Factors Impacting Provider Treatment Decision-Making in Early Glottic Cancer.

OBJECTIVES: Transoral laser microsurgery (TLMS) and radiotherapy (XRT) are mainstays of treatment for early glottic carcinoma (EGC). Here, we investigated case-dependent provider treatment preferences and identify factors which impact decision-making in EGC. METHODS: This cross-sectional survey of laryngologists, head-and-neck surgeons, and radiation oncologists presented five diagrammatic cases of progressively advanced EGC (T1/2, N0). Respondents indicated preference for TLMS or XRT and ranked factors which influenced their recommendation for each case. Analysis utilized descriptive statistics, Fischer's exact tests, and Kruskal-Wallis tests for nonparametric data. RESULTS: A total of 141 complete responses (69.5% laryngologists) were received. Most respondents practiced in academic settings (93.5%) and within multidisciplinary teams (94.0%). Anterior commissure involvement was the most important a priori tumor factor for case-independent treatment recommendation (Likert Scale: 4.22/5), followed by Laterality (Likert Scale: 4.02/5). Across all specialties, TLMS was recommended for unilateral T1a lesions. Laryngologists continued recommending TLMS in T2 lesions (41.0%) more than head-and-neck surgeons (5.0%) and radiation oncologists (0.0%). Across all cases, survival and voice outcomes were the most important clinical factors impacting treatment decisions. Radiation oncologists weighed voice more heavily than laryngologists in more complex presentations of EGC (rank: 1.6 vs. 2.7, Kruskall-Wallis: p < 0.05). CONCLUSIONS: In more complex clinical presentations of EGC, preference for TLMS compared to XRT differed across specialists, despite similar rankings of factors driving these treatment recommendations. This may be driven by differing experiences and viewpoints on case-dependent voice outcomes following TLMS versus XRT, suggesting a need for increased understanding of how tumor location and depth impact voice outcomes. LEVEL OF EVIDENCE: V Laryngoscope, 2024.

Developing the POTOMAC Model: A Novel Prediction Model to Study the Impact of Lymphopenia Kinetics on Survival Outcomes in Head and Neck Cancer Via an Ensemble Tree-Based Machine Learning Approach.

PURPOSE: Lymphopenia is associated with poor survival outcomes in head and neck squamous cell carcinoma (HNSCC), yet there is no consensus on whether we should limit lymphopenia risks during treatment. To fully elucidate the prognostic role of baseline versus treatment-related lymphopenia, a robust analysis is necessary to investigate the relative importance of various lymphopenia metrics (LMs) in predicting survival outcomes. METHODS: In this prospective cohort study, 363 patients were eligible for analysis (patients with newly diagnosed, nonmetastatic HNSCC treated with neck radiation with or without chemotherapy in 2015-2019). Data were acquired on 28 covariates: seven baseline, five disease, seven treatment, and nine LMs, including static and time-varying features for absolute lymphocyte count (ALC), neutrophil-to-lymphocyte ratio, and immature granulocytes (IGs). IGs were included, given their hypothesized role in inhibiting lymphocyte function. Overall, there were 4.0% missing data. Median follow-up was 2.9 years. We developed a model (POTOMAC) to predict survival outcomes using a random survival forest (RSF) procedure. RSF uses an ensemble approach to reduce the risk of overfitting and provides internal validation of the model using data that are not used in model development. The ability to predict survival risk was assessed using the AUC for the predicted risk score. RESULTS: POTOMAC predicted 2-year survival with AUCs at 0.78 for overall survival (primary end point) and 0.73 for progression-free survival (secondary end point). Top modifiable risk factors included radiation dose and max ALC decrease. Top baseline risk factors included age, Charlson Comorbidity Index, Karnofsky Performance Score, and baseline IGs. Top-ranking LMs had superior prognostic performance when compared with human papillomavirus status, chemotherapy type, and dose (up to 2, 8, and 65 times higher in variable importance score). CONCLUSION: POTOMAC provides important insights into potential approaches to reduce mortality in patients with HNSCC treated by chemoradiation but needs to be validated in future studies.

Improving Quality Metrics in Radiation Oncology: Implementation of Pretreatment Peer Review for Stereotactic Body Radiation Therapy in Patients with Thoracic Cancer.

Purpose: Traditional peer reviews occur weekly, and can take place up to 1 week after the start of treatment. The American Society for Radiation Oncology peer-review white paper identified stereotactic body radiation therapy (SBRT) as a high priority for contour/plan review before the start of treatment, considering both the rapid-dose falloff and short treatment course. Yet, peer-review goals for SBRT must also balance physician time demands and the desire to avoid routine treatment delays that would occur in the setting of a 100% pretreatment (pre-Tx) review compliance requirement or prolonging the standard treatment planning timeline. Herein, we report on our pilot experience of a pre-Tx peer review of thoracic SBRT cases. Methods and Materials: From March 2020 to August 2021, patients undergoing thoracic SBRT were identified for pre-Tx review, and placed on a quality checklist. We implemented twice-weekly meetings for detailed pre-Tx review of organ-at-risk/target contours and dose constraints in the treatment planning system for SBRT cases. Our quality metric goal was to peer review ≥90% of SBRT cases before exceeding 25% of the dose delivered. We used a statistical process control chart with sigma limits (ie, standard deviations [SDs]) to access compliance rates with pre-Tx review implementation. Results: We identified 252 patients treated with SBRT to 294 lung nodules. When comparing pre-Tx review completion from initial rollout to full implementation, our rates improved from 19% to 79% (ie, from 1 sigma limit [SDs]) below to >2 sigma limits (SDs) above. Additionally, early completion of any form of contour/plan review (defined as any pre-Tx or standard review completed before exceeding 25% of the dose delivered) increased from 67% to 85% (March 2020-November 2020) to 76% to 94% (December 2020-August 2021). Conclusions: We successfully implemented a sustainable workflow for detailed pre-Tx contour/plan review for thoracic SBRT cases in the context of twice-weekly disease site-specific peer-review meetings. We reached our quality improvement objective to peer review ≥90% of SBRT cases before exceeding 25% of the dose delivered. This process was feasible to conduct in an integrated network of sites across our system.

Radiotherapy, lymphopenia and improving the outcome for glioblastoma: a narrative review.

BACKGROUND AND OBJECTIVE: Standard treatment for glioblastoma includes maximal safe resection followed by adjuvant radiation and concurrent temozolomide for 6 weeks, followed by 6 months of maintenance temozolomide; additionally, concurrent high doses of corticosteroids are required for many patients to reduce intracranial pressure and reduce inflammatory side effects. This combination of cytotoxic therapies (including radiotherapy, temozolomide, and corticosteroids) often results in severe treatment-related lymphopenia that can persist beyond the duration of therapy. METHODS: Papers on treatment-related lymphopenia were retrieved to analyze the role of lymphocytes in tumor control, the role of radiotherapy in inducing lymphopenia, understand other contributing factors to lymphopenia and investigate strategies (including altered radiation approaches) that may reduce the impact of lymphopenia for patients with glioblastoma in the future. KEY CONTENT AND FINDINGS: Radiation, in particular, plays an important role in lymphopenia. Lymphocytes are considered the most radiosensitive cells in the human body, and ionizing radiation often results in apoptotic response and rapid death of lymphocytes within hours of exposure. As a result, radiotherapy can lead to systemic immunosuppression including lymphopenia which is permissive of tumor growth and is linked to impaired local control and reduced survival. For this reason, interactions between radiotherapy treatment and the immune response to tumor is the subject of active study. This study also explores promising lymphocyte-medicated immune therapies which have developed clinical use for many non-glioblastoma cancer types, with promising preclinical results in glioblastoma treatment. CONCLUSIONS: Limiting treatment-related lymphopenia is especially important in improving treatment outcomes for glioblastoma. Research on strategies to reduce the impact of lymphopenia may promote improved treatment outcomes for glioblastoma patients.

3D-printed Magnetic Resonance (MR)-based gynecological phantom for image-guided brachytherapy training.

PURPOSE/OBJECTIVES: There is a clinical need to develop anatomic phantoms for simulation-based learning in gynecological brachytherapy. Here, we provide a step-by-step approach to build a life-sized gynecological training phantom based on magnetic resonance imaging (MRI) of an individual patient. Our hypothesis is that this phantom can generate convincing ultrasound (US) images that are similar to patient scans. METHODS: Organs-at-risk were manually segmented using patient scans (MRI). The gynecological phantom was constructed using positive molds from 3D printing and polyvinyl chloride (PVC) plastisol. Tissue texture/acoustic properties were simulated using different plastic softener/hardener ratios and microbead densities. Nine readers (residents) were asked to evaluate 10 cases (1 ultrasound image per case) and categorize each as a "patient" or "phantom" image. To evaluate whether the phantom and patient images were equivalent, we used a multireader, multicase equivalence study design with two composite null hypotheses with proportion (pr) at H01: pr ≤ 0.35 and H02: pr ≥ 0.65. Readers were also asked to review US videos and identify the insertion of an interstitial needle into the pelvic phantom. Computed Tomography (CT) and magnetic resonance (MR) images of the phantom were acquired for a feasibility study. RESULTS: Readers correctly classified "patient" and "phantom" scans at pr = 53.3% ± 6.2% (p values 0.013 for H01 and 0.054 for H02, df = 5.96). Readers reviewed US videos and identified the interstitial needle 100% of the time in transabdominal view, and 78% in transrectal view. The phantom was CT and MR safe. CONCLUSIONS: We have outlined a manufacturing process to create a life-sized, gynecological phantom that is compatible with multi-modality imaging and can be used to simulate clinical scenarios in image-guided brachytherapy procedures.

Clinical features and surgical outcomes of intracranial and spinal cord subependymomas.

OBJECTIVE: Subependymomas are low-grade ependymal tumors whose clinical characteristics, radiographic features, and postsurgical outcomes are incompletely characterized due to their rarity. The authors present an institutional case series and a systematic literature review to achieve a better understanding of subependymomas. METHODS: Adult patients with histologically confirmed subependymoma or mixed subependymoma-ependymoma surgically treated at a tertiary hospital between 1992 and 2020 were identified. A systematic literature review of the PubMed, Embase, Web of Science, and Google Scholar databases from inception until December 4, 2020, was conducted according to PRISMA guidelines. Data extracted from both groups included demographics, radiographic features, tumor characteristics, management, and follow-up variables. RESULTS: Forty-eight unique patients with subependymoma were identified by chart review; of these patients, 8 (16.7%) had mixed subependymoma-ependymoma tumors. The median age at diagnosis was 49 years (IQR 19.8 years), and 26 patients (54.2%) were male. Forty-two patients (87.5%) had intracranial subependymomas, and 6 (12.5%) had spinal tumors. The most common presentation was headache (n = 20, 41.7%), although a significant number of tumors were diagnosed incidentally (n = 16, 33.3%). Among the 42 patients with intracranial tumors, 15 (35.7%) had hydrocephalus, and the most common surgical strategy was a suboccipital approach with or without C1 laminectomy (n = 26, 61.9%). Gross-total resection (GTR) was achieved in 33 cases (68.7%), and 2 patients underwent adjuvant radiotherapy. Most patients had no major postsurgical complications (n = 34, 70.8%), and only 1 (2.1%) had recurrence after GTR. Of 2036 reports initially identified in the systematic review, 39 were eligible for inclusion, comprising 477 patients. Of 462 patients for whom tumor location was reported, 406 (87.9%) were intracranial, with the lateral ventricle as the most common location (n = 214, 46.3%). Spinal subependymomas occurred in 53 patients (11.5%), with 3 cases (0.6%) in multiple locations. Similar to the case series at the authors' institution, headache was the most common presenting symptom (n = 231, 54.0%) among the 428 patients whose presentation was reported. Twenty-seven patients (6.3%) were diagnosed incidentally, and 36 cases (8.4%) were found at autopsy. Extent of resection was reported for 350 patients, and GTR was achieved in 250 (71.4%). Fifteen of 337 patients (4.5%) had recurrence or progression. CONCLUSIONS: The authors' case series and literature review demonstrate that patients with subependymoma are well managed with resection and generally have a favorable prognosis.

Label-free imaging of human brain tissue at subcellular resolution for potential rapid intra-operative assessment of glioma surgery.

Background: Frozen section and smear preparation are the current standard for intraoperative histopathology during cancer surgery. However, these methods are time-consuming and subject to limited sampling. Multiphoton microscopy (MPM) is a high-resolution non-destructive imaging technique capable of optical sectioning in real time with subcellular resolution. In this report, we systematically investigated the feasibility and translation potential of MPM for rapid histopathological assessment of label- and processing-free surgical specimens. Methods: We employed a customized MPM platform to capture architectural and cytological features of biological tissues based on two-photon excited NADH and FAD autofluorescence and second harmonic generation from collagen. Infiltrating glioma, an aggressive disease that requires subcellular resolution for definitive characterization during surgery, was chosen as an example for this validation study. MPM images were collected from resected brain specimens of 19 patients and correlated with histopathology. Deep learning was introduced to assist with image feature recognition. Results: MPM robustly captures diagnostic features of glioma including increased cellularity, cellular and nuclear pleomorphism, microvascular proliferation, necrosis, and collagen deposition. Preliminary application of deep learning to MPM images achieves high accuracy in distinguishing gray from white matter and cancer from non-cancer. We also demonstrate the ability to obtain such images from intact brain tissue with a multiphoton endomicroscope for intraoperative application. Conclusion: Multiphoton imaging correlates well with histopathology and is a promising tool for characterization of cancer and delineation of infiltration within seconds during brain surgery.

A 55-Year-Old Man With Cough and Hematochezia.

CASE PRESENTATION: A 55-year-old man presented to the ED with a 3-week history of worsening cough and shortness of breath. He had blood-tinged sputum, fever, night sweats, and a 2.7 kg weight loss within the same period. For the past few days, he had taken amoxicillin-clavulanate for presumed sinusitis. Despite this, his symptoms persisted, prompting him to seek further evaluation. His medical history was significant for ulcerative colitis and he had some bloody diarrhea for the past few weeks. Medications included aspirin, mesalamine, multivitamins, folic acid, and herbal supplements including gingko biloba, ginseng, and turmeric-ginger. He never smoked and drank alcohol occasionally. Family history was notable for stroke and myocardial infarction.

AI-Assisted In Situ Detection of Human Glioma Infiltration Using a Novel Computational Method for Optical Coherence Tomography.

PURPOSE: In glioma surgery, it is critical to maximize tumor resection without compromising adjacent noncancerous brain tissue. Optical coherence tomography (OCT) is a noninvasive, label-free, real-time, high-resolution imaging modality that has been explored for glioma infiltration detection. Here, we report a novel artificial intelligence (AI)-assisted method for automated, real-time, in situ detection of glioma infiltration at high spatial resolution.Experimental Design: Volumetric OCT datasets were intraoperatively obtained from resected brain tissue specimens of 21 patients with glioma tumors of different stages and labeled as either noncancerous or glioma-infiltrated on the basis of histopathology evaluation of the tissue specimens (gold standard). Labeled OCT images from 12 patients were used as the training dataset to develop the AI-assisted OCT-based method for automated detection of glioma-infiltrated brain tissue. Unlabeled OCT images from the other 9 patients were used as the validation dataset to quantify the method detection performance. RESULTS: Our method achieved excellent levels of sensitivity (∼100%) and specificity (∼85%) for detecting glioma-infiltrated tissue with high spatial resolution (16 µm laterally) and processing speed (∼100,020 OCT A-lines/second). CONCLUSIONS: Previous methods for OCT-based detection of glioma-infiltrated brain tissue rely on estimating the tissue optical attenuation coefficient from the OCT signal, which requires sacrificing spatial resolution to increase signal quality, and performing systematic calibration procedures using tissue phantoms. By overcoming these major challenges, our AI-assisted method will enable implementing practical OCT-guided surgical tools for continuous, real-time, and accurate intraoperative detection of glioma-infiltrated brain tissue, facilitating maximal glioma resection and superior surgical outcomes for patients with glioma.

Intraoperative imaging techniques for glioma surgery.

Gliomas are CNS neoplasms that infiltrate the surrounding brain parenchyma, complicating their treatment. Tools that increase extent of resection while preventing neurological deficit are essential to improve prognosis of patients diagnosed with gliomas. Tools such as intraoperative MRI, ultrasound and fluorescence-guided microsurgery have been used in the surgical resection of CNS gliomas with the goal of maximizing extent of resection to improve patient outcomes. In addition, emerging experimental techniques, for example, optical coherence tomography and Raman spectroscopy are promising techniques which could 1 day add to the increasing armamentarium used in the surgical resection of CNS gliomas. Here, we present the potential advantages and limitations of these imaging techniques for the purposes of identifying gliomas in the operating room.

Robust and fast characterization of OCT-based optical attenuation using a novel frequency-domain algorithm for brain cancer detection.

Cancer is known to alter the local optical properties of tissues. The detection of OCT-based optical attenuation provides a quantitative method to efficiently differentiate cancer from non-cancer tissues. In particular, the intraoperative use of quantitative OCT is able to provide a direct visual guidance in real time for accurate identification of cancer tissues, especially these without any obvious structural layers, such as brain cancer. However, current methods are suboptimal in providing high-speed and accurate OCT attenuation mapping for intraoperative brain cancer detection. In this paper, we report a novel frequency-domain (FD) algorithm to enable robust and fast characterization of optical attenuation as derived from OCT intensity images. The performance of this FD algorithm was compared with traditional fitting methods by analyzing datasets containing images from freshly resected human brain cancer and from a silica phantom acquired by a 1310 nm swept-source OCT (SS-OCT) system. With graphics processing unit (GPU)-based CUDA C/C++ implementation, this new attenuation mapping algorithm can offer robust and accurate quantitative interpretation of OCT images in real time during brain surgery.

Detection of human brain cancer infiltration ex vivo and in vivo using quantitative optical coherence tomography.

More complete brain cancer resection can prolong survival and delay recurrence. However, it is challenging to distinguish cancer from noncancer tissues intraoperatively, especially at the transitional, infiltrative zones. This is especially critical in eloquent regions (for example, speech and motor areas). This study tested the feasibility of label-free, quantitative optical coherence tomography (OCT) for differentiating cancer from noncancer in human brain tissues. Fresh ex vivo human brain tissues were obtained from 32 patients with grade II to IV brain cancer and 5 patients with noncancer brain pathologies. On the basis of volumetric OCT imaging data, pathologically confirmed brain cancer tissues (both high- and low-grade) had significantly lower optical attenuation values at both cancer core and infiltrated zones when compared with noncancer white matter, and OCT achieved high sensitivity and specificity at an attenuation threshold of 5.5 mm(-1) for brain cancer patients. We also used this attenuation threshold to confirm the intraoperative feasibility of performing in vivo OCT-guided surgery using a murine model harboring human brain cancer. Our OCT system was capable of processing and displaying a color-coded optical property map in real time at a rate of 110 to 215 frames per second, or 1.2 to 2.4 s for an 8- to 16-mm(3) tissue volume, thus providing direct visual cues for cancer versus noncancer areas. Our study demonstrates the translational and practical potential of OCT in differentiating cancer from noncancer tissue. Its intraoperative use may facilitate safe and extensive resection of infiltrative brain cancers and consequently lead to improved outcomes when compared with current clinical standards.

New considerations in radiation treatment planning for brain tumors: neural progenitor cell-containing niches.

The purpose of this critical review is to explore the controversy regarding the relationship between radiation dose to the neural progenitor cell (NPC) niches and patient outcomes, in terms of both toxicity and tumor control. NPCs in the subventricular zone (SVZ) and hippocampus are paradoxically associated with long-term neurocognitive sequelae of brain irradiation, as well as resistance to therapy and tumor recurrence. The reconciliation of these somewhat opposing functions is challenging. Current literature suggests that radiation and other treatments against the NPC in the hippocampus and the SVZ may influence patient outcome. As a result, both the SVZ and the hippocampus could have important implications on radiation treatment planning strategies, and future laboratory and clinical evaluations will be critical in designing studies to optimize treatment outcome, effectiveness, and safety.

Ultrasound elastography as a tool for imaging guidance during prostatectomy: initial experience.

BACKGROUND: During laparoscopic or robotic assisted laparoscopic prostatectomy, the surgeon lacks tactile feedback which can help him tailor the size of the excision. Ultrasound elastography (USE) is an emerging imaging technology which maps the stiffness of tissue. In the paper we are evaluating USE as a palpation equivalent tool for intraoperative image guided robotic assisted laparoscopic prostatectomy. MATERIAL/METHODS: Two studies were performed: 1) A laparoscopic ultrasound probe was used in a comparative study of manual palpation versus USE in detecting tumor surrogates in synthetic and ex-vivo tissue phantoms; N=25 participants (students) were asked to provide the presence, size and depth of these simulated lesions, and 2) A standard ultrasound probe was used for the evaluation of USE on ex-vivo human prostate specimens (N=10 lesions in N=6 specimens) to differentiate hard versus soft lesions with pathology correlation. Results were validated by pathology findings, and also by in-vivo and ex-vivo MR imaging correlation. RESULTS: In the comparative study, USE displayed higher accuracy and specificity in tumor detection (sensitivity=84%, specificity=74%). Tumor diameters and depths were better estimated using USE versus with manual palpation. USE also proved consistent in identification of lesions in ex-vivo prostate specimens; hard and soft, malignant and benign, central and peripheral. CONCLUSIONS: USE is a strong candidate for assisting surgeons by providing palpation equivalent evaluation of the tumor location, boundaries and extra-capsular extension. The results encourage us to pursue further testing in the robotic laparoscopic environment.

Preliminary study of injury from heating systemically delivered, nontargeted dextran-superparamagnetic iron oxide nanoparticles in mice.

AIM: To assess the potential for injury to normal tissues in mice due to heating systemically delivered magnetic nanoparticles in an alternating magnetic field (AMF). MATERIALS & METHODS: Twenty three male nude mice received intravenous injections of dextran-superparamagnetic iron oxide nanoparticles on days 1-3. On day 6, they were exposed to AMF. On day 7, blood, liver and spleen were harvested and analyzed. RESULTS: Iron deposits were detected in the liver and spleen. Mice that had received a high-particle dose and a high AMF experienced increased mortality, elevated liver enzymes and significant liver and spleen necrosis. Mice treated with low-dose superparamagnetic iron oxide nanoparticles and a low AMF survived, but had elevated enzyme levels and local necrosis in the spleen. CONCLUSION: Magnetic nanoparticles producing only modest heat output can cause damage, and even death, when sequestered in sufficient concentrations. Dextran-superparamagnetic iron oxide nanoparticles are deposited in the liver and spleen, making these the sites of potential toxicity. Original submitted 16 August 2011; Revised submitted 21 March 2012; Published online 26 July 2012.

Inter- and intrafraction patient positioning uncertainties for intracranial radiotherapy: a study of four frameless, thermoplastic mask-based immobilization strategies using daily cone-beam CT.

PURPOSE: To determine whether frameless thermoplastic mask-based immobilization is adequate for image-guided cranial radiosurgery. METHODS AND MATERIALS: Cone-beam CT localization data from patients with intracranial tumors were studied using daily pre- and posttreatment scans. The systems studied were (1) Type-S IMRT (head only) mask (Civco) with head cushion; (2) Uni-Frame mask (Civco) with head cushion, coupled with a BlueBag body immobilizer (Medical Intelligence); (3) Type-S head and shoulder mask with head and shoulder cushion (Civco); (4) same as previous, coupled with a mouthpiece. The comparative metrics were translational shift magnitude and average rotation angle; systematic inter-, random inter-, and random intrafraction positioning error was computed. For strategies 1-4, respectively, the analysis for interfraction variability included data from 20, 9, 81, and 11 patients, whereas that for intrafraction variability included a subset of 7, 9, 16, and 8 patients. The results were compared for statistical significance using an analysis of variance test. RESULTS: Immobilization system 4 provided the best overall accuracy and stability. The mean interfraction translational shifts (± SD) were 2.3 (± 1.4), 2.2 (± 1.1), 2.7 (± 1.5), and 2.1 (± 1.0) mm whereas intrafraction motion was 1.1 (± 1.2), 1.1 (± 1.1), 0.7 (± 0.9), and 0.7 (± 0.8) mm for devices 1-4, respectively. No significant correlation between intrafraction motion and treatment time was evident, although intrafraction motion was not purely random. CONCLUSIONS: We find that all frameless thermoplastic mask systems studied are viable solutions for image-guided intracranial radiosurgery. With daily pretreatment corrections, symmetric PTV margins of 1 mm would likely be adequate if ideal radiation planning and targeting systems were available.

Analytical approximations for the amplitude and period of a relaxation oscillator.

BACKGROUND: Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. RESULTS: We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10x less sensitive to protein decay rates), efficiency (2x more efficient), and dynamic range (30 to 60 decibel increase). The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. CONCLUSION: Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.