Technical Note: The development of a multi-physics simulation tool to estimate the background dose by systemic targeted alpha therapy.

PURPOSE: To predict biological effects of targeted alpha therapy (TAT) in preclinical studies, dosimetry calculations based on the micro-level distributions of emitters are essential. Due to the saturation of the tumor antigenic sites and bonding breaks by decay, some of Alpha-immuno-conjugate and decay daughters may inevitably be transported by convection and diffusion along with blood or lymphatic circulation. This results in highly nonuniform and unsteady distributions of irradiation sources. Since the micro-level distribution of emitters cannot be measured and obtained in patients with current technology, a modeling toolset to give more insight of the internal dose could be an alternative. METHODS: A multi-physics model based on a Monte Carlo microdosimetry technique and computational fluid dynamics (CFD) modeling was developed and applied to multiple internal irradiation sources. The CFD model tracks the path of the radionuclides and the dose model is capable of evaluating the time-dependent absorbed dose to the target. RESULTS: The conceptual model is capable of handling complex nonuniform irradiation sources in vasculature. The results from the simulations indicate that the assumption of homogeneous and motionless distribution of the administered activity used in the conventional dose calculation tends to significantly underestimate or overestimate the absorbed dose to the vascular system in various scenarios. CONCLUSION: Modeling the in vivo transport of radionuclides has the potential to improve the accuracy of TAT dose estimates. It could be the first step to develop a simulation tool set for assessing absorbed dose to tumor or normal tissues and predict the corresponding biological responses in the future.

Dual energy imaging using a clinical on-board imaging system.

Dual energy (DE) imaging consists of obtaining kilovoltage (kV) x-ray images at two different diagnostic energies and performing a weighted subtraction of these images. A third image is then produced that highlights soft tissue. DE imaging has been used by radiologists to aid in the detection of lung malignancies. However, it has not been used clinically in radiotherapy. The goal of this study is to assess the feasibility of performing DE imaging using a commercial on-board imaging system. Both a simple and an anthropomorphic phantom were constructed for this analysis. Planar kV images of the phantoms were obtained using varied imaging energies and mAs. Software was written to perform DE subtraction using empirically determined weighting factors. Tumor detectability was assessed quantitatively using the signal-difference-to-noise ratio (SDNR). Overall DE subtraction suppressed high density objects in both phantoms. The optimal imaging technique, providing the largest SDNR with a dose less than our reference technique was 140 kVp, 1.0 mAs and 60 kVp, 3.2 mAs. Based on this analysis, DE subtraction imaging is feasible using a commercial on-board imaging system and may improve the visualization of tumors in lung cancer patients undergoing image-guided radiotherapy.

Part I. Molecular and cellular characterization of high nitric oxide-adapted human breast adenocarcinoma cell lines.

There is a lack of understanding of the casual mechanisms behind the observation that some breast adenocarcinomas have identical morphology and comparatively different cellular growth behavior. This is exemplified by a differential response to radiation, chemotherapy, and other biological intervention therapies. Elevated concentrations of the free radical nitric oxide (NO), coupled with the up-regulated enzyme nitric oxide synthase (NOS) which produces NO, are activities which impact tumor growth. Previously, we adapted four human breast cancer cell lines: BT-20, Hs578T, T-47D, and MCF-7 to elevated concentrations of nitric oxide (or high NO [HNO]). This was accomplished by exposing the cell lines to increasing levels of an NO donor over time. Significantly, the HNO cell lines grew faster than did each respective ("PARENT") cell line even in the absence of NO donor-supplemented media. This was evident despite each "parent" being morphologically equivalent to the HNO adapted cell line. Herein, we characterize the HNO cells and their biological attributes against those of the parent cells. Pairs of HNO/parent cell lines were then analyzed using a number of key cellular activity criteria including: cell cycle distribution, DNA ploidy, response to DNA damage, UV radiation response, X-ray radiation response, and the expression of significant cellular enzymes. Other key enzyme activities studied were NOS, p53, and glutathione S-transferase-pi (GST-pi) expression. HNO cells were typified by a far more aggressive pattern of growth and resistance to various treatments than the corresponding parent cells. This was evidenced by a higher S-phase percentage, variable radioresistance, and up-regulated GST-pi and p53. Taken collectively, this data provides evidence that cancer cells subjected to HNO concentrations become resistant to free radicals such as NO via up-regulated cellular defense mechanisms, including p53 and GST-pi. The adaptation to NO may explain how tumor cells acquire a more aggressive tumor phenotype.

Dose-volume factors to select patient-specific image-guidance action thresholds in prostate cancer.

For radiation delivery tracking systems that monitor intrafraction prostate motion, generalized departmental threshold protocols may be used. The purpose of this study is to determine whether predefined action thresholds can be generally applied or if patient-specific action thresholds may be required. Software algorithms were developed in the MatLab (The Mathworks Inc., Natick, MA) software environment to simulate shifts of the patient structure set consisting of prostate, bladder, and rectum. These structures were shifted by 1/2 10 mm in each direction in 1 mm increments to simulate displacements during treatment, without taking into consideration organ deformity. Dose-volume data at each shift were plotted and analyzed. A linear relationship was observed between planning dose-volume parameters and shifted dose-volume parameters. For a 5 mm anterior shift, it was observed that individual rectal V70 values increased by absolute magnitudes of 6-15%, dependent on the planning rectal V70 of each patient. Likewise, for a 5 mm inferior shift, individual bladder V70 values increased by 1-14%, dependent on planning bladder V70. This linear relationship was observed for all levels of shifts up to 10 mm. Since rectum and bladder dose-volume changes due to patient shifts are dependent on dose-volume parameters, this study suggests that patient-specific action thresholds may be necessary.

The dosimetric effects of tissue heterogeneities in intensity-modulated radiation therapy (IMRT) of the head and neck.

The dosimetric effects of bone and air heterogeneities in head and neck IMRT treatments were quantified. An anthropomorphic RANDO phantom was CT-scanned with 16 thermoluminescent dosimeter (TLD) chips placed in and around the target volume. A standard IMRT plan generated with CORVUS was used to irradiate the phantom five times. On average, measured dose was 5.1% higher than calculated dose. Measurements were higher by 7.1% near the heterogeneities and by 2.6% in tissue. The dose difference between measurement and calculation was outside the 95% measurement confidence interval for six TLDs. Using CORVUS' heterogeneity correction algorithm, the average difference between measured and calculated doses decreased by 1.8% near the heterogeneities and by 0.7% in tissue. Furthermore, dose differences lying outside the 95% confidence interval were eliminated for five of the six TLDs. TLD doses recalculated by Pinnacle3's convolution/superposition algorithm were consistently higher than CORVUS doses, a trend that matched our measured results. These results indicate that the dosimetric effects of air cavities are larger than those of bone heterogeneities, thereby leading to a higher delivered dose compared to CORVUS calculations. More sophisticated algorithms such as convolution/superposition or Monte Carlo should be used for accurate tailoring of IMRT dose in head and neck tumours.

Comparison of dose calculated by an intensity modulated radiotherapy treatment planning system and an independent monitor unit verification program.

A comparison of isocenter dose calculated by a commercial intensity modulated radiation therapy treatment planning system and independent monitor unit verification calculation (MUVC) software was made. The percent disparity between the treatment plan and MUVC doses were calculated for 507 treatments (head and neck, prostate, abdomen, female pelvis, rectum and anus, and miscellaneous) from 303 patients. The MUVC calculated dose was, on average, 1.4% higher than the treatment planning dose, with a 1.2% standard deviation. The distribution of the disparities appeared to be Gaussian in shape with some variation by treatment site. Based on our analysis, disparities outside the range of +/-3% about the mean value should be checked and resolved prior to treatment delivery.

Using serial imaging data to model variabilities in organ position and shape during radiotherapy.

A model is proposed for incorporating the effects of organ motion into the calculation of dose in a statistical fashion based on serial imaging measurements of organ motion. These measurements can either come from a previously studied population of patients, or they can be specific to the particular patient undergoing therapy. The statistical distribution underlying the measurements of organ motion, including the changes in organ shape, is reconstructed non-parametrically without requiring any assumptions about its functional form. The model is thus capable of simulating organ motions that are not present in the original measurements, yet nonetheless come from the same underlying statistical distribution. The present model overcomes two particular limitations of many organ motion models: (a) the fact that they do not account for changes in organ shape, and (b) the fact that they make physically unrealistic assumptions about the functional form of the statistical distribution of organ motion, such as assuming that it is Gaussian. The present model can form the foundation of methods for the more accurate and clinically relevant calculation of the dose to the target volume and normal tissues.

Numerical analysis of a model of organ motion using serial imaging measurements from prostate radiotherapy.

We previously proposed a model for incorporating the effects of organ motion, including the changes in organ shape, into the calculation of dose in a statistical fashion based on serial imaging measurements of organ motion. In the present paper, numerical studies were used to investigate how the accuracy of the statistical calculation of dose depends on the number of organ motion measurements provided as input into the model. The dose calculated statistically with the model was consistently more accurate than the one obtained by directly resampling the serial measurements of organ motion. It was also more robust relative to the random variabilities present in the input organ motion measurements. The results confirm that the model can reproduce the statistical distribution of the organ motions measured in a serial imaging study, including the changes in organ shape, without making any assumptions about the functional form of this distribution. The model allows a more accurate calculation of dose to be performed from a given number of measurements of organ motion than would otherwise be obtained by directly resampling the measured data. It thus maximizes the information that is extracted from serial imaging measurements.

Initial clinical experience with intensity-modulated whole-pelvis radiation therapy in women with gynecologic malignancies.

OBJECTIVE: Our goal in this article to describe our initial experience with intensity-modulated whole-pelvis radiation therapy (IM-WPRT) in gynecologic malignancies. METHODS: Between February and August 2000, 15 women with cervical (9) or endometrial (6) cancer received IM-WPRT. All patients received a treatment planning computed tomography (CT) scan. On each scan, the target volume (upper vagina, parametrial tissues, presacral region, uterus, and regional lymph nodes) and normal tissues (small bowel, bladder, and rectum) were identified. Using commercially available software, an IM-WPRT plan was generated for each patient. The goal was to provide coverage of the target with the prescription dose (45 Gy) while minimizing the volume of small bowel, bladder, and rectum irradiated. Acute gastrointestinal (GI) and genitourinary (GU) toxic effects in these women were compared with those seen in 25 patients treated with conventional WPRT. RESULTS: IM-WPRT plans provided excellent coverage of the target structures in all patients and were highly conformal, providing considerable sparing of the bladder, rectum, and small bowel. Treatment was well tolerated, with grade 0-1 GI and GU toxicity in 46 and 93% of patients, respectively. IM-WPRT patients had a lower rate of grade 2 GI toxicity (53.4% vs 96%, P = 0.001) than those treated with conventional WPRT. Moreover, the percentage of women requiring no or only infrequent antidiarrheal medications was lower in the IM-WPRT group (73.3% vs 20%, P = 0.001). While grade 2 GU toxicity was also lower in the IM-WPRT patients (6.7% vs 16%), this difference did not reach statistical significance (P = 0.38). CONCLUSION: IM-WPRT provides excellent coverage of the target structures while sparing critical neighboring structures in gynecology patients. Treatment is well tolerated with less acute GI toxicity than conventional WPRT. More patients and longer follow-up are needed to evaluate the full merits of this approach.

Intensity-modulated whole pelvic radiation therapy in patients with gynecologic malignancies.

PURPOSE: To evaluate the ability of intensity-modulated radiation therapy (IMRT) to reduce the volume of small bowel irradiated in women with gynecologic malignancies receiving whole pelvic radiotherapy (WPRT). METHODS AND MATERIALS: Ten women with cervical (5) or endometrial (5) cancer undergoing WPRT were selected for this analysis. A planning CT scan of each patient was obtained following administration of oral, i.v., and rectal contrast. The clinical target volume (CTV) was defined as the proximal vagina, parametrial tissues, uterus (if present), and regional lymph nodes. The CTV was expanded uniformly by 1 cm in all directions to produce a planning target volume (PTV). The bladder, rectum, and small bowel were also delineated in each patient. Two plans were created: a standard "4-field box" with apertures shaped to the PTV in each beam's eye view and an IM-WPRT plan designed to conform to the PTV while minimizing the volume of normal tissues irradiated. Both plans were normalized to deliver 45 Gy to the PTV. Isodose distributions and dose-volume histograms (DVH) were compared. RESULTS: The IM-WPRT plan reduced the volume of small bowel irradiated in all 10 patients at doses above 30 Gy. At the prescription dose, the average volume of small bowel irradiated was reduced by a factor of two (17.4 vs. 33.8%, p = 0.0005). In addition, the average volume of rectum and bladder irradiated at the prescription dose was reduced by 23% in both cases (p = 0.0002 and p = 0.0005, respectively). The average PTV doses delivered by the conventional and IM-WPRT plans were 47.8 Gy and 47.4 Gy, respectively. Corresponding maximum doses were 50.0 Gy and 54.8 Gy, respectively. However, on average, only 3.2% of the PTV received greater than 50.0 Gy in the IM-WPRT plans. CONCLUSION: Our results suggest that IM-WPRT is an effective means of reducing the volume of small bowel irradiated in women with gynecologic malignancies receiving WPRT. This approach potentially offers a method for reducing small bowel complications in patients with gynecologic malignancies.

Tumor control probability model for alpha-particle-emitting radionuclides.

Alpha-particle emitters are currently being evaluated for the treatment of metastatic disease. The dosimetry of alpha-particle emitters is a challenge, however, because the stochastic patterns of energy deposition within cellular targets must be taken into account. We propose a model for the tumor control probability of alpha-particle emitters which takes into account these stochastic effects. An expression for cell survival, which is a function of the microdosimetric single-event specific-energy distribution, is multiplied by the number of cells within the tumor cluster. Poisson statistics is used to model the probability of zero surviving cells within the cluster. Based on this analysis, a number of observations have been made: (1) The dose required to eradicate a tumor is nearly a linear function of the cell survival parameter z(0). (2) Cells with smaller nuclei will require more dose to achieve the same level of tumor control probability, relative to cells with larger nuclei, for an identical source-target configuration and cell sensitivity. (3) As the targeting of alpha-particle emitters becomes more specific, the dose required to achieve a given level of tumor control decreases. (4) Additional secondary effects include cell shape and the initial alpha-particle energy.

Values of "S," , and <(z1)2> for dosimetry using alpha-particle emitters.

In a recent paper [J. Nucl. Med. 38, 1923-1929 (1997)], the authors presented a dosimetry system which combines the computational ease of the MIRD schema with additional information provided by microdosimetry for use with alpha-particle emitters. In addition to the absorbed dose (average specific energy) to the targets (cell nuclei), this system gives the spread (standard deviation) in values of this specific energy received by individual targets. It also gives the fraction of targets receiving zero (or any number of) hits. In this paper, input quantities are presented for alpha-particle energies and cell and nuclear sizes appropriate for the radionuclides being investigated. The quantities include S values for the usual determination of the absorbed dose along with the microdosimetric quantities, and <(z1)2>, the average and average square, respectively, of the single-hit specific energy. Using analytical procedures described previously [Med. Phys. 19, 1385-1393 (1992)], the single-hit distributions of specific energy are determined for the given alpha-particle energies, source locations, and target sizes. From these distributions, the values for the input quantities are calculated. Sources considered are (1) those located inside and on the surface of the target cell and an unbounded source in the medium external to the cell; (2) those distributed uniformly on either side of a plane boundary or on the surface of the plane with a spherical target at various distances from the plane; and (3) those located either inside or on the surface of a spherical boundary centered externally to the target. Examples show how the input quantities are used to provide the spread in specific-energy values and the probability of any number of hits for nuclei of cells exposed to these sources. Thus a complete micro-dosimetric analysis involving the calculation of multi-hit specific energy distributions is not necessary to provide this information. Such information may be useful in interpreting the biological response due to alpha-particle emitters.

Radiotoxicity of bismuth-213 bound to membranes of monolayer and spheroid cultures of tumor cells.

Monoclonal antibody 13A to murine CD44 was used to bind the alpha-particle emitter 213Bi to cell surfaces of cultured EMT-6 or Line 1 tumor cells. Data on kinetics and saturation of binding, cell shape and nuclear size were used to calculate the absorbed dose to the nuclei. Treatment of monolayer cells with [213Bi]MAb 13A produced a classical exponential survival curve with no apparent shoulder. Microdosimetry analyses indicated that 1.4-1.7 Gy produced a 37% surviving fraction (D0). Multicellular spheroids were shown to bind [213Bi]MAb 13A mainly on the outer cell layer. Relatively small amounts of activity added to the spheroids resulted in relatively large absorbed doses. The result was that 3-6-fold less added radioisotope was necessary to kill similar fractions of cells in spheroids than in monolayer cells. These data are consistent with the interpretation that the alpha particles from a single 213Bi atom bound to one cell can penetrate and kill adjacent cells. Flow cytometry was used to sort cells originating from the periphery or from the interior of spheroids. Cells from the outside of the [213Bi]MAb 13A exposed spheroids had a lower surviving fraction per administered activity than cells from the interior. Cells were killed efficiently in spheroids up to 20-30 cells in diameter. The data support the hypothesis that alpha-particle emitters should be very efficient at killing cells in micrometastases of solid tumors.

The use of microdosimetric moments in evaluating cell survival for therapeutic alpha-particle emitters.

In evaluating the efficacy of alpha-particle emitters, a cell survival curve is often determined for a particular source-target configuration. Investigators often wish to use this information about survival for a different source-target configuration which might be more appropriate for a therapeutic application. Since the population cell survival parameter, D0, is a function of the source-target configuration, it is important to determine the individual cell survival parameter, z0, which is more fundamental. Unlike D0, z0 does not depend upon the microdosimetric variations in the specific energy distribution resulting from changes in the source-target configuration. Instead it is determined by the cell sensitivity and the radiation quality. However, the calculation of z0 from the data on survival involves computing the microdosimetric specific energy distributions of the radiation. This paper describes an approximate but sufficiently accurate method for determining z0 from D0 if the first and second moments of the single-hit specific energy distributions are known or can be estimated. Examples of applications are given. This may alleviate the need for multihit microdosimetric calculations.

Late rectal sequelae following definitive radiation therapy for carcinoma of the uterine cervix: a dosimetric analysis.

PURPOSE: This study attempted to correlate patient, treatment, and dosimetric factors with the risk of late rectal sequelae in patients treated with radiation therapy (RT) for cervical carcinoma. METHODS AND MATERIALS: A total of 183 patients with cervical carcinoma (67 Stage I, 93 Stage II, and 23 Stage III) treated with definitive RT with a minimum of 2 years follow-up were evaluated. Treatment consisted of external beam pelvic RT (EBRT) followed by intracavitary RT (ICRT) consisting of one or two insertions. Complications were scored and analyzed as a function of 25 patient and treatment factors. Conventional total rectal doses were obtained by adding together the EBRT and ICRT rectal doses. To account for differences in dose rate between the ICRT and EBRT, and variations in EBRT fractionation schemes, biologically equivalent rectal doses (BED) were calculated using a linear quadratic model. In addition, the influence of the varying proportions of EBRT and ICRT rectal doses were evaluated. RESULTS: Twenty-eight patients (15.3%) developed late rectal sequelae (13 Grade 1, 3 Grade 2, and 12 Grade 3). Diabetes (p = 0.03), Point A dose (p = 0.04), and conventional EBRT dose (p = 0.03) were the most significant factors on multivariate analysis. Logistic regression analysis demonstrated a low risk (<10%) of late rectal sequelae below conventional and biological rectal doses of 75 Gy and 135 BED, respectively. The percentage of rectal dose delivered by the EBRT significantly influenced the dose-response relationship. A defined threshold percentage above which rectal sequelae were more common was identified over the range of doses evaluated. This threshold was 87% at a total rectal dose of 60 Gy and decreased to 60% at 80 Gy. CONCLUSION: Diabetes, Point A, and EBRT doses are the most significant factors associated with the risk of late rectal sequelae in patients treated with RT for cervical carcinoma. The percentage of rectal dose delivered by the EBRT significantly affects the conventional and biological dose-response relationship. This suggests that the volume of rectum irradiated is an important and independent parameter in the development of late rectal sequelae.

Dosimetric framework for therapeutic alpha-particle emitters.

UNLABELLED: Alpha-particle emitters are currently being considered for the treatment of metastatic disease. However, the dosimetry of alpha-particle emitters is a challenge because the dimensions of subcellular targets (e.g., the cell nucleus) are of the same order of magnitude as the range of the particle. Hence, a single dose value is often not representative of the dose delivered to a cell population. Here, we propose a dosimetry system that combines the calculational ease of the Medical Internal Radiation Dosimetry (MIRD) system with the additional information provided by microdosimetry. METHODS: Beginning with the microdosimetric, single-event specific-energy spectrum, we derived expressions for the first and second moments. Using the MIRD S-factor along with these moments, we determined not only the mean absorbed dose but also the s.d. and the fraction of cells receiving zero (or any number of) hits. RESULTS: Using the formalism developed here, we have generated tables for a simple example to demonstrate the use of this method. CONCLUSION: We have developed a formalism for the rapid determination of not only the mean absorbed dose but also the s.d. and fraction of cells receiving zero hits. These parameters are potentially useful in analyzing the biological outcome for cells exposed to alpha-particle irradiation.

A new source localization algorithm with no requirement of one-to-one source correspondence between biplane radiographs.

Conventional source localization algorithms require a one-to-one source correspondence between films. This requirement makes source localization cumbersome and error prone because multiple sources must be carefully digitized and some sources can be obscured or missed. A new source localization algorithm is described in this paper. The algorithm fits a ribbon or needle image on film to a linear-quadratic equation, then analytically determines the 3-D ribbon locus by its image on the other projection, and finally localizes the sources in the ribbon by tracing along the ribbon image. Only three points per ribbon per film are required, and corresponding points need not be identified on the other film. Phantom experiments and tests on clinical cases demonstrate that the source localization algorithm can increase the efficiency by a factor of up to 5, improve accuracy to about 1 mm, and reconstruct obscured or shifted sources without decreased accuracy and efficiency. The simplicity and minimal entry of data make this technique desirable for clinical use.

Relationships between cell survival and specific energy spectra for therapeutic alpha-particle emitters.

Cell survival studies are a means of quantifying the biological effects of radiation. However, for alpha-particle sources, the dose-response relationship is complicated by the dominance of microdosimetric effects. In this work, we relate observed cell survival to the microdosimetric energy deposition spectra. The chord length distributions through spherical cell nuclei for sources distributed inside of, on the surface of and outside of the critical target are used as approximate analytical representations of the single-event specific energy spectra. Mathematical relationships are derived which relate cell survival to the Laplace transform of the single-event specific energy spectrum. The result is an analytical relationship between D0 (the observed slope of the cell survival curve) and Z0 (the specific energy required to reduce the survival probability of a single cell to 1/e). These studies indicate that for small energy deposition events, Z0 is approximately equal to D0. However, as the maximum energy deposited by a single event is increased, there are marked deviations between Z0 and D0. These differences between Z0 and D0 are also related to the shape of the single-event spectrum. This technique provides a powerful tool for relating observed cell survival to microdosimetric quantities for therapeutic alpha-particle emitters.

Electron-photon field matching in the treatment of paranasal sinus tumors: a case report.

The treatment planning of paranasal sinus tumors is technically demanding due to the compact anatomy of the region and the close proximity of critical structures. In the majority of cases, conventional approaches utilizing 2 or 3 photon fields are adequate. However, in patients with locally advanced disease, these standard techniques may result in the unnecessary treatment of surrounding structures. We present here a case in which, because of the complex tumor geometry, conventional techniques would result in treating through both orbits. A novel treatment approach has been devised in which opposed lateral photon fields are matched to an anterior electron field (both in depth and in profile) to provide a uniform dose distribution to the target volume, while minimizing the dose to certain critical structures. The treatment design, in particular the methodology of electron-photon field matching as well as the specification of tissue compensation and customized blocking, is discussed.

Eye shielding for patients treated with total body irradiation.

The incidence of cataracts in patients who have received total body irradiation (TBI) is about 20% and increases to 40% if the patient is treated for graft-versus-host disease. At our institution, all TBI patients are treated with two lateral opposed 24 MV photon fields. No attempt is usually made to shield the eyes during the TBI treatment because of the amount of lead required to adequately attenuate megavoltage photon beams, the difficulty in properly positioning an eye shield and the possibility of compromising the effectiveness of the treatment. However, we were asked to treat a TBI patient who is a professional pilot, and thus his livelihood is contingent upon maintaining perfect vision. A custom eye shield was constructed out of lead and ionization chamber and film measurements were performed under TBI conditions to determine the thickness and location of the eye block to optimize the competing effects of increased scatter and attenuation from the lead. Phantom data were also obtained for 6 MV irradiation for comparison with 24 MV. In-vivo patient and phantom measurements with thermoluminescent dosimeters showed that with visual positioning of the eye block the dose was reduced from 16 to 20% across the orbits of both eyes.