Monday, August 5, 2019
Non Hodgkins Lymphoma: Types, Causes and Symptoms
Non Hodgkins Lymphoma: Types, Causes and Symptoms Lymphoma is a type of cancer that affects the lymphatic system. Lymphoma is divided into two types called Hodgkins lymphoma and non-Hodgkins lymphoma. Non-Hodgkins lymphomas (NHL) are a range of diseases emerging from clonal proliferation of lymphocytes which is a type of white blood cells resulting in cancer or tumour formation of lymphatic system.1 An estimated 8,000 new cases of NHL has been diagnosed annually in the United Kingdom at the end of the 20th century.2 NHL is a common hematologic malignancy and ranked eighth as the most common malignancy.2 Male has 1.5 times likelihood than female from being diagnosed with NHL. From the early seventies, cases of NHL have increased by threefold for both male and female throughout many countries beside United Kingdom.2 In 2007, non-Hodgkin lymphoma (NHL) caused 4,533 deaths in United Kingdom. Males and females share almost similar number of deaths but males has higher age standardized mortality rate. However, not all patients die from NHL as infections may be one of the causes. Non-Hodgkin lymphoma has 53% overall 5-year relative survival in an analysis3 conducted over 22 European countries with age adjusted figures 48% in men and 54% in womean. In Scotland, the total number of diagnosed non-Hodgkins lymphoma cases from 1990-1994 were 1,598 for men and 1,708 in women. The percentage of age standardized survival rate for patients diagnosed after one year and five years with 95% confidence interval were 63.5 (61.1-66.1) and 41.0 (38.2-44.0) respectively.3 NHL has no established cause factor and people diagnosed with NHL have no known risk factors. However, NHL can be associated with chronic inflammatory diseases such as rheumatoid arthritis, coeliac disease, and Sjà ¶gren syndrome.4 Study by Lens and Newton-Bishop show association between NHL and cutaneous melanoma.5 Besides that, the risk of developing NHL increases with chronic infection from viruses and bacteria such as Epstein-Barr virus, human T-lymphotropic virus 1(HTLV-1) and human immunodeficiency virus (HIV).2 There was a strong link between Burkitt lymphoma and Epstein-Barr virus6 while adult T-cell lymphoma can be caused by HTLV-1.7 It has been noted that prevalence of NHL was higher in people with HIV infections compared to healthy adults.8 One study conducted by Stolte et al9 showed that there was association between Helicobacter pylori infection and mucosa-associated lymphoid tissue (MALT) lymphomas. It has also been noted that primary effusion lymphomas can be associat ed with human herpes virus while ocular adenexal lymphomas can be associated with Chlamydia psittaci.10 Moreover, evidence has shown association between splenic or large cell lymphomas and hepatitis C infections.11 The risk of developing NHL increases when a person was immunocompromised such as undergoing organ transplant12 or patients with AIDS and autoimmune diseases. Certain chemotherapy drugs and radiotherapy may increase the risk of developing NHL within 10 to 15 years after treatment.4 Solvents, pesticides and other chemical factors have also been associated with causes of NHL.2 Diagnosis In this case, a male patient has been recently diagnosed with NHL but the type of NHL and pathology were unconfirmed. Lymphoma can be divided into two types: indolent and aggressive. Indolent lymphomas such as follicular, marginal zone and lymphoplasmacytic lymphoma13 are commonly accompanied by slow, progressing and painless peripheral lymphadenopathy. There might be history of patients with enlarged lymph nodes before regressing without diagnosis made. These spontaneous regressions of lymph nodes may occur, preventing biopsy diagnostic test from being done and patient was treated for an assumed infection. It is uncommon to see primary extranodal lymphoma or systemic symptoms occurring at early stages but can be encountered as disease progresses. Examples of systemic B-symptoms are fever, weight loss, and night sweats. Indolent lymphoma can undergo histologic transformation or changes to a different, more aggressive usually large-cell lymphoma type. Indolent lymphomas are usually sl ow growing and it may respond to treatment but relapse tend to occur frequently.14 Aggressive lymphomas such as diffuse large B-cell lymphoma are different from indolent with most patients presenting with lymphadenopathy or involvement of extranodal sites. Common extranodal sites affliated are gastrointestinal tract, skin, bone marrow, sinuses, thyroid, or central nervous system. It is usual to see presence of systemic B-symptoms in a third of patients with aggressive lymphomas. Aggressive lymphomas are fast growing and are treatable than indolent lymphomas.14 NHL has been hard to diagnose and recognizing people that has high risk of NHL is difficult. Patient can only be identified correctly after development of lymphadenopathy or other symptoms related to NHL. Even though with the advancement in imaging techniques, histology is mandatory to confirm diagnosis of NHL type before progressing to treatment. It is common to use surgical biopsy either by incisional or excisional with latter being recommended to provide biopsy specimens to be reviewed by hematopathologists. The morphologic appearance obtained with additional information from immunophenotype, genetics and clinical features were then used to classify NHL with definite clinical unit. These were the basis for World Health Organization (WHO) (Table 1) classification of neoplastic diseases arising from hematopoietic and lymphoid tissues. Fine-needle aspiration or large bore-needle biopsies can also be used to diagnose NHL but was discourage for initial diagnosis due to difficulty in co nfirming a specific diagnosis.15 Table 1. World Health Organization (WHO) Classification of non-Hodgkins lymphomas.15 B-cell neoplasms Precursor B-cell neoplasm Precursor B-lymphoblastic leukemia/lymphoma (precursor B-cell acute lymphoblastic leukemia) Mature (peripheral) B-cell neoplasms B-cell chronic lymphocytic leukemia/small lymphocytic lymphoma B-cell prolymphocytic leukemia Lymphoplasmacytic lymphoma Splenic marginal zone lymphoma Hairy cell leukemia Plasma cell myeloma/plasmacytoma Extranodal marginal zone B-cell lymphoma of MALT Nodal marginal zone lymphoma Follicular lymphoma Mantle cell lymphoma Diffuse large B-cell lymphoma Mediastinal large B-cell lymphoma Primary effusion lymphoma Burkitts lymphoma/Burkitt cell leukemia T-Cell and NK-Cell Neoplasms Precursor T-cell neoplasm Precursor T-lymphoblastic lymphoma/leukemia Mature (peripheral) T-cell neoplasms T-cell prolymphocytic leukemia T-cell granular lymphocytic leukemia Aggressive NK-cell leukemia Adult T-cell lymphoma/leukemia (HTLV-1) Extranodal NK/T-cell lymphoma, nasal type Enteropathy-type T-cell lymphoma Hepatosplenic T-cell lymphoma Subcutaneous panniculitis-like T-cell lymphoma Mycosis fungoides and Sà ©zary syndrome Anaplastic large-cell lymphoma, T/null cell, primary cutaneous type Peripheral T-cell lymphoma, unspecified Angioimmunoblastic T-cell lymphoma Anaplastic large-cell lymphoma, T/null cell, primary systemic type MALT, mucosa-associated lymphoid tissue; NK, natural killer. Source: Data from Zelenetz and Horwitz Lymphoma has been categorized into stages following modified Ann Arbor Staging System (Table 2) originally developed for Hodgkin disease. This system as shown in table 2 was based on area of involvement, presence or absence of extranodal involvement and B symptoms such as weight loss more than 10% of body weight, fever, and drenching night sweats.15 Histology and morphology of lymphoma largely determined the treatment outcome and prognosis. Due to different outcomes of patients with lymphoma and limitation of clinical staging, International Prognostic Index (IPI) (Table 3) was developed from 2,031 patients with 5 independent, easily obtained clinical features such as patient age, Ann Arbor stage, serum lactate dehydrogenase level, number of extranodal sites and performance status to predict survival. The IPI (Table 3) served as a guide for clinical management, clinical trial design and interpretation. However, this IPI was designed for aggressive lymphoma. Thus, the Follicular Lymphoma International Prognostic Index (FLIPI) (Table 4) was developed from 4,167 patients for indolent lymphoma with clinical features such as patients age, Ann Arbor stage, haemoglobin level, number of nodal areas and serum lactacte dehydrogenase level. Examples of nodal areas are cervical, para-aortic, inguinocrural, celiac and other ancillary nodal si tes. FLIPI can help determine significantly different mortality risk of patients with indolent lymphomas and improve decision on different aggressive therapy options that may benefit certain patient groups.15 Treatment Non-Hodgkins lymphoma can be treated by a range of treatments available such as radiation therapy / radiotherapy, surgery, stem cell transplant, single-agent or combination chemotherapy, immunotherapy or radioimmunconjugate therapy. Treatments can consist of one or a combination of the options available with different treatments having different duration and doses. In this case scenario, the patient was recently diagnosed with NHL. Due to the lack of information, NHL diagnosed can be assumed to be either indolent lymphoma or aggressive lymphoma. Being 28 year old, patient was eligible for more aggressive treatment compared to patients aged 60 and above.16 Indolent Lymphoma Indolent lymphomas such as follicular lymphoma and MALT lymphoma were not treated at early stages if there were no symptoms present with doctors adopting watch-and-wait approach. In a study conducted by Division of Oncology, Stanford University Medical Center, 43 patients with follicular lymphoma stage I or stage II were observed after deferment of radiation due to a variety of reasons. After a median of 86 months of follow-up, 63% had not been treated and survival was almost the same to the patients that has undergo radiation.17 In this situation, toxic side effects of treatments should be considered against the advantages of undergoing treatments. Patients with low grade, stage I-II NHL lymphoma with localized disease can be treated either with surgery18 or radiation therapy. Radiation therapy as shown in a study conducted by Stanford University can be used to treat limited stage, low grade lymphomas of 177 patients with good remission rate.19 Another study conducted on 103 patient s with stage I and II MALT lymphoma showed 77% disease-free survival rate with radiotherapy.20 Surgery can be done in situations where low grade MALT lymphoma is localized and there is a risk of perforation but if the lymphoma progresses to a more advance stage, then surgery no longer present as first line treatment.21 As lymphoma mainly affects systemic system, surgery is normally used to establish diagnosis. Besides that, stem cell transplant can be used to treat NHL but was limited to younger patients and difficulty in determination of the time to treat patients. A study on autologous stem cell transplant after high dose therapy showed higher response rate compared to immunochemotherapy.22 Chemotherapy options for indolent lymphomas ranged from single-agents such as cyclophosphamide, chlorambucil or doxorubicin to combinations such as cyclophosphamide, vincristine and prednisone (CVP)23 chemotherapy. More aggressive combination of chemotherapy that combines cyclophosphamide, doxorubicin, vincristine, and prednisone (CHOP) can also be use. In a study conducted in 228 stage III or IV follicular lymphoma patients that were treated randomly either with cyclophosphamide, a less toxic single agent or combination of cyclophosphamide, doxorubicin, vincristine, prednisone and bleomycin (CHOP-B) showed no initial advantage to combination treatment eventhough in an unplanned subgroup analysis showed improved disease control and survival.24 Cyclophosphamide is a nitrogen mustard alkylating agent that acts by causing DNA damage and interfere with cell replication. Besides fatigue, nausea, vomiting, bone marrow suppression and alopecia that were normally associated with anticancer treatment, prolonged use of cyclophosphamide might result in severely affected gametogenesis.25 Chlorambucil has similar mechanism of action to cyclophosphamide with lesser side effects but development of widespread rashes may occur.25 Doxorubicin is a cytotoxic, anthracyclines antibiotic that acts by intercalating DNA. Common side effects are present with additional potential cardiomyopathy and severe tissue necrosis due to extravasation when administering doxorubicin. Vincristine is a vinca alkaloids and act by depolymerising microtubules and thus inhibiting mitosis. It may not have significant myelosuppression along with other common side effects but may cause neurotoxicity and severe tissue necrosis due to extravasation.25 Prednisone is a pr odrug that is converted in liver to prednisolone that has a marked antitumour effect in NHL. However, it may cause immunosuppression, adrenal suppression, mood and behaviour changes, gastro-intestinal effects with mineralocorticoid and glucocorticoid side effects. Bleomycin is a cytotoxic antibiotic that is metabolized to produce superoxide and hydroxyl free radicals which results in DNA damage. However it can cause skin pigmentation and dose related pulmonary fibrosis.26 In addition to chemotherapy, immunotherapy is becoming a standard treatment for indolent lymphoma. Rituximab is a recombinant chimeric monoclonal antibody that targets protein CD20 which is primarily found on the surface of malignant and normal human B cells involved with B-cell proliferation and differentiation. It is said to induce apoptosis of CD20 cells.25,26 Rituximab was generally well tolerated when used compared to other conventional chemotherapy with distinct reduction of haemotological events like severe neutropenia and associated infections.27 Studies28,29,30 conducted on the usage of rituximab for recently diagnosed follicular NHL as single first line therapy showed good response rates around 52% to 73% and a 12-month progression free survival. Rituximab can be combined with chemotherapy such as CHOP as CHOP-R to treat indolent B-cell lymphoma. The trial of CHOP vs CHOP-R31 conducted in 1999 showed 95% overall response rate for CHOP-R with 55% achieving complete remission and 40% in partial remission. Addition of cytokines such as interferon ÃŽà ±32, interleukin 233, and interleukin 1234 to rituximab therapy conducted in studies shown that good efficacy profile can be obtained but further studies need to be conducted to confirm. Interferon ÃŽà ± has antitumour therapeutic effect but is not side effect free with additional myelosuppression, ocular side effects, cardiovascular problems, hypersensitivity on top of common anticancer side effects. Interferon-ÃŽà ± can be incorporated into chemotherapy as a new approach in treating NHL. Incorporation of interferon-ÃŽà ± into anthracycline-containing has been demonstrated to increase the remission rate and remission duration. However the data has not been conclusive and further information must be obtained before making it as standard treatment. German Low Grade Lymphoma Study Group has been conducting trial with continuous higher dose interferon maintenance therapy yield 45% relapse-free patie nts.35 Besides rituximab, Food Drug Administration in United States has approved two anti-CD20 radioimmunotherapy agents: iodine I 131 tositumomab36 and yttrium Y 90 ibritumomab tiuxetan37 for treatment of lymphoma. Both agents contain murine antibodies that target CD20 with ÃŽà ²-emitting radioisotopes but iodine I 131 tositumomab can also emit gamma radiation. Both still cause side effects although milder with significant one being myelosuppression. University of Michigan conducted a phase II trial where 76 patients were given treatment of iodine I 131 tositumomab as initial treatment for follicular lymphoma and resulted in 75% of complete response and 95% of overall response.38 Yttrium Y 90 ibritumomab tiuxetan has been shown to be effective when used in consolidation therapy after rituximab39 or in relapsed/refractory B-cell NHL.40 Radioimmunotherapy was deemed better than radiotherapy due to prevention of normal tissues from being exposed to radiation and systemic radiation can be a chieved to known and unknown tumour cells. There is another emerging strategy to counter low-grade NHL by administering vaccine to boost patients immune system which leads to tumour rejection by patients body. Trials conducted showed promising results among relapsed patients following chemotherapy with prolonged disease free progression and overall survival. This strategy has not been approved by FDA but personalized vaccine therapy has been received positively in its effectiveness as first line in countering slow progressing NHL. Vaccine therapy was deemed too slow for aggressive NHL but trials were ongoing to determine its efficacy.41 The management of indolent NHL have to depend on considerations such as symptoms, age, comorbidities, extent of disease, prior therapy and others. Most decisions on management of indolent NHL depend on physicians trying to optimize the treatment options to treat this chronic illness.15 Aggressive Lymphoma Aggressive NHL consist mainly of diffuse large B cells demands almost similar treatments to indolent lymphoma. As explained above, radiotherapy is one of the options available. The early treatment for early stage aggressive NHL was radiotherapy alone with relative cure rates of 50% for stage I and decreases to 20% for stage II. Therefore, combination of radiotherapy and a chemotherapy regimen were used to improve the chances of survival for aggressive NHL patients. A study conducted among 400 patients with localized immediate or high grade NHL compared the results of one group receiving 8 cycles of CHOP alone and another receiving 3 cycles of CHOP and radiotherapy. The study showed patients under combined CHOP and radiotherapy has statistically significant overall survival rate than patients receiving CHOP alone. Life-threatening side effects that were encountered by both groups were statistically significant in comparison with fewer patients under combined CHOP and radiotherapy suff ering from adverse effects. Therefore, combination of CHOP and radiotherapy are better for treatment of localized NHL compared to CHOP alone.42 There was another alternative treatment available for patients with aggressive NHL called high-dose therapy with autologous stem cell transplant (HDT ASCT). A number of trials among intermediate and high risk patients have been conducted to determine its efficacy following initial chemotherapy but there were conflicting results resulting in this treatment for not being first-line.43 Combination therapy has been known to be better than single therapy and used to increase the percentage of patients entering complete remission. In 1976 and 1980, CHOP regimen44 as explained above and COMLA regimen45 which includes cyclophosphamide, vincristine, methotrexate with leucovorin rescue, and cytarabine were published respectively. Both regimens have been shown to present a possible cure rate of approximately 30% for patients with aggressive lymphoma achieving long-term remission. In the ensuing years, new second and third generation of aggressive NHL regimens showed 55% to 65% patients being cured. An example of second regimen treatment was m-BACOD consisting of methotrexate, bleomycin, doxorubicin, cyclophosphasmide, vincristine, and dexamethasone.46 Third generation regimens were such as MACOP-B made up of methotrexate, doxorubicin, cyclophosphamide, vincristine, prednisone and bleomycin47 and ProMACE-CytaBOM compromising prednisone, methotrexate, cyclophosphamide, etopo side, cytarabine, bleomycin, vincristine and methotrexate.48 The effectiveness of all these regimens were not known as many of these studies were conducted with relatively small number of patients until 1993, a trial called national high priority intergroup Phase III was held to do a comparison between CHOP, MACOP-B, ProMACE-CytaBOM and m-BACOD regarding effectiveness and side effects.49 The four regimens demonstrate equivalent outcomes but CHOP showed the lowest side effects. Based on this trial, CHOP regimen became the standard treatment for NHL in the United States. Another regimen called ACVBP consisting of doxorubicin, cyclophosphamide, vindesine, bleomycin, and prednisone has been developed by Groupe dEtude des Lymphomes de LAdulte (GELA) in Europe which were compared in poor risk patients against CHOP and results favour ACVBP.50 In another trial, etoposide and CHOP termed CHOEP was shown to increase complete remission rate and survival rate in 18 to 60 year-old patient in a t rial that compared 3 week CHOP-21, 2 week CHOP-14 with CHOEP-21, CHOEP-14. CHOEP was recommended in the conclusion of this trial if the patient is young with good prognostic feature of aggressive lymphoma.51 Etoposide is a synthetic analogue to vinca alkaloids and binds to DNA and topoisomerase II complex in phase G2 to prevent DNA replication and causes strand to break.26 Etoposide is still associated with toxic effects such as alopecia, myelosuppression, nausea and vomiting.25 Immunotherapy also played a part in treatment of aggressive lymphoma with rituximab as a single agent. GELA has shown that the overall response of rituximab as a single agent was 37% with patients suffering from relapsed and refractory diffuse large B-cell lymphoma.52 A randomized controlled trial has been conducted by Mab Thera International Trial (MInT) Group to investigate CHOP-like chemotherapy against CHOP-like chemotherapy with rituximab. The result showed that rituximab combined with cheomotherapy increased overall survival and with no significant increase in side effects.53 Rituximab and CHOP regimen is the most common chemotherapy regimen for diffuse large B-cell NHL. British Columbia Cancer Agency (BCCA) implemented a new policy on 1 March 2001 recommending all patients newly diagnosed with advanced stage diffuse large B-cell lymphoma to be treated with CHOP and rituximab based on evidences from trials conducted by GELA and MInT Group.54 Treatment recommendation. As stated earlier, limited information was available for this case scenario. Patient is only known as 28 year old male recently diagnosed with NHL. An appropriate treatment that could be given as first line is CHOP regimen with addition of rituximab (CHOP-R) based on evidences given above. CHOP-R has significant better results compared to CHOP alone and addition of rituximab does not increase side effects. CHOP-R can also be used for both indolent and aggressive lymphoma with positive outcomes as stated above although symptomless indolent lymphoma may require watch-and wait strategy. However in terms of cost-effectiveness, CHOP-R is more expensive than CHOP alone but CHOP-R is preferred due to its increased efficacy profile and similar side effects. In conclusion, CHOP-R can be given every 14 or 21 days with the course of treatment ranging from 3 to 8 cycles. CHOP-R cycle started with the first day drug administration consisting of rituximab, cyclophosphamide, vincristine and doxorub icin through injection into a vein or through drip and prednisone was taken orally from day 1 to day 5. Conflict: Newton Vs Leibniz Conflict: Newton Vs Leibniz Mathematicians everywhere contributed to the development of Calculus. However, the two most known founders of calculus are Isaac Newton and Gottfried Wilhelm Leibniz. Nowadays, the credit is handed over to both men. Nevertheless, a controversy took place over which of them deserved the recognition. The controversy was both intense and widespread. Isaac Newton: Isaac Newton is known as one of the greatest scientists who have ever lived; in addition, he is recognized as one of the most accomplished mathematicians that England has ever seen. Newton became fascinated in mathematics at an early age. Later in life, he created Calculus. However, he did not publish it until later. This was an enormous mistake. His life: In 1643, Newton was born. Later, in 1655, Newton began the discovery of calculus with the general binomial series which led to him discovering integration, differentiation, and infinite processes. Thirty two years later, 1687, Newton published his work in a book called The Mathematical Principles of Natural Philosophy. At the age of eighty four, in 1727, Newton died. Gottfried Leibniz: Gottfried Leibniz is known as a worldwide scientist. He became a leading international philosopher as well as, a worldwide known comprehensive thinker. He studied forces and weight. He wrote about economics, theology, biology, geology, law, politics, metaphysics, and mathematics. He claims that he invented Calculus independently from Newton, but is it true? His life: In 1646, Leibniz was born in Germany. When Leibniz was 27 years old, in 1673, he moved to England. In 1675, Leibniz began using the integral symbol, which no one ever used before. In 1676, Leibniz developed the Leibniz Calculus. 8 years later, 1684, Leibniz published a superior system of calculus about notation which was easier to use. At the age of 70, 1716, Leibniz died in his home country, Germany. What is Calculus? Calculus is the branch of mathematics that deals with limits, functions, derivatives, integrals, and infinite series. Calculus has two branches: Differential Calculus: Differential calculus is the study of the derivative of a function. It is the study of how a function changes when its input changes. Differentiation is the process of finding the derivative. The derivative at any point equals to the slope of the tangent line of the functions graph. Basically, the derivative of a function determines the best linear approximation. Integral Calculus: Integral Calculus is the study of the properties, definitions, and applications of both, the indefinite integral and the definite integral. Integration is the method of finding the value of an integral. Integral Calculus is related to two linear operations. Indefinite Integral: The anti-derivative, inverse of derivative Definite integral: When you input a function in the definite integral, it outputs a number. This gives you the area between the graph and the x-axis. The Calculus Controversy: The conflict was an argument between Isaac Newton and Gottfried Leibniz over who first invented calculus. Newton claims that he began working on a form of calculus in 1666, but he did not publish. Gottfried Leibniz began to work on his calculus in 1674, and he published his work in a paper in 1684. Newton created his clumsy method of fluxions, in 1655. However, he feared condemnation. Therefore, he did not publish his work until 1704. The fact that he fought with Leibniz before publishing anything raises the question: Was it Newton who invented Calculus? Leibniz developed his calculus in 1673; he used many symbols that we still use today- derivatives as dy/dx and many more. Leibniz published his work in 1684, 20 years before Newton. The last years of Leibnizs life were poisoned by a controversy with Newton over whether he discovered calculus separately, or whether he had invented another form of ideas that were Newtons. Newton influenced the quarrel. In 1673, Leibniz travelled to England. He met some of the leading scientists, like Robert Hookes and showed them his unfinished calculating machine. He did not meet Newton, but he was shown Newtons unpublished work. After Leibniz came back from England his two miraculous yeasr began. After these two years he was considered a creative genius. One of his inventions was calculus. Leibniz needed to contact a broader scientific community, so he became in contact with Christian Huygens, a Danish scientist, and Collins and Henry Oldenburg, secretary of the Royal Society. Leibniz sent his ideas to Collin. In return, Collin sent Leibniz the latest ideas circulating the Royal Society. In Leibnizs defense, however, some documents sent did not reach Leibniz until after he developed his own way. It was clear that he had developed his own ideas on differentiation and integration. Both Newton and Leibniz had partners who helped them develop calculus. Johann Bernoulli, who used Leibniz calculus to maximize function, motivated Leibniz to fight with Newton. Newton was surrounded by people who Leibniz called enfants perdus, the lost children. Newton led the attack, and they continued to carry the battle. Leibniz was accused of plagiarism, a charge that doesnt carry on when you look at the evidence: 1. He published his method years before Newton published anything on Fluxions. 2. He always referred to his discovery as his own invention. 3. The way he developed his ideas of calculus were different than the way Newton developed his ideas. 4. Leibniz came up with ideas of differential and integral calculus before and of Newtons work was published. In June 1676, Newton wrote to Oldenburg, describing the binomial theory. He also stated that all curves can be reduced to infinite series. Moreover, he stated that areas, lengths of curves, and volumes can be obtained through series. Afterwards, Leibniz sent Newton a letter to clarify series. Newton replied by talking about finding the maxima and minima, differentials, and many other topics. However, he did not mention anything about fluxions. Later, Leibniz published his calculus in 1684. When Newton published his work, Newton found out that Leibnizs calculus was very similar to his. Newton also came to know later on that Leibniz has learnt ideas from Collins and Oldenburg; these ideas came from Newton and Gregory. In 1672, Leibniz learnt mathematics and got letters from Collins. What was unusual was that Newton sent Collins similar letters at the same time describing fluxions. Newton then accused Leibniz of copying his work. However, the case leaned towards Leibniz. In defense to the accusation, Leibniz said that when he was shown the works of Newton, but he did not learn anything useful because he did not know much mathematics at the time. Leibniz also said that Collins notes were irrelevant to the subject of calculus. Leibniz died dishonored; on the other hand, Newton was given a state funeral. However, History does authenticate Leibniz. As time goes on, the strength of the controversy decreases. And, Leibniz slowly finds his place as one of the best scientists of all time. All in all, Newton was known to be the first inventor of calculus because there is proof that he developed his theory of fluxions first. He also created differentials, and they were later explained by Leibniz. On the other hand, Leibniz also created calculus independently from Newton. Leibniz described his calculus in a different way than Newton. I personally think that Newton made a mistake by not publishing his work as soon as he created it. This is what led to the controversy. I also think that both men deserve the title of calculus inventors just as equally.
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