Lattice-Based Radiotherapy and Chemoimmunotherapy for Oropharyngeal Squamous Cell Carcinoma

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of squamous cell carcinoma of the oropharynx, which includes the sites tonsil, base of tongue, soft palate, or posterior oropharyngeal wall. Histologic variants will be included (papillary squamous cell carcinoma and basaloid squamous cell carcinoma). Cytologic diagnosis from a cervical lymph node is sufficient in the presence of clinical evidence of a primary tumor in the oropharynx. * Clinical stage T1-T4, N1-N3, M0 * If tissue is positive for p16 by immunohistochemical staining (\>70% staining), patient must have \>10 pk-year smoking history * Zubrod Performance Status of 0-1 * Primary tumor ≥ 3 cm OR at least one lymph node ≥ 3 cm OR primary tumor and lymph node ≥ 3 cm * One of the following combinations of imaging is required within 8 weeks of registration: CT scan of the neck (with contrast) and a whole body PET/CT; or, an MRI of the neck (with contrast) and a whole body PET/CT. Note: A CT scan of the neck and/or a PET/CT performed for the purposes of radiation planning may serve as both staging and planning tools. * Patients must provide their personal smoking history prior to registration. Patients with HPV positive oropharyngeal carcinoma must have a cumulative personal smoking history that exceeds 10 pack-years. Number of pack-years = \[Frequency of smoking (number of cigarettes per day) x duration of cigarette smoking (years)\] / 20. Note: Twenty cigarettes is considered equivalent to one pack. Cigar and pipe tobacco consumption is not included in calculating lifetime pack-years. * Negative serum pregnancy test within 14 days prior to registration for women of childbearing potential. Female subjects of childbearing potential and male subjects with female partners of childbearing potential must be willing to avoid pregnancy. Female subjects of childbearing potential who are undergoing RT or who are partners to male subjects in the study should avoid sexual activity or use a highly effective method of birth control during sexual intercourse. Acceptable, highly effective methods of birth control include: intrauterine device (IUD)/intrauterine hormone releasing system (IUS), bilateral tube occlusion, vasectomized partner, combined (estrogen and progesterone containing) or progesterone-only hormonal contraceptives (oral, intravaginal, transdermal, injectable). * Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception (abstinence/protection) for the duration of treatment/study participation. * The patient must provide study-specific informed consent prior to study entry. * Adequate renal function within 2 weeks prior to registration, defined as follows: * Serum creatinine ≤ 1.5 mg/dl or creatinine clearance (CC) ≥ 50 ml/min determined by 24 hour collection or estimated by Cockcorft-Gault formula. * Adequate hematologic function within 2 weeks prior to registration, defined as follows: Absolute neutrophil count (ANC) ≥ 1,500 cells/mm3; Platelets ≥ 100,000 cells/mm3; and Hemoglobin ≥ 8.0 g/dl. Note: the use of transfusion or other intervention to achieve Hgb ≥ 8.0 g/dl is acceptable * Patients who are HIV positive but who have no prior AIDS-defining illness and have CD4 cells of at least 350/mm3 are eligible. HIV-positive patients must not have multi-drug resistant HIV infection or other concurrent AIDS-defining conditions. Patients must not be sero-positive for Hepatitis B (Hepatitis B surface antigen positive or anti-hepatitis B core antigen positive) or sero-positive for Hepatitis C (anti-Hepatitis C antibody positive). However, patients who are immune to hepatitis B (anti-Hepatitis B surface antibody positive) are eligible (e.g. patients immunized against hepatitis B). * The patient must provide study-specific informed consent prior to study entry. Exclusion Criteria: * Cancers considered to be from an oral cavity site (oral tongue, floor of mouth, alveolar ridge, buccal or lip), or the nasopharynx, hypopharynx, or larynx, even if p16 positive; * Carcinoma of the neck of unknown primary site origin (even if p16 positive) * Distant metastasis or adenopathy below the clavicles; * Gross total excision of both primary and nodal disease; this includes tonsillectomy, local excision of primary site, and nodal excision that removes all clinically and radiographically evident disease. * Simultaneous primary cancers or separate bilateral primary tumor sites; * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 1095 days (3 years) (for example, carcinoma in situ of the breast, oral cavity, or cervix are all permissible); * Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable; * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields; * Severe, active co-morbidity defined as follows: 1. Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months; 2. Transmural myocardial infarction within the last 6 months; 3. Acute bacterial or fungal infection intravenous antibiotics at the time of registration; 4. Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days of registration; 5. Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects; note, however, that laboratory tests for liver function and coagulation parameters are not required for entry into this protocol other than those listed in 5.1. 6. Acquired immune deficiency syndrome (AIDS) based upon the current CDC definition with immune compromise greater than that noted in section 5.1; note, however, that HIV testing is not required for entry into this protocol. The need to exclude patients with AIDS from this protocol is necessary because the treatments involved in this protocol may be significantly immunosuppressive. Protocol-specific requirements may also exclude immune-compromised patients. * Pregnancy; this exclusion is necessary because the treatment in this study may be significantly teratogenic * Prior allergic reaction to cisplatin. * Exclusion Criteria for MRI: Normal MRI exclusion criteria will apply, including those on the following list. A standard MRI safety form will be used to identify potential conditions warranting exclusion. * Electrical implants such as cardiac pacemakers or perfusion pumps * Ferromagnetic implants such as aneurysm clips, surgical clips, prostheses, artificial heart, valves with steel parts, metal fragments, shrapnel, bullets, tattoos near the eye, or steel implants * Ferromagnetic objects such as jewelry or metal clips in clothing * Claustrophobia * History of seizures * Patients with GFR \< 15 ml/min/1.73m2 or who are on dialysis will not have DCE-MRI scan. These patients will have conventional anatomical MRI without contrast and DW-MRI.