Experimental Comparison of Two Degrees-of-Freedom Vortex-Induced Vibration on High and Low Aspect Ratio Cylinders with Small Mass Ratio

Vortex-induced motion (VIM) is a specific way for naming the vortex-induced vibration (VIV) acting on floating units. The VIM phenomenon can occur in monocolumn production, storage and offloading system (MPSO) and spar platforms, structures presenting aspect ratio lower than 4 and unity mass ratio, i.e., structural mass equal to the displaced fluid mass. These platforms can experience motion amplitudes of approximately their characteristic diameters, and therefore, the fatigue life of mooring lines and risers can be greatly affected. Two degrees-of-freedom VIV model tests based on cylinders with low aspect ratio and small mass ratio have been carried out at the recirculating water channel facility available at NDF-EPUSP in order to better understand this hydro-elastic phenomenon. The tests have considered three circular cylinders of mass ratio equal to one and different aspect ratios, respectively L/D = 1.0, 1.7, and 2.0, as well as a fourth cylinder of mass ratio equal to 2.62 and aspect ratio of 2.0. The Reynolds number covered the range from 10 000 to 50 000, corresponding to reduced velocities from 1 to approximately 12. The results of amplitude and frequency in the transverse and in-line directions were analyzed by means of the Hilbert-Huang transform method (HHT) and then compared to those obtained from works found in the literature. The comparisons have shown similar maxima amplitudes for all aspect ratios and small mass ratio, featuring a decrease as the aspect ratio decreases. Moreover, some changes in the Strouhal number have been indirectly observed as a consequence of the decrease in the aspect ratio. In conclusion, it is shown that comparing results of small-scale platforms with those from bare cylinders, all of them presenting low aspect ratio and small mass ratio, the laboratory experiments may well be used in practical investigation, including those concerning the VIM phenomenon acting on platforms. [DOI: 10.1115/1.4006755]

Influence of miniscrew dental root proximity on its degree of late stability

Purpose of this study was to evaluate the influence of miniscrew dental root proximity on its late stability degree. 40 miniscrews were inserted between maxillary second premolars and first molars for anterior retraction. Post-surgical radiographs were used to measure the septum width in the insertion site, insertion height, distal and mesial distance from miniscrew to dental root, and the smallest distance between miniscrew and dental root. The miniscrews were divided in two groups according to septum width: ?3 mm (20 miniscrews) and >3 mm (20 miniscrews). The soft tissue in the insertion site, sensitivity during load, plaque around the miniscrew, and evaluation period were also considered. The results showed no significant difference in miniscrew mobility degree and success rate between groups. Miniscrew dental root proximity did not influence the stability and success rate when the distance between the miniscrew and dental root indicated no periodontal ligament invasion. The overall success rate was 90% and no variable was associated with miniscrew failure. Nevertheless, patient sensitivity was frequently associated with some degree of mini-implant mobility. The septum width did not influence the stability and success rate of this anchorage system, but the extreme root proximity did.

One and two degrees-of-freedom Vortex-Induced Vibration experiments with yawed cylinders

Vortex-Induced Vibration (VIV) experiments were carried out with yawed cylinders. The purpose was to investigate the validity of the Independence Principle (IP) for properly describing the flow characteristics and the dynamics of structures subjected to oblique flow. Five yaw angles in relation to the direction perpendicular to the free stream velocity were tested, namely View the MathML sourceθ=0°,10°,20°,30° and 45°. Both the upstream and downstream orientations were tested. The models were mounted on a leaf spring apparatus that allows experiments with one or two degrees of freedom. The Reynolds numbers based on the component normal to the cylinder axis fell in the interval 3×10343×1034. The mass ratio parameter was m⁎=2.6m⁎=2.6 and the cylinder aspect ratio was L/D≈13L/D≈13 for all the experiments. Time histories of displacement and hydrodynamic forces were acquired. Considering only the component of the free stream which is normal to the cylinder axis, the results of amplitude and force coefficients agreed reasonably well with the non-yawed ones for yaw angles up to 20° for both one and two degrees-of-freedom experiments. This indicates the validity of the IP for this yaw angle range. For yaw angles larger than 20°, a decrease in the maximum amplitude was observed. The decrease in the oscillation amplitudes was related to a larger modulation in the phase shift between force and displacement. Differences in the results for upstream and downstream were observed and were more evident for the larger yaw angle. These differences can be associated to the asymmetric cylinder end conditions.

Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps

The g-factor is a constant which connects the magnetic moment $vec{mu}$ of a charged particle, of charge q and mass m, with its angular momentum $vec{J}$. Thus, the magnetic moment can be writen $ vec{mu}_J=g_Jfrac{q}{2m}vec{J}$. The g-factor for a free particle of spin s=1/2 should take the value g=2. But due to quantum electro-dynamical effects it deviates from this value by a small amount, the so called g-factor anomaly $a_e$, which is of the order of $10^{-3}$ for the free electron. This deviation is even bigger if the electron is exposed to high electric fields. Therefore highly charged ions, where electric field strength gets values on the order of $10^{13}-10^{16}$V/cm at the position of the bound electron, are an interesting field of investigations to test QED-calculations. In previous experiments [H"aff00,Ver04] using a single hydrogen-like ion confined in a Penning trap an accuracy of few parts in $10^{-9}$ was obtained. In the present work a new method for precise measurement of magnetic the electronic g-factor of hydrogen-like ions is discussed. Due to the unavoidable magnetic field inhomogeneity in a Penning trap, a very important contribution to the systematic uncertainty in the previous measurements arose from the elevated energy of the ion required for the measurement of its motional frequencies. Then it was necessary to extrapolate the result to vanishing energies. In the new method the energy in the cyclotron degree of freedom is reduced to the minimum attainable energy. This method consist in measuring the reduced cyclotron frequency $nu_{+}$ indirectly by coupling the axial to the reduced cyclotron motion by irradiation of the radio frequency $nu_{coup}=nu_{+}-nu_{ax}+delta$ where $delta$ is, in principle, an unknown detuning that can be obtained from the knowledge of the coupling process. Then the only unknown parameter is the desired value of $nu_+$. As a test, a measurement with, for simplicity, artificially increased axial energy was performed yielding the result $g_{exp}=2.000~047~020~8(24)(44)$. This is in perfect agreement with both the theoretical result $g_{theo}=2.000~047~020~2(6)$ and the previous experimental result $g_{exp1}=2.000~047~025~4(15)(44).$ In the experimental results the second error-bar is due to the uncertainty in the accepted value for the electron's mass. Thus, with the new method a higher accuracy in the g-factor could lead by comparison to the theoretical value to an improved value of the electron's mass. [H"af00] H. H"affner et al., Phys. Rev. Lett. 85 (2000) 5308 [Ver04] J. Verd'u et al., Phys. Rev. Lett. 92 (2004) 093002-1

Analysis and Implementation of Multiphase-Multilevel Inverter for Open-Winding Loads

Research work carried out in focusing a novel multiphase-multilevel ac motor drive system much suitable for low-voltage high-current power applications. In specific, six-phase asymmetrical induction motor with open-end stator winding configuration, fed from four standard two-level three-phase voltage source inverters (VSIs). Proposed synchronous reference frame control algorithm shares the total dc source power among the 4 VSIs in each switching cycle with three degree of freedom. Precisely, first degree of freedom concerns with the current sharing between two three-phase stator windings. Based on modified multilevel space vector pulse width modulation shares the voltage between each single VSIs of two three-phase stator windings with second and third degree of freedom, having proper multilevel output waveforms. Complete model of whole ac motor drive based on three-phase space vector decomposition approach was developed in PLECS - numerical simulation software working in MATLAB environment. Proposed synchronous reference control algorithm was framed in MATLAB with modified multilevel space vector pulse width modulator. The effectiveness of the entire ac motor drives system was tested. Simulation results are given in detail to show symmetrical and asymmetrical, power sharing conditions. Furthermore, the three degree of freedom are exploited to investigate fault tolerant capabilities in post-fault conditions. Complete set of simulation results are provided when one, two and three VSIs are faulty. Hardware prototype model of quad-inverter was implemented with two passive three-phase open-winding loads using two TMS320F2812 DSP controllers. Developed McBSP (multi-channel buffered serial port) communication algorithm able to control the four VSIs for PWM communication and synchronization. Open-loop control scheme based on inverse three-phase decomposition approach was developed to control entire quad-inverter configuration and tested with balanced and unbalanced operating conditions with simplified PWM techniques. Both simulation and experimental results are always in good agreement with theoretical developments.

Comparing the demonstration of freedom from Trichinella infection of domestic pigs by traditional and risk-based surveillance

Traditionally, the routine artificial digestion test is applied to assess the presence of Trichinella larvae in pigs. However, this diagnostic method has a low sensitivity compared to serological tests. The results from artificial digestion tests in Switzerland were evaluated over a time period of 15 years to determine by when freedom from infection based on these data could be confirmed. Freedom was defined as a 95% probability that the prevalence of infection was below 0.0001%. Freedom was demonstrated after 12 years at the latest. A new risk-based surveillance approach was then developed based on serology. Risk-based surveillance was also assessed over 15 years, starting in 2010. It was shown that by using this design, the sample size could be reduced by at least a factor of 4 when compared with the traditional testing regimen, without lowering the level of confidence in the Trichinella-free status of the pig population.

Osseointegration of hollow cylinder based spinal implants in normal and osteoporotic vertebrae: a sheep study

INTRODUCTION: Osteoporosis is not only responsible for an increased number of metaphyseal and spinal fractures but it also complicates their treatment. To prevent the initial loosening, we developed a new implant with an enlarged implant/bone interface based on the concept of perforated, hollow cylinders. We evaluated whether osseointegration of a hollow cylinder based implant takes place in normal or osteoporotic bone of sheep under functional loading conditions during anterior stabilization of the lumbar spine. MATERIALS AND METHODS: Osseointegration of the cylinders and status of the fused segments (ventral corpectomy, replacement with iliac strut, and fixation with testing implant) were investigated in six osteoporotic (age 6.9 +/- 0.8 years, mean body weight 61.1 +/- 5.2 kg) and seven control sheep (age 6.1 +/- 0.2 years, mean body weight 64.9 +/- 5.7 kg). Osteoporosis was introduced using a combination protocol of ovariectomy, high-dose prednisone, calcium and phosphor reduced diet and movement restriction. Osseointegration was quantified using fluorescence and conventional histology; fusion status was determined using biomechanical testing of the stabilized segment in a six-degree-of-freedom loading device as well as with radiological and histological staging. RESULTS: Intact bone trabeculae were found in 70% of all perforations without differences between the two groups (P = 0.26). Inside the cylinders, bone volume/total volume was significantly higher than in the control vertebra (50 +/- 16 vs. 28 +/- 13%) of the same animal (P<0.01), but significantly less (P<0.01) than in the near surrounding (60 +/- 21%). After biomechanical testing as described in Sect. "Materials and methods", seven spines (three healthy and four osteoporotic) were classified as completely fused and six (four healthy and two osteoporotic) as not fused after a 4-month observation time. All endplates were bridged with intact trabeculae in the histological slices. CONCLUSIONS: The high number of perforations, filled with intact trabeculae, indicates an adequate fixation; bridging trabeculae between adjacent endplates and tricortical iliac struts in all vertebrae indicates that the anchorage is adequate to promote fusion in this animal model, even in the osteoporotic sheep.

[Serological and clinical proof of freedom from Equine Infectious Anemia (EIA) in imported and domestic horses in Switzerland]

Since 1991, no cases of Equine Infectious Anemia (EIA) have been reported in Switzerland. Risk factors for introduction of the virus into Switzerland are still present or have even increased as frequent inapparent infections, large numbers of imported horses, (since 2003) absence of compulsory testing prior to importation, EIA cases in surrounding Europe, possible illegal importation of horses, frequent short-term stays, poor knowledge of the disease among horse owners and even veterinarians. The aim of this study was to provide evidence of freedom from EIA in imported and domestic horses in Switzerland. The serum samples from 434 horses imported since 2003 as well as from 232 domestic horses fifteen years of age or older (since older horses have naturally had a longer time of being exposed to the risk of infection) were analysed using a commercially available ELISA test. All samples were seronegative, indicating that the maximum possible prevalence that could have been missed with this sample was 0.5% (95% confidence).

Light curing through glass ceramics with a second- and a third-generation LED curing unit: effect of curing mode on the degree of conversion of dual-curing resin cements

Objectives The aim of this study was to measure the degree of conversion (DC) of five dual-curing resin cements after different curing modes with a second- and a third-generation light-emitting diode (LED) curing unit. Additionally, irradiance of both light curing units was measured at increasing distances and through discs of two glass ceramics for computer-aided design/manufacturing (CAD/CAM). Materials and methods Irradiance and spectra of the Elipar FreeLight 2 (Standard Mode (SM)) and of the VALO light curing unit (High Power Mode (HPM) and Xtra Power Mode (XPM)) were measured with a MARC radiometer. Irradiance was measured at increasing distances (control) and through discs (1.5 to 6 mm thickness) of IPS Empress CAD and IPS e.max CAD. DC of Panavia F2.0, RelyX Unicem 2 Automix, SpeedCEM, BisCem, and BeautiCem SA was measured with an attenuated total reflectance–Fourier transform infrared spectrometer when self-cured (negative control) or light cured in SM for 40 s, HPM for 32 s, or XPM for 18 s. Light curing was performed directly (positive control) or through discs of either 1.5- or 3-mm thickness of IPS Empress CAD or IPS e.max CAD. DC was analysed with Kruskal–Wallis tests followed by pairwise Wilcoxon rank sum tests (α = 0.05). Results Maximum irradiances were 1,545 mW/cm2 (SM), 2,179 mW/cm2 (HPM), and 4,156 mW/cm2 (XPM), and all irradiances decreased by >80 % through discs of 1.5 mm, ≥95 % through 3 mm, and up to >99 % through 6 mm. Generally, self-curing resulted in the lowest DC. For some cements, direct light curing did not result in higher DC compared to when light cured through ceramic discs. For other cements, light curing through ceramic discs of 3 mm generally reduced DC. Conclusions Light curing was favourable for dual-curing cements. Some cements were more susceptible to variations in curing mode than others. Clinical relevance When light curing a given cement, the higher irradiances of the third-generation LED curing unit resulted in similar DC compared to the second-generation one, though at shorter light curing times.

Region Specific Response of Intervertebral Disc Cells to Complex Dynamic Loading: An Organ Culture Study Using a Dynamic Torsion-Compression Bioreactor

The spine is routinely subjected to repetitive complex loading consisting of axial compression, torsion, flexion and extension. Mechanical loading is one of the important causes of spinal diseases, including disc herniation and disc degeneration. It is known that static and dynamic compression can lead to progressive disc degeneration, but little is known about the mechanobiology of the disc subjected to combined dynamic compression and torsion. Therefore, the purpose of this study was to compare the mechanobiology of the intervertebral disc when subjected to combined dynamic compression and axial torsion or pure dynamic compression or axial torsion using organ culture. We applied four different loading modalities 1. control: no loading (NL), 2. cyclic compression (CC), 3. cyclic torsion (CT), and 4. combined cyclic compression and torsion (CCT) on bovine caudal disc explants using our custom made dynamic loading bioreactor for disc organ culture. Loads were applied for 8 h/day and continued for 14 days, all at a physiological magnitude and frequency. Our results provided strong evidence that complex loading induced a stronger degree of disc degeneration compared to one degree of freedom loading. In the CCT group, less than 10\% nucleus pulposus (NP) cells survived the 14 days of loading, while cell viabilities were maintained above 70\% in the NP of all the other three groups and in the annulus fibrosus (AF) of all the groups. Gene expression analysis revealed a strong up-regulation in matrix genes and matrix remodeling genes in the AF of the CCT group. Cell apoptotic activity and glycosaminoglycan content were also quantified but there were no statistically significant differences found. Cell morphology in the NP of the CCT was changed, as shown by histological evaluation. Our results stress the importance of complex loading on the initiation and progression of disc degeneration.

Evaluation of a new six degrees of freedom couch for radiation therapy

Purpose: The aim of this work is to evaluate the geometric accuracy of a prerelease version of a new six degrees of freedom (6DoF) couch. Additionally, a quality assurance method for 6DoF couches is proposed. Methods: The main principle of the performance tests was to request a known shift for the 6DoF couch and to compare this requested shift with the actually applied shift by independently measuring the applied shift using different methods (graph paper, laser, inclinometer, and imaging system). The performance of each of the six axes was tested separately as well as in combination with the other axes. Functional cases as well as realistic clinical cases were analyzed. The tests were performed without a couch load and with a couch load of up to 200 kg and shifts in the range between −4 and +4 cm for the translational axes and between −3° and +3° for the rotational axes were applied. The quality assurance method of the new 6DoF couch was performed using a simple cube phantom and the imaging system. Results: The deviations (mean ± one standard deviation) accumulated over all performance tests between the requested shifts and the measurements of the applied shifts were −0.01 ± 0.02, 0.01 ± 0.02, and 0.01 ± 0.02 cm for the longitudinal, lateral, and vertical axes, respectively. The corresponding values for the three rotational axes couch rotation, pitch, and roll were 0.03° ± 0.06°, −0.04° ± 0.12°, and −0.01° ± 0.08°, respectively. There was no difference found between the tests with and without a couch load of up to 200 kg. Conclusions: The new 6DoF couch is able to apply requested shifts with high accuracy. It has the potential to be used for treatment techniques with the highest demands in patient setup accuracy such as those needed in stereotactic treatments. Shifts can be applied efficiently and automatically. Daily quality assurance of the 6DoF couch can be performed in an easy and efficient way. Long-term stability has to be evaluated in further tests.

Assessment of patient setup errors in IGRT in combination with a six degrees of freedom couch

PURPOSE The range of patient setup errors in six dimensions detected in clinical routine for cranial as well as for extracranial treatments, were analyzed while performing linear accelerator based stereotactic treatments with frameless patient setup systems. Additionally, the need for re-verification of the patient setup for situations where couch rotations are involved was analyzed for patients treated in the cranial region. METHODS AND MATERIALS A total of 2185 initial (i.e. after pre-positioning the patient with the infrared system but before image guidance) patient setup errors (1705 in the cranial and 480 in the extracranial region) obtained by using ExacTrac (BrainLAB AG, Feldkirchen, Germany) were analyzed. Additionally, the patient setup errors as a function of the couch rotation angle were obtained by analyzing 242 setup errors in the cranial region. Before the couch was rotated, the patient setup error was corrected at couch rotation angle 0° with the aid of image guidance and the six degrees of freedom (6DoF) couch. For both situations attainment rates for two different tolerances (tolerance A: ± 0.5mm, ± 0.5°; tolerance B: ± 1.0 mm, ± 1.0°) were calculated. RESULTS The mean (± one standard deviation) initial patient setup errors for the cranial cases were -0.24 ± 1.21°, -0.23 ± 0.91° and -0.03 ± 1.07° for the pitch, roll and couch rotation axes and 0.10 ± 1.17 mm, 0.10 ± 1.62 mm and 0.11 ± 1.29 mm for the lateral, longitudinal and vertical axes, respectively. Attainment rate (all six axes simultaneously) for tolerance A was 0.6% and 13.1% for tolerance B, respectively. For the extracranial cases the corresponding values were -0.21 ± 0.95°, -0.05 ± 1.08° and -0.14 ± 1.02° for the pitch, roll and couch rotation axes and 0.15 ± 1.77 mm, 0.62 ± 1.94 mm and -0.40 ± 2.15 mm for the lateral, longitudinal and vertical axes. Attainment rate (all six axes simultaneously) for tolerance A was 0.0% and 3.1% for tolerance B, respectively. After initial setup correction and rotation of the couch to treatment position a re-correction has to be performed in 77.4% of all cases to fulfill tolerance A and in 15.6% of all cases to fulfill tolerance B. CONCLUSION The analysis of the data shows that all six axes of a 6DoF couch are used extensively for patient setup in clinical routine. In order to fulfill high patient setup accuracies (e.g. for stereotactic treatments), a 6DoF couch is recommended. Moreover, re-verification of the patient setup after rotating the couch is required in clinical routine.

Time to endovascular reperfusion and degree of disability in acute stroke.

OBJECTIVE Faster time from onset to recanalization (OTR) in acute ischemic stroke using endovascular therapy (ET) has been associated with better outcome. However, previous studies were based on less-effective first-generation devices, and analyzed only dichotomized disability outcomes, which may underestimate the full effect of treatment. METHODS In the combined databases of the SWIFT and STAR trials, we identified patients treated with the Solitaire stent retriever with achievement of substantial reperfusion (Thrombolysis in Cerebral Infarction [TICI] 2b-3). Ordinal numbers needed to treat values were derived by populating joint outcome tables. RESULTS Among 202 patients treated with ET with TICI 2b to 3 reperfusion, mean age was 68 (±13), 62% were female, and median National Institutes of Health Stroke Scale (NIHSS) score was 17 (interquartile range [IQR]: 14-20). Day 90 modified Rankin Scale (mRS) outcomes for OTR time intervals ranging from 180 to 480 minutes showed substantial time-related reductions in disability across the entire outcome range. Shorter OTR was associated with improved mean 90-day mRS (1.4 vs. 2.4 vs. 3.3, for OTR groups of 124-240 vs. 241-360 vs. 361-660 minutes; p < 0.001). The number of patients identified as benefitting from therapy with shorter OTR were 3-fold (range, 1.5-4.7) higher on ordinal, compared with dichotomized analysis. For every 15-minute acceleration of OTR, 34 per 1,000 treated patients had improved disability outcome. INTERPRETATION Analysis of disability over the entire outcome range demonstrates a marked effect of shorter time to reperfusion upon improved clinical outcome, substantially higher than binary metrics. For every 5-minute delay in endovascular reperfusion, 1 of 100 patients has a worse disability outcome. Ann Neurol 2015;78:584-593.

Repair of Annulus fibrosus with Genipin-enhanced Fibrin Hydrogel and silk membrane- fleece

Introduction Low back pain is often caused by a trauma causing disc herniation and /or disc degeneration. Although there are some promising approaches for nucleus pulposus repair, the inner tissue of the intervertebral disc (IVD) so far no treatment or repair is available for annulus fibrosus (AF) injuries. Here we aimed to develop a new method to seal and repair AF injuries by using a silk fleece composite and a genipin enhanced hydrogel. Methods Bovine (b) IVDs were harvested under aseptic conditions and kept in free swelling conditions for 24h in high-glucose DMEM containing 5% bovine serum for equilibration (1). A circular 2mm biopsy punch (Polymed Medical Center, Switzerland) was used to form a reproducible defect in the AF. For filling the defect and keeping the silk composite in place a human-derived fibrin gel (Baxter Tisseel, Switzerland) enhanced with 4.2mg/ml of the cross linker genipin (Wako Chemicals GmbH, Germany) was used. The silk composite consists of a mesh- and a membrane side (Spintec Engineering GmbH, Germany); the membrane is facing outwards to form a seal. bIVDs were cultured in vitro for 14 days either under dynamic load in a custom-built bioreactor under physiological conditions (0.2MPa load and ±2° torsion at 0.2Hz for 8h/day) or static diurnal load of 0.2MPa (2). At the end of culture discs were checked for seal failure, disc height, metabolic activity, cell death by necrosis (LDH assay), DNA content and glycosaminoglycan content. Results Silk composite maintained its position throughout the 14 days of culture under loaded conditions. Although repaired discs performed slightly lower in cell activity, DNA and GAG content were in the range of the control. Also LDH resulted in similar values compared to control discs (Fig 1). Height loss in repaired discs was in the same range as for static diurnal loaded control samples. For dynamically loaded samples the decrease was comparable to the injured, unrepaired discs. Fig 1 LDH of repaired discs compared to control disc after 24h in free swelling conditions for equilibration and first three loading cycles. Conclusions Silk-genipin-fibrin reinforced hydrogel is a promising approach to close AF defects as tested by two degree of freedom loading. In further experiments cytocompatibility of genipin has to be investigated. References 1. Chan SC, Gantenbein-Ritter B. Preparation of intact bovine tail intervertebral discs for organ culture. J Vis Exp 2012, Feb 2;60(60):e3490. 2. Walser J, Ferguson SJ, Gantenbein-Ritter B. Design of a mechanical loading device to culture intact bovine caudal motional segments of the spine under twisting motion. In: Davies J, editors. Replacing animal models: a practical guide to creating and using biomimetic alternatives. Chichester, UK: John Wiley & Sons, Ltd.; 2012. p. 89-105. Acknowledgements This project is funded by the Gerbert Rüf Stiftung project # GRS-028/13 and the Swiss National Science Project SNF #310030_153411.

Design of long-term animal bioassay for low-dose extrapolation using a multistage model

Conventional designs of animal bioassays allocate the same number of animals into control and dose groups to explore the spontaneous and induced tumor incidence rates, respectively. The purpose of such bioassays are (a) to determine whether or not the substance exhibits carcinogenic properties, and (b) if so, to estimate the human response at relatively low doses. In this study, it has been found that the optimal allocation to the experimental groups which, in some sense, minimize the error of the estimated response for low dose extrapolation is associated with the dose level and tumor risk. The number of dose levels has been investigated at the affordable experimental cost. The pattern of the administered dose, 1 MTD, 1/2 MTD, 1/4 MTD,....., etc. plus control, gives the most reasonable arrangement for the low dose extrapolation purpose. The arrangement of five dose groups may make the highest dose trivial. A four-dose design can circumvent this problem and has also one degree of freedom for testing the goodness-of-fit of the response model.^ An example using the data on liver tumors induced in mice in a lifetime study of feeding dieldrin (Walker et al., 1973) is implemented with the methodology. The results are compared with conclusions drawn from other studies. ^