma: a randomized prospective study. (2003 Ortner ME, Gastroenterology. 2003 Nov;125(5):1355-63.)
 * Prospective randomized open-label. 39 patients with unresectable CCA, 20 to stenting + PDT vs. 19 to stenting alone
 * Median survival: stent + PDT 16.4 months vs. stent alone 3.3 months (p<0.001); Also improvement in biliary drainage and quality of life
 * Conclusion : "PDT, given in addition to best supportive care, improves survival in patients with NCC. The study was terminated prematurely because PDT proved to be so superior to simple stenting treatment that further randomization was deemed unethical."


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IB Biology/Option G - Ecology and Conservation

Return to IB Biology Originally obtained from and edited by Robert Wiblin.

Ecology of Species
Ecology is the scientific study of the interrelations between the living organisms and their environment including both the abiotic and biotic factors with emphasis on the interspecific and intraspecific relations between them.

Outline the factors that affect the distribution of plant species including temperature, water, light, soil pH, salinity, and mineral nutrients.
 * High temperature denatures enzymes and retards growth of plants; the rate of transpiration (loss of :water) is also increased. Low temperatures decrease enzyme activity and freezing temperatures inactivate enzymes. Most plants live in moderate temperature zones.
 * Water is needed for enzyme activity, transport, photosynthesis, support, and many other things. There is a low diversity of plants in deserts and polar regions.
 * Light is important for photosynthesis and flowering. Dark areas have small numbers of plants.
 * Soil pH is important for absorption of nutrients. If soil is acidic, desertification can occur; the use of limestone can neutralise the soil.
 * Salinity has an affect on the absorption through osmosis. High salinity causes plants to lose water through osmosis. Halophytes live in high salinity.
 * Mineral nutrients are needed for many vital functions. Nitrogen is needed to manufacture proteins, enzymes, nucleotides, vitamins, and other compounds. Phosphorous is used in the formation of phospholipid and other structures.

Explain the factors that affect the distribution of animal species including temperature, water, breeding sites, food supply and territory.
 * Temperatures affect the concentration of animals. Only especially adapted organisms can live in extreme temperatures.
 * Water is needed for vital functions, so only animals that can conserve water are found in deserts.
 * Breeding sites are needed for growth and protection of young. Some need specific areas to breed. High animal diversity is found in areas with varied topographical nature.
 * Food supply is important for survival since animals are heterotrophs. High animal diversity is once again found in the rain forest.
 * Some animals are territorial and need large areas for feeding, mating, and protecting their young. Some are territorial during breeding season and occupy areas to prevents others from approaching them. There is high animal distribution where there is room to occupy territory and defend against other members of the species.

Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables.
 * The t-test can be used to measure whether there is a significant difference between the means of two populations. For example if you measure the weight of rabbits on two islands the t-test formula will work out whether there is a significant difference based on the difference between the means and the degree of variation among them. A table of critical t values is used to determine the probability that the difference is simply random chance.

Explain what is meant by the niche concept, including an organism's spatial habitat, its feeding activities and its interactions with other organisms.
 * A niche is all the characteristics, biotic and abiotic, specific to a species. It includes the habitat, nutrition, and relationships. For example, the place that the species sleeps, lives, breeds, its food source and relationship with other species.

Explain the principle of competitive exclusion.
 * First proposed by Lokta and Volterra, competitive exclusion takes place when two species need the same resources, and will therefore compete until one species is removed. In any situation where two species are very similar and are vying for the same food source or breeding ground, one would be somewhat more capable of controlling the resources or reproducing rapidly. The other is run out of existence. Experiments with bacteria populations in the lab of Russian ecologist G.F. Gause demonstrated that this concept was accurate in practice. This principle was termed competitive exclusion.

 * No two species can live in the same niche, because there is competition for the resources of the land and only one species will survive.

Ecology of Communities
Explain the following interactions between species, giving two examples of each: competition, herbivory, predation, parasitism, and mutualism.
 * Competition is when two species need the same resource such as a breeding site or food. Usually one of the species will out-compete the other. The Douglas Fir and Western Hemlock are trees that compete in the USA.
 * Herbivory is the relation between an animal and a plant. Different animals feed on different plants. Deer feed on tree leaves, rabbit feed on grass, giraffes on trees.
 * Predation is the relation between the predator, which is usually bigger, and the prey, which is usually smaller. An example would be a fox and a rabbit, or bonitos on anchovies.
 * Parasitism is the relation between the host and the parasite. The parasite causes harm to the host to get food and other resources. Examples of parasites are the malaria protist and tapeworm in humans.
 * Mutualism is where two members of different species benefit and neither suffers. Examples include rumen bacteria/protazoa that digest cellulose in the digestive systems of cows, providing the cow with an energy source and the bacteria with a stable habitat. Lichens and Chlorella/Chlorohydra, an algae, also exhibit such a relation. The lichen provide an means of attaching to the surface, and the algae photosynthesize to produce a source of sugars and nutrients.

Define gross production, net production, and biomass.
 * Gross production is the total amount of organic matter produced per unit area per unit time by a trophic level in an ecosystem.
 * Net production of an ecosystem is gross production less the material expended by the plants in respiration.
 * Both of these are measured in kJ per squared meter per year.
 * Biomass is the dry mass of organic matter in organisms of an ecosystem.

Calculate values for gross production and biomass from given data.
 * Gross Production - Respiration = Net Production

Discuss the difficulties of classifying organisms into trophic levels.
 * It is difficult due to the fact that some organisms can be secondary, tertiary, and may be quaternary consumers at the same time, such as humans. It is difficult to place them on a certain level of the food pyramid.
 * For this reason, an alternate method of classification - the food web - has been developed. The food web displays relationships not as a simple hierarchy but rather a complex network, with the various feeding relationships between species existing as connections and the animals themselves existing as the hubs.

Explain the small biomass and low numbers of organisms in higher trophic levels.
 * There is a decreasing biomass of organisms in the higher trophic levels because energy is lost between levels in the form of heat (respiration), waste, and dead material. Around 10-20% of the energy proceeds on to the next trophic level.

Construct a pyramid of energy given appropriate information.
 * The lowest bar of the pyramid of energy represents gross primary productivity, the next bar is the energy ingested as food by primary consumers, and so on. The arrows demonstrate the direction of energy flow. The units are energy per unit area per unit time.

Describe ecological succession using one example
 * Ecological succession is the gradual change in the composition of a community with time in an ecosystem. If succession occurs in a lifeless area it is primary succession. It can start after things such as volcanoes, fire or flood.
 * The process is usually goes: lichen, moss, ferns, flowerings plants, conifers.
 * For example on the Volcan Osorno in south Chile after ash covers the ground: mosses spread over the ash. Small herbs and ferns arrive and through the activity of their roots, soil formation starts to occur. Shrubs and bushes grow and replace these. Then flowering trees grow, then conifers, and other larger trees producing a forest.

Explain the effects of living organisms on the abiotic environment with reference to the changes occurring during ecological succession to climax communities
 * Living organisms can help with soil development, as a plant grows, their roots grow deeper down and break rock into small particles, helping soil formation. Plants enrich the soil with minerals as they die and decompose. The plant roots hold the soil particles together, preventing soil erosion and retain nutrients. The water that evaporates from many plant leaves condenses and comes down in the form of rain. The presence of organic materials in the soil and the presence of roots and root hair help in the retention of water and slows down drainage.

Biodiversity and Conservation
'''Discuss reasons for the conservation of biodiversity using rainforests as an example. Reasons should include ethical, ecological, economic, and aesthetic arguments.'''
 * Biodiversity is highest in the tropical rainforests.
 * Ethical reasons for conserving biodiversity are that all species have a right to live on this planet. Many People have a cultural connection to the biological world. Future humans have a right to enjoy a healthy planet as we do today.
 * Ecological reasons are that species live with great interaction and dependence on each other. If one species dies out, a food chain is disrupted, therefore disrupting all of the other species as well. Species are adapted to particular conditions while other species may take a long time to adapt themselves. They help to dramatically reduce carbon dioxide levels.
 * Aesthetic reasons are that the tropical rain forest is one of the most beautiful attractions on this planet. There is variety everywhere in the rainforest. Many artists have been inspired by the diversity of life around them.
 * Economic reasons include that the rainforest is a source of materials important to human life. They regulate the weather and recycle nutrients and detoxify water. Medicinal substances can be taken from a variety of plants in the rain forest, new crop plants may be uncovered and ecotourism offers a new source of funds for the many impoverished nations these forests exist in.

Outline the factors that caused the extinction of one named animal and one named plant species.
 * The Arizona Jaguar became extinct due to an increased demand for its fur. As the human population increased in the areas inhabited by the jaguar, the hunting and shooting increased and the last of this rare animal was shot in 1905 in New Mexico.
 * The Fluffy groundsel is a kind of herbal plant with clusters of yellow flowers. It became extinct because of farming, building, road construction and other sorts of human impact in the American South West.

Outline the use of the Simpson diversity index.
 * The Simpson diversity index is a measure of species diversity
 * D = (N(N-1))/(summation of n(n-1)). D is the diversity index, N is the total number of organisms of all species found, n is the number of individuals of a particular species.
 * A high value of D suggests a stable and ancient ecosystem and a low D value could suggest pollution, recent succession or agricultural management.
 * The index is determined by counting organisms on randomly chosen parts of an area. Monitoring over time shows changes in an ecosystem.

Explain the use of biotic indices and indicator species in monitoring environmental change.
 * Indicator species are highly sensitive to environmental changes and their populations increase or decrease significantly depending on changes in the environment. They are good indicators of change. Frog populations are very vulnerable to pollution and other forms of change, while sludge worms are good indicators of low oxygen concentration in waterways.
 * Biotic indices are calculated via the number of tolerant and intolerant species at a time. The numbers of these organisms in the indicator species populations can be monitored over time directly so they are easy to keep track of.

Outline the damage caused to marine ecosystems by the over-exploitation of fish.
 * If the population of fish is fished excessively and the number of adult fish fall below a critical level, spawning fails which can lead to fish population crashes and destroy the fishing industry.
 * This occurred in Peru to anchoveta fishers in 1973 when the haul plummeted to nothing.

Discuss the international measures that would promote the conservation of fish.
 * International measures are necessary because many fish move through the oceans of multiple countries. Fish stocks in the ocean have fallen very significantly over the last 50 years due to excessive fishing. Enforcement is very difficult for any rules.
 * International measures that could be taken are monitoring of stocks and of reproduction rates, quotas for catches of species with low stocks, moratoria on catching endangered species, minimum net sizes, so that immature fish are not caught, and banning of drift nets, which catch many different species of fish indiscriminately.
 * The ICES is a name example of an international agency that advises limits on catching fish.

Discuss the advantages of in situ conservation of endangered species (terrestrial and aquatic nature reserves).
 * These are places where the animal is found in its own natural habitat and is not allowed to be disturbed by humans and their activities.
 * This keeps the animals out of danger zones and allows them to live and reproduce naturally in its own environment. Most animals typically survive at a much greater rate using in situ conservation, and preserving their habitat allows other species to live there also, thus preserving other animals and biodiversity. Greater genetic variety is also ensured.
 * However, sometimes numbers reach such low levels that the animals cannot be left unprotected in the wild or a habitat is being destroyed and this will not be stopped.

Outline the management of nature reserves.
 * A nature reserve is maintained by controlling alien species. Those that are not originally supposed to be in the area are removed.
 * They restore degraded areas where human impact has destroyed the ecosystem by methods such as reforestation and species reintroduction.
 * They promote the recovery of threatened species through feeding, for example.
 * They also control the exploitation by humans. Logging is controlled along with land clearing. If trees are cut down, more are planted.

Outline the use of ex situ conservation measures including captive breeding of animals, botanic gardens, and seed banks.
 * For captive breeding, animals kept in zoos or parks are allowed to reproduce in order to give them a chance to increase in number, with the possibility of eventually reintroducing some of the offspring into the wild. Unfortunately many do not reproduce. Elephants are an example.
 * Botanic gardens are sites where many plant species are planted in controlled environments to maintain their species. The Botanic Gardens of Kew has a massive collection of 50,000 species.
 * Seed banks are where seeds are kept in cold and dry storage, since they stay in good condition for hundred of years.

Discuss the role of international agencies and conservation measures including CITES and WWF.
 * CITES is an agreement that aims to control and regulate cross-border trade in endangered wildlife and wildlife products and so reduce poaching. Elephant poaching for example has been reduced through its listing on the agreement.
 * WWF is an independent organisation that attempts to save biodiversity and wildlife through political lobbying and monitoring projects. They try to keep areas from being cut down by buying areas of land and establishing them as nature reserves.

AHL The Nitrogen Cycle
State that all chemical elements occurring in organisms are part of biogeochemical cycles and that these cycles involve water, land and the atmosphere.

Explain that all biogeochemical cycles summarize the movement of elements through the biological components of ecosystems (food chains) to form complex organic molecules, and subsequently simpler inorganic forms which can be used again.
 * All chemical elements occurring in organisms are part of biogeochemical cycles and these cycles involve water, land and the atmosphere.
 * The simple inorganic forms are absorbed and converted into complex organic forms but then broken down again into simple forms and released into the environment for reabsorption.

Explain that chemoautotrophs can oxidise inorganic substances as a direct energy source to synthesize ATP.

State that chemoautotrophy is found only among bacteria.
 * Only bacteria can make their food through chemoautotrophy. They perform reactions using inorganic substances such as nitrates, ammonia and sulphur. The oxidisation of these substances results in energy. The energy is then used to fix carbon dioxide into glucose as in the Calvin cycle.

Draw a diagram of a nitrogen cycle. See Nitrogen cycle
 * Gaseous nitrogen is converted into biomass nitrate for plants and bacteria through the process of nitrogen fixation. Other bacteria also release nitrogen back into the air. When plants and animals die, proteins are broken down - deamination occurs, ammonia is formed, oxidation occurs producing nitrite, more oxidation occurs producing nitrate, then it can follow this path through another plant again or continue through bacteria in the soil. Ammonia is also formed by nitrogen gas through lighting and the Haber process (produces fertilizer).
 * This nitrogen cycle is not the only one present in an ecosystem that returns complex molecules to simple and simple to complex over and over again. The vast majority of other organic substances, such as potassium are also recycled in this manner, thus allowing ecosystems to survive without a constant influx of new organisms or nutrients.

Outline the roles of Rhizobium, Azobacter, Nitrosomonous, Nitrobacter and Pseudomonas dentrificans in the nitrogen cycle.
 * Rhizobium Azobacter are nitrogen fixing bacteria that can create nitrate from nitrogen gas. Nitosomonous oxidises ammonia to form nitrite. Nitrobacter oxidizes nitrite to form nitrate. Pseudomonas is a dentrifying bacteria that creates free nitrogen in the air from nitrate. The first four of these take inorganic nitrogen compounds found in the soil and transform them into a substance that can be used by plants and the last returns them to the atmosphere, away from plants.

Describe the conditions that favour dentrification and nitrification.
 * A harmful type of bacteria are denitrifying bacteria. They converts nitrate into free nitrogen gas. This decreases soil fertility and plant growth. These kind of bacteria are usually only found in water-logged soils. Water logging results in poor aeration and deficiency of oxygen in the soil.

Discuss the action taken by farmers/gardeners to increase the nitrogen fertility of the soil including fertilizers, ploughing /digging and crop rotation (use of legumes).
 * Nitrification occurs in ploughed soil because then the oxygen gets into the soil and makes it unfavourable for dentrifying bacteria.
 * Farmers plough the soil to make air space between the soil particles. The oxygen makes it an unfavourable condition for dentrifying bacteria and encourage the growth of nitrogen fixing bacteria.
 * Fertilizers are another option used to ensure proper nitrogen levels in the soil: processed from inorganic nitrogen, they provide a guaranteed heavy source of nitrogen compounds to plants. However, they have a tendency to leach out of the soil rapidly, and can often harm to the surrounding environment.
 * The final method, crop rotation, involves rotating crop planting between the crop the farmer wishes to grow and some kind of legume crop. Legumes form symbiotic relationships with nitrogen-fixing bacteria, allowing these bacteria to produce their own source of nitrates from inorganic or atmospheric nitrogen. Under favourable conditions, these plants can produce enough excess nitrogen that it renews the soil's store of nitrates capable of being used by plants next year. The following year, non-legume crops are planted on the field the legumes previously grown on.

AHL Impacts of Humans on Ecosystems
Describe the role of atmospheric ozone in absorbing ultra violet (UV) radiation.
 * Ozone exists in the upper atmosphere and is formed from oxygen. It absorbs UV light from the sun, breaking down and converting the UV energy into heat. This results in the conversion of UV light energy into heat energy. The ozone layer is continually formed and destroyed and protects the Earth from most dangerous UV radiation.

Outline the effects of UV radiation on living tissues and biological productivity.
 * UV radiation can kill phytoplankton, the sea-going organisms that account for a significant portion of net photosynthesis that occurs in the biosphere. This affects the whole oceanic food web.
 * The radiation retards the growth of terrestrial plants by slowing their rate of photosynthesis, usually a result of radiative damage and subsequent mutations in plant leaves. High levels of UV light can also kill symbiotic bacteria that fixes nitrogen in the root nodules of legumes.
 * Increases in UV exposure will increase rates of skin cancer, sunburn and eye cataracts in animals

Outline the chemical effect of chlorine on the ozone layer.
 * Chlorine (broken away from CFC molecules by UV light) reacts with ozone and breaks down into oxygen. One chlorine can break down thousands of ozone molecules. This leads to depletion of the ozone layer and the passage of UV light through the ozone hole.

Discuss methods of reducing the manufacture and release of ozone depleting substances including recycling refrigerants, reducing production of gas-blown plastics and using CFC-free propellants.
 * In 1987, after research had shown that CFCs were depleting the ozone layer, the Montreal protocol was created which set deadlines for the replacement of CFCs with non-ozone depleting substances.
 * Two of the largest sources of ozone-depleting substances come from the production of recycling refrigerants, gas blown plastics and the use of (CFCs) for propellants in spray cans, hairspray, etc. These chemicals have largely been removed and most corporations now recycle the refrigerants used rather than produce entirely new ones.
 * Nitrogen oxides also deplete the ozone layer and can be reduced through reduced use of fossil fuels, less polluting combustion engines and cleaner plane engines.
 * Ozone levels should start returning to normal around 2010 and be normal again by 2050 due to these measures.

Outline the consequences of releasing raw sewage and nitrate fertiliser into rivers.
 * Water polluted nitrate fertilisers will become rich in nutrients. The algae absorb large amounts of nitrates and this results in quick growth and reproduction of these algae and so the ecosystem becomes overpopulated with algae (algal blooms). This blocks the sun from reaching the photosynthetic plants at deeper levels and blocks the entry of carbon dioxide and oxygen from the atmosphere. The algae exceed their carrying capacity, the nutrients run out and they start to die quickly, encouraging the growth of the bacteria which digest them and increase the biochemical oxygen demand. They consume a large amount of oxygen and this results in deoxygenation of the water and aerobic organisms die. Finally, anaerobic bacteria develop producing poisonous hydrogenous compounds like H2S. By now most aquatic life has died.
 * When raw sewage is released bacteria grow first, deoxygenate the water and release the phosphates and nitrates used by algae. These grow and reoxygenate the water, after which they are eaten. At this time aquatic life may recover.
 * Raw sewage can also release pathogens into the bathing and drinking water supplies, causing the risk of human and animal infection when this water is used.

Outline the origin, formation and biological consequences of acid precipitation on plants and animals.
 * Acid precipitation occurs primarily because of the presence in the atmosphere of sulphur oxides and nitrogen oxides that react with water in the air to form acids like sulphuric acid and nitric acid. Sulphur and nitrogen oxides come from the combustion of fossil fuels and industries.
 * The acidic rain helps release aluminium ions from soil into waterways. Aluminium is acidic too and toxic to fish. Both lower the pH of lakes and contaminate freshwater habitats. It affects fish, amphibians and aquatic invertebrates the most, due to the destruction of their freshwater lake and river environment.
 * Calcium, magnesium and potassium ions are leached out of the soil, reducing fertility and plant growth.

State that biomass can be used as a source of fuels such as methane and ethanol.
 * Biomass, like wood, is already burnt for fuel. Biomass can also be used as a source of fuels such as methane and ethanol.

Explain the principles involved in the generation of methane from biomass, including the conditions needed, organisms involved and the basic chemical reactions that occur.
 * Any organic rubbish, such as remains of food, are placed in a sealed container. Methanogenic bacteria such as methanobacillus and methanococcus are added. The container must be sealed to ensure anaerobic conditions. Bacteria decompose organic material in the rubbish to organic acids and alcohol. Bacteria use these as a source of hydrogen. The hydrogen is used to reduce carbon dioxide into methane. The methane is then burnt as a source of energy. The digested material is rich in nutrients and used as fertiliser.


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Cookbook:Cottage Cheese

| Cheese

Cottage cheese is a class of tangy fresh cheeses. The term cottage cheese is often confused with or inappropriately applied to other fresh curd cheeses, such as queso fresco, paneer, and quark.

Characteristics
All varieties of cottage cheese are made by culturing milk before setting with rennet, cutting, and cooking the curds as when making several other cheeses. The curds are then drained of whey, which is where the varieties begin to differentiate themselves.

Cottage cheese
Cottage cheese proper is the moistest of the varieties, which is caused both by draining less of the whey and by mixing the curds with a variable but small amount of soured milk and/or cream. The curds can range from small to large, though they often maintain their individual character, and the exact moisture and fat contents will differ depending on the producer.

Farmer's cheese
This variety is made by pressing a large amount amount of liquid from the curds instead of simply draining it. It tends to have a grainy texture instead of distinct pieces of curd, which together with the lower moisture content makes farmer's cheese sliceable and crumbly. Some European varieties may be more like quark in texture or may even be called quark.

Pot cheese
Pot cheese is somewhere between cottage and farmer's cheeses, without a precise definition. Generally speaking, it is drier than the former but moister than the latter.

Selection and storage
Because moisture content is often critical to dishes, it's important to make sure you select the correct variety. Since the terminology may be used imprecisely, when in doubt, try to clarify what exactly is called for in a given recipe. As a fresh cheese, it must be stored in the fridge —depending on the preservative and moisture content, it can last for a little while before becoming unsafe to eat, but it will get increasingly sour and watery as it ages.

Use
Cottage cheeses can be eaten straight or with fruit, much like yogurt, or incorporated into other dishes. Farmer's cheese is often used as a filling in a variety of sweet and savory pastries, dumplings, and custards. These include pierogi, some European varieties of cheesecake, and blintzes.

Substitution
Depending on the desired application, different cottage cheeses may be substituted for each other. For example, moist cottage cheese proper can be pressed and milled to produce a dry, grainy farmer's cheese. A particularly dry and/or curd-y quark may also make a reasonable substitute for cottage cheese if required. Try and see what exact characteristics are required for the recipe, and then adjust accordingly.

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See.

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User talk:Shuangdong

Copyright problem with Image:Soft.gif
--Derbeth 16:02, 6 October 2005 (UTC)

 * Please stop uploading images without copyright information. You must have seen warning on the upload page: we delete images with unknown status and may block notorious uploaders of such images. Please complete information about all of your images. If you have any questions, leave me a message. --Derbeth talk 10:17, 28 November 2005 (UTC)

 * Thanks, but can you fix license for your older images? You can find them in "my contributions" / namespace: image. --Derbeth talk 08:11, 9 December 2005 (UTC)

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You wrote this image is public domain, but you didn't write source of the image. Without source URL we cannot verify if it is really public domain. Can you add it?

Sorry for all these inconveniences from me, but it is neccessary. --Derbeth talk 19:27, 11 December 2005 (UTC)

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Digital Circuits

Introduction
This book will serve as an introduction to Digital Circuits. This book will rely heavily on the concepts of Discrete Math, but will not require any previous knowledge of the subject because all necessary math concepts will be developed in the text. This book will, however, assume a knowledge of basic electrical principles such as current, voltage, and resistance, so the reader may want to brush up on their Circuit Theory.

A mechanical engineer learns to think of everything as a spring. An electrical engineer starts off with building blocks of resistors (circuit theory) and NAND gates. From NAND gates, every part of a computer can be built. Most electronics purchased today contain a huge variety of special purpose chips including a CPU. Mass produced commercial circuits are cheaper to build this way. But digital design is typically implemented today in a chip that can be potentially turned into anything. Most digital courses today plunge straight into programming a. In any case "design" is important. This course focuses on the design and leaves the FPGA programming for another course.

Digital Basics

 * Binary Systems
 * Digital Circuit Types
 * Design Techniques
 * Logic Operations
 * Number Representations
 * Representations
 * Gates
 * Karnaugh Maps

Combinational Circuits

 * Multiplexers-Demultiplexers
 * Encoders-Decoders

Sequential Circuits

 * Latches
 * Flip-Flops
 * Registers and Counters

State Machines

 * Finite State Machines
 * Optimization

Arithmetic Circuits

 * Adders
 * Subtractors
 * Multipliers
 * ALU

Semiconductors

 * Transistor Basics
 * Transistor technologies used in digital circuits

Function Evaluation

 * Direct Digital Synthesizer (DDS)
 * CORDIC
 * Sigma-Delta Modulators

Practical Digital Design

 * I/O Interfacing

Appendices

 * Common Integrated Circuits
 * 7400 Series

Wikimedia Resources

 * Embedded Systems
 * Programmable Logic
 * VHDL for FPGA Design - Principles and Practices
 * Semiconductors
 * Computer Science:Logic

Books

 * Horowitz and Hill, "The Art of Electronics", ISBN 0521370957
 * Tocci, Widmer, and Moss, "Digital Systems: Principles and Applications 10th Edition", ISBN 0131725793

Digitaalipiirit

title: Digital Circuits


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For general information: Unless otherwise noted (none so far), all images submitted by me are made by me:

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Talk:Digital Circuits

I set up a basic outline that I think is pretty good, although we can probably add some things and delete some other things. I think we can move some more advanced topics into a different wikibook on "Digital Signal Processing", or something similar. --Whiteknight 18:28, 6 October 2005 (UTC)

I had several text books that I was going to use to verify alot of my information before i wrote it down, but i left those books at home (i am away at school), and can't get to them for a little while. I would rather write nothing then write something that is factually incorrect or incomplete. Other people may feel free to write about these topics, but i wont add anything for a little while. --Whiteknight 14:19, 7 October 2005 (UTC)

Changed a little of the outline to reflect more like a text book, so that a reader can go though the book in a sequential direction --Asm2750 23:05, 23 March 2006 (UTC)

 * I made more changes still. See my note below. --Whiteknight (talk) (current) 18:23, 28 April 2006 (UTC)

Glad to be on board, I'll try to flesh out many of the headings and provide the extra sections nessecary to bring this book into a more developed state. --HL-SDK (talk) 22:51, 2 October 2008 (UTC)

Combinational vs. sequential Circuits
According to wikipedia, and what I understood before, Combinational circuits have outputs that depend only on inputs, and not past states. Therefore, latches, flip fops and registers would be sequential logic, not combinational. I think combinational circuits would be decoders, multiplexers, and arithmetic circuits.Hithisishal (talk) 01:59, 18 October 2008 (UTC)

Karnaugh Maps
I think that Karnaugh Maps should probably go under the section with optimizations. Maybe shannon's expansion should also. --Whiteknight 22:51, 15 October 2005 (UTC)

I decided to put back the Karnaugh Map in the logic area, due to the fact that it is pretty much the first thing you learn after boolean algebra, and is one of the foundations of digital logic. --Asm2750 23:05, 23 March 2006 (UTC)

 * Kept the Karnaugh map page where it was essentially, as per your decision, but i made it a top-level page. --Whiteknight (talk) (current) 18:22, 28 April 2006 (UTC)

What this book is not
i've done this on a few of the other books, but i feel that it is important to lay down precisely what the scope of a new wikibook is, so that it doesnt grow out of control, and suffer from "feature creep." Here is what i think this book should be, although these guidelines are certainly not set in stone:

 * 1) This is not a Computer Science book. We are not here to teach programming, although i dont think it would be out of the question to include some examples using an HDL such as Verilog or VHDL. However, if we do include programming examples, we should definately not teach how to program because that is a topic best left reserved to the fine people on the CS bookshelf.
 * 2) This is not a physics book. We are not talking about the physical concepts concerning transistors. In fact, i dont think we should talk about transistors much at all, except in a macroscopic sense.
 * 3) This book has a limited scope, and a target audience. This book is designed to talk about what a logic gate is, and how they are used in the design of more complicated circuits. An engineer can walk down to a local electronics store and purchase a set of logic gate ICs. There is no sense reinventing the wheel. There has been an amazing amount of information written on the properties of silicon, or on the construction of a transistor, and there is no need to reproduce that here.

This is my 2 cents, and i would like to hear some input because this wikibook is still in the very early stages of development, and can easily be redirected if necessary. --Whiteknight 22:04, 17 October 2005 (UTC)

 * Many textbooks have been dedicated to digital circuits.
 * Other textbooks (such as our own Electronics Wikibook) include "digital circuits" as one chapter of a larger work.

 * If I suddenly remember some crucial fact about digital circuits that new learners simply must learn, do I put it in the Digital Circuits Wikibook, or into the "Digital Circuits" section of the Electronics Wikibook? --DavidCary (talk) 12:59, 14 August 2008 (UTC)

Big Changes
As of April 28th, I made a few big changes to the aesthetics of this book: If anybody has any questions about these changes, or thinks that they should be reverted or whatever, leave me a message and let me know. --Whiteknight (talk) (current) 18:26, 28 April 2006 (UTC)
 * 1) I flattened out the naming scheme. No more "Digital Circuits/Chapter/Page" notation.
 * 2) I put 4 headings per page, at least. This way there is an automatic TOC on each page, and each page looks like it has substantial information
 * 3) Changed the page naming scheme for all pages from "Digital Circuits:Page" to "Digital Circuits/Page". This is a better convention for all pages.
 * 4) I combined material from subpages into the main pages, so that all pages have a good amount of information on them.
 * 5) I changed some of the "section" headings on the Table of Contents

Another Restructure
I've been busy with college and work for the last few months so I havent had any time to work on this book. But I'm thinking of moving some subjects around again. I'll take a look at this again in a week or two. -- asm2750 17:50, 8 December 2006

Templates and resources
Here is a list of templates and category resources that are used in this book:

 * Template:Digital Circuits Page
 * Template:Digital Circuits Stub
 * Category:Electric Circuits
 * /Stubs

More information for each is available on their respective pages. --Whiteknight (talk) (projects) 16:52, 28 June 2006 (UTC)

 * And some more:
 * Template:Digital Circuits/Exercise — template for writing exercise and solutions
 * Template:Truthtable1 — one-input, one-output truth table
 * Template:Truthtable2 — two-input, one-output truth table
 * Template:Truthtable3 — three-input, one-output truth table
 * Again for more info, see the respective page. Inductiveload (talk) 18:14, 30 April 2009 (UTC)

merge
I suggest merging the Digital Electronics Wikibook into the Digital Circuits wikibook. A box of "digital circuits" is practically synonymous with a box of "digital electronics", right?

Some of the current contents of the Digital Electronics Wikibook look like they would be better suited for a "Computer Architecture" book -- is Microprocessor Design/Computer Architecture and Computer Systems Engineering the closest we have right now? --68.0.124.33 (talk) 22:17, 16 February 2010 (UTC)

I teach digital electronics using givone "digital principles and design" and would like to move to a wikibook. We offer both an engineering and technology digital course. The labs may overlap, but the text can not. There has to be a clear boundary. The text books are going to differentiate the courses more than the labs. This text aligns more with the engineering course. I want to expand it. The digital math is missing X0R and lots of examples right now .. sample homework problems that push design rather than troubleshooting. I agree the design has to lead to FPGA programming. I don't think technologists are going to be troubleshooting this code. 1sfoerster (discuss • contribs) 19:26, 26 August 2012 (UTC)

 * Dear 1sfoerster,
 * Why does there have to be a clear boundary? --DavidCary (discuss • contribs) 04:32, 1 March 2015 (UTC)

copy-and-paste
One edit of the Digital Circuits/Multipliers page appears to be a word-for-word copy-and-paste from "Booth Recoding" by Geoff Knagge. I suspect Geoff Knagge wrote the original and someone copied it to Wikipedia rather than vice versa, since his version is the only one with the "figure 2" referred to in the text.

What should we do about it? --DavidCary (discuss • contribs) 04:32, 1 March 2015 (UTC)
 * I've reverted the edit knowing it's a full copy and paste without source. --atcovi (talk) 04:36, 1 March 2015 (UTC)

Endianness, bytes, word length
Should there be a mention of bit ordering (endianness) ? How about word length? If we are adding two numbers we have to assume they are the same length for carry-in and carry out. There is some mention that N bits can represent 2^N possible values. How about error correcting codes and parity checking?

I’m just thinking out loud. . . GreenChileNM (discuss • contribs) 22:14, 1 August 2020 (UTC)

title: Talk:Digital Circuits


text: User talk:194.153.128.11

title: User talk:194.153.128.11


text:
Muggles' Guide to Harry Potter/Magic/Crucio

Overview
Crucio, also known as the Cruciatus Curse, causes extreme amounts of pain on the victim. Along with the Imperius Curse and the Killing Curse, the Cruciatus Curse is considered to be one of the most terrible curses in the magical world, called the Unforgivable Curses; the use of any of the three on another human being is punishable by a life sentence in Azkaban.

Extended Description
Bellatrix Lestrange and three other of Lord Voldemort's Death Eaters used this curse on Neville Longbottom's parents, torturing them into a state of irreversible madness. Since that time, they have resided in a special ward at St. Mungo's Hospital.

Harry Potter attempts this curse on Bellatrix Lestrange after she kills Harry Potter's godfather, Sirius Black. However, when Harry casts this curse it does not have the same effect as Lestrange's or other Dark Wizards'. As Bellatrix explains to Harry, he has to mean it in order for the curse to have its desired effect. In Harry's case, he is consumed with a righteous anger rather than a malicious intent.

Draco Malfoy attempts to use this curse on Harry at one point, but is forestalled by Harry's use of Sectumsempra.

Harry uses this curse again on Amycus Carrow, who has just spat at Professor McGonagall. The curse is much more effective this time, as Harry feels hatred towards Carrow.

It hardly needs to be mentioned that this is one of Voldemort's favorite spells. Voldemort uses this spell on his own followers numerous times as punishment, and twice uses it on Harry. The second time, it is ineffective, because the wand he is using has chosen Harry as its master.

Analysis
Neville's parents and their spell-caused insanity prove to be a plot point. Because of his parents' permanent incapacity, Neville is raised by his grandmother, and ends up very uncertain of his own magical ability. Once he comes into his strength, however, he seems to be adamant that what befell his parents will not be his own fate. Whether this is the reason he is able to destroy Nagini, Voldemort's pet snake and final Horcrux, is never definitively stated, but we feel that without the strength Neville found within himself as a result of his parents' fate, Neville would not have been able to act.

Questions

 * 1) Why was Voldemort's Cruciatus Curse ineffective against Harry in the Forbidden Forest after Harry's "near-death" experience?
 * 2) Does the wand in any way define the power of the Cruciatus curse?

Greater Picture
In Harry Potter and the Order of the Phoenix, Harry attempts to use the Cruciatus Curse against Bellatrix Lestrange, in self-defense, but fails. Bellatrix taunts him for this failure, and tells Harry he has "to really mean it", that he has to really hate someone for that curse to be effective. Just as the Patronus charm depends upon having a mind filled with happy thoughts, so must the Unforgivable Curses depend on having the mind filled with unrighteousness hate or anger. Harry truly realizes this when he casts the Cruciatus Curse on Amycus Carrow after Carrow spits in the face of Professor McGonagall in the Ravenclaw dormitory, stating his understanding of the anger one must feel to make such a curse be effective.


text:
Muggles' Guide to Harry Potter/Magic/Expecto Patronum

Overview
"This ancient and mysterious charm conjures a magical guardian, a projection of all your most positive feelings. The Patronus Charm is difficult, and many witches and wizards are unable to produce a full, corporeal Patronus, a guardian which generally takes the shape of the animal with whom they share the deepest affinity. You may suspect, but you will never truly know what form your Patronus will take until you succeed in conjuring it."— Miranda Goshawk (author of the Standard Book of Spells)

Expecto Patronum, or the Patronus Charm, will cast a Patronus, which can appear as simply white vapour, or in more advanced casters, as a silvery-white animal shape. If it takes the shape of an animal, it is called a corporeal Patronus. This spell is used to ward off Dementors, which are the guardians of Azkaban. In Fantastic Beasts and Where to Find Them we are told that this spell is also useful against Lethifolds, but we do not see them used this way in the main series.

Extended Description
"That's very, very advanced magic ..." — Hermione Granger on the difficulty and complexity of the charm

Harry learns this spell from Remus Lupin in Harry Potter and the Prisoner of Azkaban. Harry's ability to cast a corporeal Patronus in his third year of magical studies shows his ability as a wizard, as it is a very advanced spell which is thought to be too difficult for underage wizards, in fact many witches and wizards are unable to produce any form of Patronus. In his fifth year, when Harry takes his OWLs, his Charms examiner offers him an extra point if he can produce a corporeal Patronus. A point, or a letter grade, would be worth about 15% of his total marks, so achieving this one charm is seen as quite valuable.

The primary purpose of the Patronus, as mentioned, is as defence against Dementors. Professor Lupin describes it thus: "... a kind of anti-Dementor – a guardian which acts as a shield between you and the Dementor." And: "The Patronus is a kind of positive force, a projection of the very things that the Dementor feeds upon – hope, happiness, the desire to survive – but it cannot feel despair, as real humans can, so Dementors can't hurt it." Presumably, the Dementor, finding that the being confronting it does not suffer as a human would, retreats in confusion. In Harry Potter and the Order of the Phoenix we see Harry's Patronus charge at the Dementors; though the Patronus may have no physical body, the Dementor, being sightless, cannot see that, all it can sense is this emotional blast furnace, which is charging at it, and it will retreat to save itself.

We also see the Patronus used as a signaling spell when Professor Dumbledore sends for Hagrid in Harry Potter and the Goblet of Fire, and also when Tonks sends up a Patronus to summon someone from within the school to open the gates in Harry Potter and the Half-Blood Prince. According to the author, use of the Patronus as a communications device was pioneered by Dumbledore and is used exclusively by members of the Order of the Phoenix.

The Patronus is used extensively in Harry Potter and the Deathly Hallows, both as a communications device, as the Order of the Phoenix is now an outlaw organization, and also as defence against the Dementors who are wandering the English countryside. In particular, we see Arthur Weasley using it to warn Harry, on his birthday, of his imminent arrival with the Minister for Magic. The following day, Kingsley Shacklebolt sends his Patronus to warn the members of Bill and Fleur's wedding party that the Ministry had fallen; Arthur sends a Patronus later that night to tell Ron, Hermione, and Harry that the Weasley family is all right. We also see Patronuses used as defence against Dementors by Harry, Hermione, Luna Lovegood, Ernie Macmillan, Seamus Finnigan, and Dolores Umbridge. We see Aberforth Dumbledore's Patronus, a goat, when the Trio return to Hogsmeade in Harry Potter and the Deathly Hallows. Finally, we see Severus Snape's Patronus on two occasions.

The shape of a corporeal Patronus is significantly influenced by the personality of the caster. Harry's is a stag; Dumbledore's is a phoenix; Tonks' Patronus, as seen in Harry Potter and the Half-Blood Prince, is "something large and hairy", and has apparently changed recently. Members of Dumbledore's Army are also, some of them, able to conjure Patronuses by their last lesson: Cho Chang's is a swan, for instance, while Hermione's is an otter. Life events can change the shape of a Patronus as well; as mentioned, Professor Snape mentions that Tonks' Patronus had changed. This change apparently happened at the death of Sirius Black, and Harry initially thinks that Tonks' new Patronus has taken on Sirius' dog shape.

It is because of this connection between the caster's personality and the shape of the Patronus that it can also be used, to a certain extent, as identification of the wizard. Harry is identified, for instance, by his Patronus in Hogsmeade; the Death Eaters guarding against his return to Hogsmeade decide that Harry has arrived by the shape of the Patronus he uses to defend himself from the Dementors they send after him. This is only a weak identification, as it is possible for multiple wizards to have the same Patronus animal, and because not all wizards can successfully cast this spell; but it is unlikely that a wizard in disguise would have the same Patronus as the wizard he is trying to impersonate.

Literal Latin translation: I desire my patron.

Analysis
It should be noted that a sufficiently advanced wizard or witch can apparently cast multiple simultaneous Patronuses. We see that Professor McGonagall casts three Patronuses at once, in Harry Potter and the Deathly Hallows, when she needs to contact the three other Heads of House.

Questions

 * 1) Harry's Patronus is a Stag. His father's Animagus form is also a stag. We know from the description of the Animagus that the form the wizard takes when transformed is related to his personality. Are Patronuses and Animagus Forms related? Does this pass from father to son, and if someone's Patronus' form changed, would their Animagus form also change?
 * 2) Clearly, the form a wizard's Patronus takes is related to his personality or events in his life. If you had a Patronus, what shape would it take?
 * 3) If your Patronus was nothing like your Animagus, why would that be?

Greater Picture
There are two spells that relate a wizard or witch to an animal shape: the Patronus charm, and the Animagus transformation. In the course of the books, we see only one witch who is both Animagus and casts a visible Patronus, that being Professor McGonagall. The fact that her Animagus form is the same as her Patronus, a tabby cat, would indicate that whatever influences the shape of the one would also influence the shape of the other. It is perhaps a reasonable assumption that the shape resulting from either of these spells is related to the current mental state of the caster; but the Animagus transform, being a one-time enabling of the ability to transform, likely does not allow for change in the animal one changes to, rather enabling the transform according to the state of the caster at the time the transform was enabled, while the Patronus charm, being invoked afresh each time, reflects the caster's current state. There is more discussion of this at the entry for the Animagus transform.

While it is noted in the Extended Description that we see Professor Snape's Patronus on two occasions, we deliberately elide the shape of that Patronus as it constitutes a relatively large spoiler. Snape's Patronus takes the shape of a doe, and is seen first in the Forest of Dean, and later in Snape's memories of a conversation with Professor Dumbledore. Dumbledore recognizes it as being related to Lily Evans, as she then was, and Snape's unrequited love for her. We note that in three instances, Harry, Snape, and Tonks, the Patronus has taken a shape related to a major object of affection: Harry's is related to his father, Tonks' is related to Lupin, and Snape's to Lily. Clearly there is some indication that the Patronus form is influenced by love, requited, unrequited, or lost. Related to this we note that Hermione's Patronus is an otter, and if its form was related to love objects, we would expect it to be a weasel; Hermione, however, likely is aware that weasels and otters belong to the same family, Mustelidae.


text:
User talk:Sgowda

Molecular Biology for Masters

By

Dr. G. R. Kantharaj, M.Sc, Ph.D.

BANGALORE, INDIA

title: User talk:Sgowda


text:
Talk:Blender 3D: Noob to Pro/Basic Carpet Texture

Any tutorial would be better than no tutorial. Even if there aren't the best capabilities, in the current tutorial, you could add in the newer capabilities on the end, or as a new tutorial so that people could get an idea as to the results from different methods of doing things ((FAR better learning experience in that case)).

The idea (in my mind) is to learn the techniques first, then perfect later.
 * The rule is - if you don't know what to do, do something useful. Any content is better than nothing, polishing will come later.

There are a bunch of tutorials here that do not teach so much as they walk you through a bunch of steps without explaining what you're doing or why. This is one of those. =/ Specifically, I understand what's being done, but I'm not all that clear on what the individual options do or why they are being set to whatever values.... again, a problem in many of these tutorials. This makes experimenting on my own harder. Solution, walk the user through setting each value to multiple settings, and pointing out and explaining the differences (which are not always obvious).

ETA?
Do you have an ETA on when your new tutorial will be up?


text:
User talk:Leinad13

I'd LOVE to see your current (imperfect, though it may be) Basic Carpet Texture module... See my note on the discussion page user:Darkonc Oct 5 13:00 PDT

title: User talk:Leinad13


text:
Calculus/Volume of solids of revolution

In this section we cover solids of revolution and how to calculate their volume. A solid of revolution is a solid formed by revolving a 2-dimensional region around an axis. For example, revolving the semi-circular region bounded by the curve $$y=\sqrt{1-x^2}$$ and the line $$y=0$$ around the $$x$$-axis produces a sphere. There are two main methods of calculating the volume of a solid of revolution using calculus: the disk method and the shell method.

Disk Method
Consider the solid formed by revolving the region bounded by the curve $$y=f(x)$$, which is continuous on $$[a,b]$$ , and the lines $$x=a$$ , $$x=b$$ and $$y=0$$ around the $$x$$-axis. We could imagine approximating the volume by approximating $$f(x)$$ with the stepwise function $$g(x)$$ shown in figure 2, which uses a right-handed approximation to the function. Now when the region is revolved, the region under each step sweeps out a cylinder, whose volume we know how to calculate, i.e.
 * $$V_{\rm cylinder}=\pi r^2 h$$

where $$r$$ is the radius of the cylinder and $$h$$ is the cylinder's height. This process is reminiscent of the Riemann process we used to calculate areas earlier. Let's try to write the volume as a Riemann sum and from that equate the volume to an integral by taking the limit as the subdivisions get infinitely small.

Consider the volume of one of the cylinders in the approximation, say the $$k$$-th one from the left. The cylinder's radius is the height of the step function, and the thickness is the length of the subdivision. With $$n$$ subdivisions and a length of $$b-a$$ for the total length of the region, each subdivision has width
 * $$\Delta x=\frac{b-a}{n}$$

Since we are using a right-handed approximation, the $$k$$-th sample point will be
 * $$x_k=k\Delta x$$

So the volume of the $$k$$-th cylinder is
 * $$V_k=\pi f(x_k)^2\Delta x$$

Summing all of the cylinders in the region from $$a$$ to $$b$$, we have
 * $$V_{\rm approx}=\sum_{k=1}^n \pi f(x_k)^2\Delta x$$

Taking the limit as $$n$$ approaches infinity gives us the exact volume
 * $$V=\lim_{n\to\infty}\sum_{k=1}^n \pi f(x_k)^2\Delta x$$

which is equivalent to the integral
 * $$V=\int\limits_a^b \pi f(x)^2dx$$

Let's calculate the volume of a sphere using the disk method. Our generating region will be the region bounded by the curve $$f(x)=\sqrt{r^2-x^2}$$ and the line $$y=0$$. Our limits of integration will be the $$x$$-values where the curve intersects the line $$y=0$$, namely, $$x=\pm r$$. We have
 * $$\begin{align}V_{\rm sphere}&=\int\limits_{-r}^r \pi(r^2-x^2)dx\\

&=\pi\left(\int\limits_{-r}^r r^2dx-\int\limits_{-r}^r x^2dx\right)\\ &=\pi\left(r^2 x\bigg|_{-r}^r-\frac{x^3}{3}\bigg|_{-r}^r\right)\\ &=\pi\Big(r^2\bigl(r-(-r)\bigr)-\tfrac{1}{3}\bigl(r^3-(-r)^3\bigr)\Big)\\ &=\pi\left(2r^3-\frac{2r^3}{3}\right)\\ &=\pi\frac{6r^3-2r^3}{3}\\ &=\frac{4\pi}{3}r^3 \end{align}$$

Washer Method

The washer method is an extension of the disk method to solids of revolution formed by revolving an area bounded between two curves around the $$x$$-axis. Consider the solid of revolution formed by revolving the region in figure 3 around the $$x$$-axis. The curve $$f(x)$$ is the same as that in figure 1, but now our solid has an irregularly shaped hole through its center whose volume is that of the solid formed by revolving the curve $$g(x)$$ around the $$x$$-axis. Our approximating region has the same upper boundary, $$f_{\rm step}(x)$$ as in figure 2, but now we extend only down to $$g_{\rm step}(x)$$ rather than all the way down to the $$x$$-axis. Revolving each block around the $$x$$-axis forms a washer-shaped solid with outer radius $$f_{\rm step}(x)$$ and inner radius $$g_{\rm step}(x)$$. The volume of the $$k$$-th hollow cylinder is
 * $$\begin{align}V_k&=\pi\cdot f(x_k)^2\Delta x-\pi\cdot g(x_k)^2\Delta x\\

&=\pi\bigl(f(x_k)^2-g(x_k)^2\bigr)\Delta x\end{align}$$ where $$\Delta x=\frac{b-a}{n}$$ and $$x_k=k\Delta x$$. The volume of the entire approximating solid is
 * $$V_{\rm approx}=\sum_{k=1}^n \pi\bigl(f(x_k)^2-g(x_k)^2\bigr)\Delta x$$

Taking the limit as $$n$$ approaches infinity gives the volume
 * $$\begin{align}V&=\lim_{n\to\infty}\sum_{k=1}^n \pi\bigl(f(x_k)^2-g(x_k)^2\bigr)\Delta x\\

&=\int\limits_a^b \pi\bigl(f(x)^2-g(x)^2\bigr)dx\end{align}$$

Shell Method
The shell method is another technique for finding the volume of a solid of revolution. Using this method sometimes makes it easier to set up and evaluate the integral. Consider the solid of revolution formed by revolving the region in figure 5 around the $$y$$-axis. While the generating region is the same as in figure 1, the axis of revolution has changed, making the disk method impractical for this problem. However, dividing the region up as we did previously suggests a similar method of finding the volume, only this time instead of adding up the volume of many approximating disks, we will add up the volume of many cylindrical shells. Consider the solid formed by revolving the region in figure 6 around the $$y$$-axis. The $$k$$-th rectangle sweeps out a hollow cylinder with height $$\Big|f(x_k)\Big|$$ and with inner radius $$x_k$$ and outer radius $$x_k+\Delta x$$, where $$\Delta x=\frac{b-a}{n}$$ and $$x_k=k\Delta x$$ , the volume of which is

The volume of the entire approximating solid is
 * $$V_k$$
 * $$=\pi\bigl((x_k+\Delta x)^2-x_k^2\bigr)\Big|f(x_k)\Big|$$
 * $$=\pi\bigl((x_k^2+2x_k\Delta x+\Delta x^2)-x_k^2\bigr)\Big|f(x_k)\Big|$$
 * $$=\pi(2x_k\Delta x+\Delta x^2)\Big|f(x_k)\Big|$$
 * }
 * $$=\pi(2x_k\Delta x+\Delta x^2)\Big|f(x_k)\Big|$$
 * }
 * $$=\pi(2x_k\Delta x+\Delta x^2)\Big|f(x_k)\Big|$$
 * }
 * $$V_{\rm approx}=\sum_{k=1}^n \pi(2x_k\Delta x+\Delta x^2)\Big|f(x_k)\Big|$$

Taking the limit as $$n$$ approaches infinity gives us the exact volume

Since $$|f|$$ is continuous on $$[a,b]$$, the Extreme Value Theorem implies that $$|f|$$ has some maximum, $$M$$ , on $$[a,b]$$. Using this and the fact that $$\Delta x^2\Big|f(x_k)\Big|>0$$, we have
 * $$V$$
 * $$=\lim_{n\to\infty}\sum_{k=1}^n \pi(2x_k\Delta x+\Delta x^2)\Big|f(x_k)\Big|$$
 * $$=\pi\cdot\lim_{n\to\infty}\left(\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|+\sum_{k=1}^n \Delta x^2\Big|f(x_k)\Big|\right)$$
 * }
 * $$=\pi\cdot\lim_{n\to\infty}\left(\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|+\sum_{k=1}^n \Delta x^2\Big|f(x_k)\Big|\right)$$
 * }
 * $${\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|\le\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|+\sum_{k=1}^n \Delta x^2\Big|f(x_k)\Big|\le\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|+\sum_{k=1}^n \Delta x^2M}$$

But

So by the Squeeze Theorem
 * $$\lim_{n\to\infty}\sum_{k=1}^n \Delta x^2M$$
 * $$=\lim_{n\to\infty}\sum_{k=1}^n \left(\frac{b-a}{n}\right)^2M$$
 * $$=\lim_{n\to\infty}\frac{(b-a)^2}{n}M$$
 * $$=0$$
 * }
 * $$=0$$
 * }
 * $$=0$$
 * }
 * $$\pi\cdot\lim_{n\to\infty}\left(\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|+\sum_{k=1}^n \Delta x^2\Big|f(x_k)\Big|\right)=\pi\cdot\lim_{n\to\infty}\sum_{k=1}^n 2x_k\Delta x\Big|f(x_k)\Big|$$

which is just the integral
 * $$\int\limits_a^b 2\pi x\Big|f(x)\Big|dx$$

title: Calculus/Volume of solids of revolution


text: User:Adamforster

title: User:Adamforster