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Olfactory dysfunction is common in classical infratentorial superficial siderosis of the central nervous system. J Neurol 2022; 269:6582-6588. [PMID: 35997818 PMCID: PMC9396566 DOI: 10.1007/s00415-022-11329-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Revised: 08/04/2022] [Accepted: 08/05/2022] [Indexed: 11/12/2022]
Abstract
Background Established features of classical infratentorial superficial siderosis (iSS) include hearing loss, impaired balance, myelopathy and, less commonly, cognitive compromise. Olfactory function may be affected but dedicated studies are lacking. This study aimed to assess the prevalence of olfactory dysfunction in iSS and correlate it with auditory and cognitive functions. Methods Ten participants with iSS completed the University of Pennsylvania Smell Identification Test (UPSIT). The scores were compared with population norms; regression analysis was performed to evaluate associations between the scores and hearing thresholds (3-frequency average, 3FA) or the number of cognitive domains impaired. Imaging was reviewed for haemosiderin distribution and to exclude other causes of olfactory and hearing dysfunction. Results Eight of ten participants were male; the mean (standard deviation, SD) age was 52.5 (14.5) years. Olfactory hypofunction was identified in all participants and in six (60%) was moderate or completely absent. The mean UPSIT score of 25.5 (7.8) was significantly worse than population norms (difference in means − 10.0; 95% CI − 15.6 to − 4.4). Linear regression identified an association between UPSIT and hearing thresholds (R = 0.75; p = 0.013). The score decreases by 0.157 units (95% CI − 0.31 to − 0.002; p = 0.048) per unit increase in 3FA, after adjusting for hearing loss risk factors. There was no statistically significant association between UPSIT and cognitive function (R = 0.383; p = 0.397). Conclusion We report a high prevalence of olfactory dysfunction in iSS, the severity of which correlated with hearing loss. Olfaction appears to be a core feature of the iSS clinical syndrome that should be assessed routinely.
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Conversion to Hybrid Deep Brain Stimulation System to Enable Multi-Contact Fractionation Can be Therapeutic. Mov Disord 2022; 37:1321-1323. [PMID: 35393689 DOI: 10.1002/mds.29007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 03/09/2022] [Accepted: 03/15/2022] [Indexed: 11/09/2022] Open
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Coordinated Reset Vibrotactile Stimulation Induces Sustained Cumulative Benefits in Parkinson's Disease. Front Physiol 2021; 12:624317. [PMID: 33889086 PMCID: PMC8055937 DOI: 10.3389/fphys.2021.624317] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 02/05/2021] [Indexed: 12/19/2022] Open
Abstract
BACKGROUND Abnormal synchronization of neuronal activity in dopaminergic circuits is related to motor impairment in Parkinson's disease (PD). Vibrotactile coordinated reset (vCR) fingertip stimulation aims to counteract excessive synchronization and induce sustained unlearning of pathologic synaptic connectivity and neuronal synchrony. Here, we report two clinical feasibility studies that examine the effect of regular and noisy vCR stimulation on PD motor symptoms. Additionally, in one clinical study (study 1), we examine cortical beta band power changes in the sensorimotor cortex. Lastly, we compare these clinical results in relation to our computational findings. METHODS Study 1 examines six PD patients receiving noisy vCR stimulation and their cortical beta power changes after 3 months of daily therapy. Motor evaluations and at-rest electroencephalographic (EEG) recordings were assessed off medication pre- and post-noisy vCR. Study 2 follows three patients for 6+ months, two of whom received daily regular vCR and one patient from study 1 who received daily noisy vCR. Motor evaluations were taken at baseline, and follow-up visits were done approximately every 3 months. Computationally, in a network of leaky integrate-and-fire (LIF) neurons with spike timing-dependent plasticity, we study the differences between regular and noisy vCR by using a stimulus model that reproduces experimentally observed central neuronal phase locking. RESULTS Clinically, in both studies, we observed significantly improved motor ability. EEG recordings observed from study 1 indicated a significant decrease in off-medication cortical sensorimotor high beta power (21-30 Hz) at rest after 3 months of daily noisy vCR therapy. Computationally, vCR and noisy vCR cause comparable parameter-robust long-lasting synaptic decoupling and neuronal desynchronization. CONCLUSION In these feasibility studies of eight PD patients, regular vCR and noisy vCR were well tolerated, produced no side effects, and delivered sustained cumulative improvement of motor performance, which is congruent with our computational findings. In study 1, reduction of high beta band power over the sensorimotor cortex may suggest noisy vCR is effectively modulating the beta band at the cortical level, which may play a role in improved motor ability. These encouraging therapeutic results enable us to properly plan a proof-of-concept study.
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Multiparametric laryngeal assessment of the effect of thalamic deep brain stimulation on essential vocal tremor. Parkinsonism Relat Disord 2020; 81:106-112. [PMID: 33120071 DOI: 10.1016/j.parkreldis.2020.10.026] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/07/2020] [Revised: 10/09/2020] [Accepted: 10/12/2020] [Indexed: 11/28/2022]
Abstract
OBJECTIVE EVT is a refractory voice disorder that significantly affects quality of life. This work aims to conduct a multiparametric assessment of the effect of deep brain stimulation (DBS) of the thalamic ventral intermediate nucleus (VIM) on essential vocal tremor (EVT) and investigate the relation between DBS lead location and EVT outcomes. METHODS Nine participants underwent DBS for essential tremor and were diagnosed with co-occurring EVT in this prospective cohort study. Objective measurements including acoustic evaluation of vocal fundamental frequency (F0) and intensity modulation and subjective measurements including physiologic evaluation of the oscillatory movement of the laryngeal muscles and vocal tract and perceptual ratings of tremor severity were collected PRE and POST DBS. Finally, we investigated the relation between DBS lead location and EVT outcomes. RESULTS Acoustic modulations of F0 and intensity were significantly improved POST DBS. Physiologic assessment showed a POST DBS reduction of oscillatory movement in the laryngeal muscles and vocal tract, but not significantly. Listener and participant perception, of EVT severity was also significantly reduced. Finally, our results indicate better EVT control with increased distance to midline of left VIM thalamic stimulation. CONCLUSIONS By employing a battery of objective and subjective measures, our study supports the benefit of DBS for the treatment of EVT and specifies the acoustic and physiologic mechanisms that mediate its positive effect. We further provide preliminary results on the relation between lead location and EVT outcomes, laying the foundation for future studies to clarify the optimal DBS target for the treatment of EVT.
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Abstract P4-01-06: Diffuse optical tomography can predict pathologic complete response in patients with HER2+ or triple negative breast cancer undergoing neoadjuvant chemotherapy. Cancer Res 2017. [DOI: 10.1158/1538-7445.sabcs16-p4-01-06] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Abstract
Background
Pathologic complete response (pCR) predicts clinical outcome in women who receive neoadjuvant chemotherapy (NACT) for breast cancer. Identifying who will have a pCR early during NACT has the potential to save patients months of ineffective chemotherapy and limit unnecessary toxicity; however, no method currently is standardly used. Diffuse optical tomography (DOT) uses near-infrared light to measure concentrations of oxyhemoglobin [HbO2], deoxyhemoglobin [Hb], total hemoglobin [HbT], and oxygen saturation [SO2%], and can assess tissue structure and vascularity. As it is inexpensive, fast, and does not require radiation or intravenous contrast no radiation nor IV contrast, DOT has the potential to become an integral part of NACT to predict responses to NACT. Given the particular significance for pCR in HER2+ and triple negative breast cancer (TNBC), we prospectively evaluated whether a 2 week change in DOT parameters could predict pCR after 5 months of NACT in these subtypes.
Methods
We conducted a prospective cohort study of women with stage II-IIIC breast cancer scheduled to receive NACT with 12 weeks of weekly taxol and four cycles of doxorubicin with cyclophosphamide (AC). We evaluated the associations between residual cancer burden (RCB: 0-3; pCR= RCB 0) and changes in DOT measures. Optical imaging was performed at baseline and before the following: Taxol #3, Taxol #5, AC #1, AC #2, and surgery. Correlation and t-testing were used to evaluate the relationship between 2-week DOT changes and pathologic response.
Results
In a prospectively accrued, longitudinal clinical study with DOT, at least 20 patients with HER2+ or TNBC were enrolled. For patients with these tumor subtypes, there was a significant association between pCR after 5 months of NACT (i.e. RCB 0) and change in the following DOT parameters comparing baseline to after 2 weeks of taxol: HBO (p=0.02), HBT (p=0.02), and S02% (p=0.03). No significant association was seen with HB (p=0.20) or water (p=0.85). When looking specifically at patients with TNBC (n=at least 8 patients), these associations were particulars strong between pCR and the following DOT parameters: HBO (p=0.004), HBT (p=0.009), and S02% (p=0.04). Additional patients are anticipated in this study are anticipated to complete NACT and will be reported at SABCS.
Conclusions
Optical imaging can provide imaging biomarkers to monitor breast cancer response to NACT. Early predictions of pathologic response to NACT can be made with high accuracy as early as two weeks after treatment initiation. These findings are specifically strong in TNBC, a group for whom pCR is predictive of clinical outcome.
Citation Format: Kalinsky K, Lee S, Zhong X, Lim EA, Gunther JE, Hibshoosh H, Kim HK, Accordino M, Crew K, Hielscher A, Hershman DL. Diffuse optical tomography can predict pathologic complete response in patients with HER2+ or triple negative breast cancer undergoing neoadjuvant chemotherapy [abstract]. In: Proceedings of the 2016 San Antonio Breast Cancer Symposium; 2016 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2017;77(4 Suppl):Abstract nr P4-01-06.
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Influencing secondary school STUDENTS' conservation behavior intention through an interpretive education program on the malayan tapir. EVALUATION AND PROGRAM PLANNING 2016; 58:60-69. [PMID: 27315301 DOI: 10.1016/j.evalprogplan.2016.05.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2015] [Revised: 04/20/2016] [Accepted: 05/23/2016] [Indexed: 06/06/2023]
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Prophylactic anticoagulation in Guillain-Barré syndrome: too much of a good thing? J Neurol Neurosurg Psychiatry 2016; 87:795-7. [PMID: 26187723 DOI: 10.1136/jnnp-2015-310815] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/12/2015] [Accepted: 07/01/2015] [Indexed: 11/04/2022]
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Over the Counter Medication and Dietary Supplements Use Among Older Adults. VALUE IN HEALTH : THE JOURNAL OF THE INTERNATIONAL SOCIETY FOR PHARMACOECONOMICS AND OUTCOMES RESEARCH 2014; 17:A506. [PMID: 27201544 DOI: 10.1016/j.jval.2014.08.1540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
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Indirect Comparison of Exacerbation Frequency Between Aclidinium and Tiotropium in Patients With Chronic Obstructive Pulmonary Disease. VALUE IN HEALTH : THE JOURNAL OF THE INTERNATIONAL SOCIETY FOR PHARMACOECONOMICS AND OUTCOMES RESEARCH 2014; 17:A589. [PMID: 27202009 DOI: 10.1016/j.jval.2014.08.2016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
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Abstract P4-01-14: Two-week change in optical tomography predicts residual cancer burden score in women treated with neoadjuvant chemotherapy. Cancer Res 2013. [DOI: 10.1158/0008-5472.sabcs13-p4-01-14] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Abstract
Background: A low Residual Cancer Burden (RCB) score after neoadjuvant chemotherapy (NACT) predicts an improved survival in patients (pts) with breast cancer (BC). While an early predictor of tumor response to NACT would allow for treatment optimization, no ideal method exists. Diffuse optical tomography (DOT) is a novel, fast, and low-cost imaging approach that assesses the distribution of water (H2O), oxyhemoglobin (HbO), and deoxyhemoglobin (Hb) concentrations, as a measure of tissue vascularity, without the use of ionizing radiation or breast compression, allowing for safe repeated measurements. We hypothesize that changes in DOT parameters will predict the RCB score following NACT.
Methods: Women with stage II-IIIc invasive BC scheduled to undergo NACT with 12 cycles of a weekly taxane followed by 4 cycles of doxorubicin with cyclophosphamide were enrolled. Treatment with biologic therapies was allowed. DOT assessments were made before starting NACT, 2 weeks into treatment, and before surgery. DOT data were reconstructed into 3D images of the tumor region, from which HbO, Hb, and H2O concentrations were extracted. Final pathology specimens were scored for the RCB index (continuous measure), RCB class (0, 1, 2, 3), and a dichotomized RCB score (RCB class 0 or 1: responders to NACT; RCB class 2 or 3: non-responders). Ki-67 was measured on baseline tumor biopsies and surgical specimens. Correlation analysis, ANOVA testing, and two sample t-tests were used to evaluate the relationship between the 2-week changes in DOT parameters and the RCB score and Ki-67 level.
Results: Since July 2011, we have recruited 24 pts of a total planned accrual of 40. 19 pts have undergone surgery and complete data is available for 13 at this time. Of the 13 pts, 4 had a pCR (RCB 0), 2 had RCB 1, 6 had RCB 2, and 1 had RCB 3. The Pearson correlations between the 2-week change in HbO, Hb, and H2O with the continuous RCB index were 0.76 (p = 0.0022), 0.87 (p = 0.0001), and 0.74 (p = 0.0038), respectively. There was a significant difference in the 2-week Hb change for pts with RCB 0 compared to pts with RCB 1, 2, or 3. There were significant differences in the 2-week change in H2O and HbO for pts with RCB 0 compared to pts with RCB 2. There were also significant differences between DOT parameters by the dichotomized RCB score (table 1). Ki-67 change was correlated with 2-week H2O change (Pearson r = 0.61 p = 0.045).
2-week DOT% change by RCB class and dichotomized RCB score HbOHbOH2ORCB 0-38%-28.5%-6.7%RCB 1-3.9%-2.9%-0.2%RCB 2+2.3%-0.6%+0.7%RCB 3+1.0%+10.9%-0.4% Responders (RCB 0/1)-26.6%-20%-4.5%Non-Responders (RCB 2/3)+2.1%+1%+0.6%P value0.010.00690.014
Conclusions: Two-week DOT change is an early predictor of response to NACT as measured by the RCB score. We found significant associations between the RCB index and Ki-67 with 2-week changes in HbO, Hb, and H2O. Significantly different changes in DOT parameters were associated with the other RCB classifications. We are analyzing DOT data on the remaining pts and will conduct biomarker assessments of microvessel density changes. Additional pts are being recruited to evaluate DOT's predictive ability by tumor subtype.
Citation Information: Cancer Res 2013;73(24 Suppl): Abstract nr P4-01-14.
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Abstract P4-02-07: Early Optical Tomography Changes Predict Breast Cancer Response to Neoadjuvant Chemotherapy. Cancer Res 2012. [DOI: 10.1158/0008-5472.sabcs12-p4-02-07] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Abstract
Background: Pathologic complete response (pCR) or a low Residual Cancer Burden (RCB) score following neoadjuvant chemotherapy (NACT) predicts a superior survival in breast cancer (BC) patients. An early predictive marker of tumor response during NACT would provide a way to optimize treatment for non-responders; however, no ideal technology currently exists. Diffuse optical tomography (DOT) is a novel, fast, safe, and low-cost technique that uses near infrared light to provide 3D data on tissue vascularity without the use of radiation, making it a promising technology for assessing early tumor response to NACT. We hypothesized that a 2-week change in DOT parameters would predict response to NACT as measured by the RCB score.
Methods: Women with stage II-IIIc invasive BC scheduled to undergo NACT with 12 cycles of a weekly taxane followed by 4 cycles of doxorubicin with cyclophosphamide (AC) were enrolled. Treatment with additional biologic therapies was allowed. DOT measurements were made before starting NACT, 2 weeks into treatment, and before surgery. Concentrations of oxyhemoglobin [HbO2], deoxyhemoglobin [Hb], total hemoglobin [HbT], and tissue scattering (SC) were measured by DOT. Final pathology specimens were scored for the RCB index (continuous measure), RCB class (0, 1, 2, 3), and a dichotomized RCB score (RCB class 0 or 1: responders to NACT; RCB class 2 or 3: non-responders). Correlation analysis, ANOVA testing, and two sample t-tests were used to evaluate the relationship between the two-week changes in DOT parameters and the RCB score.
Results: Since July 2011, we have recruited 11 pts, of whom 7 have undergone surgery. Complete data is available for 6 pts. Two of 7 pts had a pCR (RCB 0), 1 had RCB 1, 3 had RCB 2, and 1 had RCB 3. The Pearson correlation between the 2-week change in [Hb] and the continuous RCB index was 0.94 (p = 0.0047), and that between the 2-week change in SC and the RCB index was 0.93 (p = 0.0073). At 2 weeks, the [Hb] decreased by 6.7% for pts whose pathology demonstrated an RCB 0 (pCR), 1.8% for RCB 1, 0.6% for RCB 2, and increased 0.7% for RCB 3. ANOVA and Tukey testing demonstrated a significant difference in the [Hb] change for pts with RCB 0 compared to pts with RCB 1, 2, or 3 (p <0.05). At 2 weeks, SC decreased by 26.5% for pts with RCB 0, 19.3% for RCB 1, 3.7% for RCB 2, and increased by 25.1% for RCB 3. There was a significant difference in the SC change for pts with RCB 0 compared to pts with RCB 3 (p <0.05). Responders (RCB 0/1) had a 5% decrease in [Hb] at 2 weeks compared to non-responders (RCB 2/3) who had a decrease in 0.18% in [Hb] (p = 0.0045), and responders had a 24% decrease in SC compared to non-responders who had an increase in 6% (p = 0.044).
Conclusions: DOT change is an early predictor of response to NACT as measured by the RCB score. We found a significant linear association between the RCB index and the 2-week change in [Hb] and SC. Significantly different changes in DOT parameters were associated with the other RCB classifications. Additional recruitment is ongoing and differences by tumor subtype will be evaluated.
*These two authors contributed equally to this study
Citation Information: Cancer Res 2012;72(24 Suppl):Abstract nr P4-02-07.
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P2-14-03: A Comparison of Biologic Differences in Tumors in a Matched Cohort of Hispanic and Caucasian Women with Early-Stage Breast Cancer Using the 21-Gene Recurrence Score Assay. Cancer Res 2011. [DOI: 10.1158/0008-5472.sabcs11-p2-14-03] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Abstract
Background: Several studies demonstrate that Hispanic women have a higher mortality rate and lower incidence of breast cancer (BC) as compared to Caucasian women. This survival pattern has also been observed in Hispanic women with untreated, early-stage BC. The Hispanic population should be considered a heterogeneous group, however, given the various racial and national backgrounds that comprise this entity. As African American (AA) similarly demonstrate a worse survival as compared to Caucasian women, a retrospective analysis of 27 tumor from AA patients (pts) showed a significantly higher expression of the 5 proliferation genes in the 21-gene recurrence score (RS) assay (Oncotype Dx) as compared to other races, with no significant difference observed in the 21-gene RS. The primary aim of this analysis is to investigate biologic differences between Hispanic women in a primarily Dominican Republic population, as compared to Caucasian women, as determined by indices in the 21-gene RS assay.
Methods: We collected data from women with early-stage breast cancer who underwent RS assay testing between 2005 and 2011. Pt charts were reviewed for ethnicity (Hispanic or other), country of origin, RS, 10-year risk of distant recurrence, and breast tumor ER/PR/HER2 expression by Oncotype Dx. Hispanic pts were matched to Caucasians in a 1:2 fashion based on age (+/− 10 years), tumor stage, and presence of lymph node metastases. Prognostically important clinicopathologic features were collected, including lymphovascular invasion (LVI) and grade. Descriptive statistics were computed. Two Sample t-testing was used to evaluate if RS was equal across by ethnicity groups.
Results: Of 214 pts who underwent RS testing, 30 (13.5%) were Hispanic: 18 from the Dominican Republic, 5 from Puerto Rico, and 1 from various Central and South American populations. The 30 Hispanic women were matched to 57 Caucasians: total population 87 pts. The mean RS for Caucasian women was 18.3 (range: 0–54) and for Caucasians: 15.5 (range: 1–38). By two Sample t test, no statistically different differences were observed between Hispanic and Caucasian women in regards to the RS (p= 0.2828) or 10-year distant recurrence score after 5 years of anti-estrogen therapy (p=0.4218). No differences were observed in median ER expression (9.4% vs. 10.1%: Hispanic vs. Caucasian), PR (7.2% vs. 7.7%), or HER2 (9.2% vs. 9.0%). LVI was numerically more frequently identified in Hispanic pts [7/30 (23.3%) vs. 8/57 (14.0%)], as were grade III tumors [7/30 (23.3%) and 4/57 (7%)].
Conclusions: Similar to the findings with AA pts, there was no significant difference in RS between Hispanic and matched Caucasian women with early-stage BCs. A numerical trend to a higher RS was seen in this Hispanic population of primarily pts from the Dominican Republic. We will evaluate for differences in the 5 genes involved in proliferation (CCNB1, MKI17, MYBL2, BIRC5, AURKA). Also, further analyses will be conducted with additional pts to determine if the numeric differences in RS, LVI, and grade are observed in a larger cohort.
Citation Information: Cancer Res 2011;71(24 Suppl):Abstract nr P2-14-03.
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Abstract
We analyze the dynamics of a spherical scaffold in rotating bioreactors (or clinostats). The idealized clinostat environment consists of a purely rotational flow that is perpendicular to a gravitational field. We confirm through a detailed analytical study that lift effects considerably alter the position of the equilibrium point reached by the scaffolds in the (vertical) direction collinear to the gravitational field. This result holds for small particle and shear Reynolds numbers. Our analysis shows that the inertial lift effect is negligible in the horizontal direction. We show that for all rotations of practical interest, and for the range of particle Reynolds number smaller than unity, the vertical coordinate of the equilibrium point is strongly affected by consideration of lift effects. For light (heavy) particles, inclusion of lift in the formation forces the equilibrium position to be below (above) the horizontal plane that contains the axis of rotation. The equilibrium point for light particles is stable and therefore is observable experimentally. The equilibrium point for heavy particles is unstable. We also estimate the stress level applied to the scaffold and derive an algebraic expression that indicates that the stress level acting on the scaffold decreases with increasing shear Reynolds number.
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