Comparison of dynamic contrast-enhanced MRI parameters of breast lesions at 1.5 and 3.0 T: a pilot study.

OBJECTIVE: To compare dynamic contrast-enhanced (DCE) MRI parameters from scans of breast lesions at 1.5 and 3.0 T. METHODS: 11 patients underwent paired MRI examinations in both Philips 1.5 and 3.0 T systems (Best, Netherlands) using a standard clinical fat-suppressed, T1 weighted DCE-MRI protocol, with 70-76 s temporal resolution. Signal intensity vs time curves were fit with an empirical mathematical model to obtain semi-quantitative measures of uptake and washout rates as well as time-to-peak enhancement (TTP). Maximum percent enhancement and signal enhancement ratio (SER) were also measured for each lesion. Percent differences between parameters measured at the two field strengths were compared. RESULTS: TTP and SER parameters measured at 1.5 and 3.0 T were similar; with mean absolute differences of 19% and 22%, respectively. Maximum percent signal enhancement was significantly higher at 3 T than at 1.5 T (p = 0.006). Qualitative assessment showed that image quality was significantly higher at 3 T (p = 0.005). CONCLUSION: Our results suggest that TTP and SER are more robust to field strength change than other measured kinetic parameters, and therefore measurements of these parameters can be more easily standardized than measurements of other parameters derived from DCE-MRI. Semi-quantitative measures of overall kinetic curve shape showed higher reproducibility than do discrete classification of kinetic curve early and delayed phases in a majority of the cases studied. ADVANCES IN KNOWLEDGE: Qualitative measures of curve shape are not consistent across field strength even when acquisition parameters are standardized. Quantitative measures of overall kinetic curve shape, by contrast, have higher reproducibility.

Monitoring anti-angiogenic therapy in colorectal cancer murine model using dynamic contrast-enhanced MRI: comparing pixel-by-pixel with region of interest analysis.

Sorafenib is a multi-kinase inhibitor that blocks cell proliferation and angiogenesis. It is currently approved for advanced hepatocellular and renal cell carcinomas in humans, where its major mechanism of action is thought to be through inhibition of vascular endothelial growth factor and platelet-derived growth factor receptors. The purpose of this study was to determine whether pixel-by-pixel analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is better able to capture the heterogeneous response of Sorafenib in a murine model of colorectal tumor xenografts (as compared with region of interest analysis). MRI was performed on a 9.4 T pre-clinical scanner on the initial treatment day. Then either vehicle or drug were gavaged daily (3 days) up to the final image. Four days later, the mice were again imaged. The two-compartment model and reference tissue method of DCE-MRI were used to analyze the data. The results demonstrated that the contrast agent distribution rate constant (K(trans)) were significantly reduced (p < 0.005) at day-4 of Sorafenib treatment. In addition, the K(trans) of nearby muscle was also reduced after Sorafenib treatment. The pixel-by-pixel analysis (compared to region of interest analysis) was better able to capture the heterogeneity of the tumor and the decrease in K(trans) four days after treatment. For both methods, the volume of the extravascular extracellular space did not change significantly after treatment. These results confirm that parameters such as K(trans), could provide a non-invasive biomarker to assess the response to anti-angiogenic therapies such as Sorafenib, but that the heterogeneity of response across a tumor requires a more detailed analysis than has typically been undertaken.

Characterizing early contrast uptake of ductal carcinoma in situ with high temporal resolution dynamic contrast-enhanced MRI of the breast: a pilot study.

Improvements in the reliable diagnosis of preinvasive ductal carcinoma in situ (DCIS) by dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) are needed. In this study, we present a new characterization of early contrast kinetics of DCIS using high temporal resolution (HiT) DCE-MRI and compare it with other breast lesions and normal parenchyma. Forty patients with mammographic calcifications suspicious for DCIS were selected for HiT imaging using T(1)-weighted DCE-MRI with ∼7 s temporal resolution for 90 s post-contrast injection. Pixel-based and whole-lesion kinetic curves were fit to an empirical mathematical model (EMM) and several secondary kinetic parameters derived. Using the EMM parameterized and fitted concentration time curve for subsequent analysis allowed for calculation of kinetic parameters that were less susceptible to fluctuations due to noise. The parameters' initial area under the curve (iAUC) and contrast concentration at 1 min (C(1 min)) provided the highest diagnostic accuracy in the task of distinguishing pathologically proven DCIS from normal tissue. There was a trend for DCIS lesions with solid architectural pattern to exhibit a negative slope at 1 min (i.e. increased washout rate) compared to those with a cribriform pattern (p < 0.04). This pilot study demonstrates the feasibility of quantitative analysis of early contrast kinetics at high temporal resolution and points to the potential for such an analysis to improve the characterization of DCIS.

The use of a reference tissue arterial input function with low-temporal-resolution DCE-MRI data.

Pharmacokinetic modeling is a promising quantitative analysis technique for cancer diagnosis. However, diagnostic dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast is commonly performed with low temporal resolution. This limits its clinical utility. We investigated for a range of temporal resolutions whether pharmacokinetic parameter estimation is impacted by the use of data-derived arterial input functions (AIFs), obtained via analysis of dynamic data from a reference tissue, as opposed to the use of a standard AIF, often obtained from the literature. We hypothesized that the first method allows the use of data at lower temporal resolutions than the second method. Test data were obtained by downsampling high-temporal-resolution rodent data via a k-space-based strategy. To fit the basic Tofts model, either the data-derived or the standard AIF was used. The resulting estimates of K(trans) and v(e) were compared with the standard estimates obtained by using the original data. The deviations in K(trans) and v(e), introduced when lowering temporal resolution, were more modest using data-derived AIFs compared with using a standard AIF. Specifically, lowering the resolution from 5 to 60 s, the respective changes in K(trans) were 2% (non-significant) and 18% (significant). Extracting the AIF from a reference tissue enables accurate pharmacokinetic parameter estimation for low-temporal-resolution data.

Detection of in situ mammary cancer in a transgenic mouse model: in vitro and in vivo MRI studies demonstrate histopathologic correlation.

Improving the prevention and detection of preinvasive ductal carcinoma in situ (DCIS) is expected to lower both morbidity and mortality from breast cancer. Transgenic mouse models can be used as a 'test bed' to develop new imaging methods and to evaluate the efficacy of candidate preventive therapies. We hypothesized that despite its microscopic size, early murine mammary cancer, including DCIS, might be accurately detected by MRI. C3(1) SV40 TAg female mice (n=23) between 10 and 18 weeks of age were selected for study. Eleven mice were subjected to in vitro imaging using a T(2)-weighted spin echo sequence and 12 mice were selected for in vivo imaging using a T(1)-weighted gradient echo, a T(2)-weighted spin echo and high spectral and spatial resolution imaging sequences. The imaged glands were carefully dissected, formalin fixed and paraffin embedded, and then H&E stained sections were obtained. The ratio of image-detected versus histologically detected cancers was obtained by reviewing the MR images and H&E sections independently and using histology as the gold standard. MR images were able to detect 12/12 intramammary lymph nodes, 1/1 relatively large (approximately 5 mm) tumor, 17/18 small (approximately 1 mm) tumors and 13/16 ducts distended with DCIS greater than 300 microm. Significantly, there were no false positives--i.e., image detection always corresponded to a histologically detectable cancer in this model. These results indicate that MR imaging can reliably detect both preinvasive in situ and early invasive mammary cancers in mice with high sensitivity. This technology is an important step toward the more effective use of non-invasive imaging in pre-clinical studies of breast cancer prevention, detection and treatment.

Quantitative analysis of water proton spectral lineshape: a novel source of contrast in MRI.

Previous work in this laboratory has demonstrated improved anatomic and functional images produced from high spectral and spatial resolution (HiSS) MRI of the water proton signal. The present work tests the hypothesis that different Fourier components of the water resonance represent anatomically and/or physiologically distinct populations of water molecules within each small image voxel. HiSS datasets were acquired from tomatoes and rodent tumors at 4.7 T using echo-planar spectroscopic imaging (spatial and spectral resolutions were 117-150 microm and 1.5-3.1 Hz, respectively). Images of each Fourier component of the water resonance (referred to as Fourier component images, or FCIs) were produced. FCIs at frequencies offset from the peak of the water resonance ('off-peak' FCIs) were compared to images of the Fourier component with largest amplitude, i.e. the water peak-height image. Results demonstrate that off-peak FCIs differ significantly from the water peak-height image and that water resonances are often asymmetric. These results show that water signal at various frequency offsets from the peak of the water resonance come from water molecules in different anatomic/physiologic environments. Off-peak FCIs are a new source of structural and functional information and may have clinical utility.

Differentiation of nonmetastatic and metastatic rodent prostate tumors with high spectral and spatial resolution MRI.

MR images can be acquired with high spectral and spatial resolution to precisely measure lineshapes of the water and fat resonances in each image voxel. Previous work suggests that the high-resolution spectral information can be used to improve image contrast, SNR, sensitivity to contrast agents and to physiologic and biochemical processes that affect local magnetic susceptibility gradients. The potential advantages of high-resolution spectroscopic imaging (SI) suggest that it might be useful for early detection and characterization of tumors. The present experiments evaluate the use of high-resolution SI to discriminate between metastatic and nonmetastatic rodent Dunning prostate tumors. SI datasets were obtained at 4.7 Tesla with an in-plane resolution of 350-500 micron in a single 1.0-mm slice, and 6-8 Hz spectral resolution, before and after i.v. injection of an iron oxide contrast agent. Images of water signal peak height in nonmetastatic tumors were smoother in the tumor interior than images of metastatic tumors (P <.004 by t-test) before contrast media injection. This difference was stronger in contrast-enhanced images (P <.0004). In addition, the boundary between the tumor and muscle was more clearly demarcated in nonmetastatic than metastatic tumors. Combinations of image texture, tumor edge morphology, and changes in T2* following contrast media injection improved discrimination between metastatic and nonmetastatic tumors. The data presented here do not demonstrate that effective discrimination between metastatic and nonmetastatic tumors depends on the use of high-resolution SI. However, the results suggest that SI and/or other MR methods that provide similar contrast might be used clinically for early and accurate detection of metastatic disease.

Applications of magnetic resonance in model systems: cancer therapeutics.

The lack of information regarding the metabolism and pathophysiology of individual tumors limits, in part, both the development of new anti-cancer therapies and the optimal implementation of currently available treatments. Magnetic resonance [MR, including magnetic resonance imaging (MRI), magnetic resonance spectroscopy (MRS), and electron paramagnetic resonance (EPR)] provides a powerful tool to assess many aspects of tumor metabolism and pathophysiology. Moreover, since this information can be obtained nondestructively, pre-clinical results from cellular or animal models are often easily translated into the clinic. This review presents selected examples of how MR has been used to identify metabolic changes associated with apoptosis, detect therapeutic response prior to a change in tumor volume, optimize the combination of metabolic inhibitors with chemotherapy and/or radiation, characterize and exploit the influence of tumor pH on the effectiveness of chemotherapy, characterize tumor reoxygenation and the effects of modifiers of tumor oxygenation in individual tumors, image transgene expression and assess the efficacy of gene therapy. These examples provide an overview of several of the areas in which cellular and animal model studies using MR have contributed to our understanding of the effects of treatment on tumor metabolism and pathophysiology and the importance of tumor metabolism and pathophysiology as determinants of therapeutic response.

Uptake of a superparamagnetic contrast agent imaged by MR with high spectral and spatial resolution.

Conventional MRI implicitly treats the proton signal as a single, narrow Lorentzian. However, water signals in vivo are often in homogeneously broadened and have multiple resolvable components. These components represent discrete populations of water molecules within each pixel which are affected differently by physiology and contrast agents. Accurate measurement of each component of the water resonance can improve anatomic and functional MR images and provide insight into the structure and dynamics of subpixelar microenvironments. This report describes high spectral and spatial resolution (HiSS) MR imaging of rodent prostate tumors before and after injection of a superparamagnetic contrast agent. HiSS datasets were used to synthesize images in which intensity is proportional to peak height, peak frequency, and linewidth. These images showed anatomic features which were not clearly delineated in conventional T(2) and gradient echo images. HiSS images obtained after injection of the contrast agent showed T *(2) and T(1) changes which were not seen in conventional images. These changes are associated with microvessel density and permeability. The results suggest HiSS with superparamagnetic contrast agents has the potential to improve characterization of tumors.

MRI measurements correctly predict the relative effects of tumor oxygenating agents on hypoxic fraction in rodent BA1112 tumors.

PURPOSE: We evaluate whether magnetic resonance imaging (MRI) with blood oxygenation level-dependent (BOLD) contrast correctly predicts the relative effects of tumor-oxygenating agents on hypoxic fraction in BA1112 rhabdomyosarcomas in WAG/Rij rats. METHODS AND MATERIALS: The response of ten tumors to carbogen (95% O(2)/5% CO(2)), a perfluorocarbon emulsion (PFC), and the combination of PFC + carbogen was studied with high spectral and spatial resolution MR imaging of the water resonance at 4.7 Tesla. Decreases in MR signal linewidth indicate increases in tumor blood oxygen levels. RESULTS: Average MR signal linewidth was decreased 2.0% by carbogen, 2.5% by PFC + air, and 4.9% by PFC + carbogen. PFC + carbogen caused a larger linewidth decrease than either treatment alone (p < 0.04 by ANOVA). Maps of pixels responding to treatment indicate that combining PFC with carbogen significantly enlarges the area of the tumor in which oxygen levels are increased (p < 0.01 by ANOVA). CONCLUSION: MRI predicts that PFC + carbogen will increase radiosensitivity more than either treatment alone; this agrees with the known effects of these treatments on hypoxic fraction. Utilizing MRI to choose the treatment that maximizes the size and extent of increases in tumor oxygenation could reduce hypoxic fraction.

A new method for imaging perfusion and contrast extraction fraction: input functions derived from reference tissues.

This study describes a new method for analysis of dynamic MR contrast data that greatly increases the time available for data acquisition. The capillary input function, CB(t), is estimated from the rate of contrast agent uptake in a reference tissue such as muscle, based on literature values for perfusion rate, extraction fraction, and extracellular volume. The rate constant for contrast uptake (the product of perfusion rate, F, and extraction fraction, E; F x E) is then determined in each image pixel using CB(t), extracellular volume (relative to the reference tissue) measured from MR and the tissue concentration of contrast media as a function of time calculated from the MR data. The "reference tissue method" was tested using rats with mammary (n = 10) or prostate (n = 15) tumors implanted in the hindlimb. Dynamic MR images at 4.7 T were acquired before and after Gd-DTPA intravenous bolus injections to determine F x E(Gd-DTPA). Acquisition parameters were optimized for detection of the first pass of the contrast agent bolus, so that "first-pass analysis" could be used as the "gold standard" for determination of F x E. The accuracy of values of F x E determined using the reference tissue method was determined based on comparison with first-pass analysis. In some cases, deuterated water (D2O) was injected i.v. immediately after Gd-DTPA measurements, and the reference tissue method was used to calculate F, based on the rate of uptake of D2O. Comparison of rate constants for Gd-DTPA uptake and D2O uptake allowed calculation of E(Gd-DTPA). Values for F x E(Gd-DTPA), F, and E(Gd-DTPA) were determined for selected regions and on a pixel-by-pixel basis. Values for F x E and E(Gd-DTPA) measured using the reference tissue method correlated well (P = .90 with a standard error of +/- .016, n = 15) with values determined based on first-pass contrast media uptake. The reference tissue method has important advantages: (a) A large volume of reference tissue can be used to determine the contrast agent input function with high precision. (b) Data obtained for 20 minutes after injection are used to calculate F or F x E. The greatly increased acquisition time can be used to increase the spatial resolution, field of view or SNR of measurements. The reference tissue method is most useful when the volume of tissue that must be imaged and/or the spatial resolution required precludes use of traditional first-pass methods.

Correlation of magnetic resonance and oxygen microelectrode measurements of carbogen-induced changes in tumor oxygenation.

PURPOSE: The aim of this work was to test the hypothesis that decreases in the linewidth of magnetic resonance (MR) water signals in tumors caused by oxygenating treatments are due to increases in capillary and venous oxygen saturation of hemoglobin, which are tightly coupled to increases in extravascular oxygen tension (pO2). To establish this link, changes measured by MR were compared to changes in tissue pO2 measured directly by oxygen microelectrodes during carbogen (95% O2/5% CO2) inhalation. METHODS AND MATERIALS: Mammary adenocarcinomas (R3230AC) in nine rats were imaged at 4.7 Tesla. T1-weighted (TR = 200 ms, flip angle = 45 degrees) spectroscopic images of the water resonance in a single slice through each tumor were acquired with spectral resolution of 3.9 Hz and bandwidth of +/-1000 Hz. In the same slices in these tumors, microelectrode measurements were made using a non-Clark style oxygen electrode with a 350-micron tip. MR and microelectrode measurements were made during alternating periods of air and carbogen inhalation. RESULTS: Water resonance linewidth decreased significantly during carbogen-induced hyperoxia. Paired Student's t-test analysis of microelectrode data indicated that pO2 was significantly (p < 0.05) increased as a result of carbogen inhalation. MR and microelectrode data averaged over each tumor demonstrated that decreased MR water signal linewidth is strongly correlated (r = 0.92, p < 0.05) with increased tumor pO2 levels. CONCLUSION: Although tumor oxygenating agents increase response to radiation in rodent tumors, clinical studies have shown only marginal effects on the radiosensitivity of human tumors. This may be, in part, because the effects of tumor oxygenating treatments are highly heterogeneous both within each tumor and among a population of tumors. The noninvasive, high-resolution MR methods that are validated by the present work could guide the design of new and more effective tumor oxygenating agents and optimize treatments for individual patients.

Fast spectroscopic imaging of water and fat resonances to improve the quality of MR images.

RATIONALE AND OBJECTIVES: The authors evaluated whether fast spectroscopic imaging of water and fat resonances can produce high-quality anatomic magnetic resonance (MR) images of rodent tumors and human breast. MATERIALS AND METHODS: Fast MR spectroscopic images of eight rats with mammary tumors were acquired by using a 4.7-T MR unit equipped with self-shielded gradient coils. MR spectroscopic images of four human breasts were acquired with a 1.5-T MR unit. RESULTS: Artifacts due to eddy currents were minimal. Images synthesized from MR spectroscopic data, in which intensity was proportional to water signal peak height, were similar to T2-weighted MR images. Boundaries of rodent mammary tumors are similar but not identical on peak height-weighted and T2-weighted images. MR spectroscopic images of human breast showed improved detail compared to gradient-echo MR images. CONCLUSION: Preliminary results suggest that incorporation of fast MR spectroscopic imaging methods into many standard clinical MR imaging procedures may substantially improve image quality.

In vivo imaging of extraction fraction of low molecular weight MR contrast agents and perfusion rate in rodent tumors.

Tissue uptake of a fully extractable MR detectable tracer, deuterated water (D2O), was compared with that of a less extractable contrast agent, Gadolinium-DTPA-dimeglumine (Gd-DTPA), in rodent tumor and muscle tissue. This dual tracer method allowed calculation of relative (to muscle) tissue perfusion and extraction fraction of Gd-DTPA in each image pixel in vivo. Solutions of Gd-DTPA and D2O were injected intravenously into Fisher female rats (n = 9) with R3230 mammary adenocarcinomas implanted in the hind limb. Perfusion rate was approximately two times greater (P < 0.005 by paired t test) in tumor than in muscle. Gd-DTPA extraction fraction at the interface between tumor and muscle was 2.0 times the extraction fraction in normal muscle (P < 0.005 by paired t test). Extraction fraction at the tumor center was 1.6 times the extraction fraction in muscle (P < 0.01 by paired t test). High extraction fraction of Gd-DTPA correlated with high capillary permeability determined from Evans Blue staining. Low molecular weight Gd-DTPA derivatives are widely used in clinical practice, and their extraction fractions are crucial determinants of image contrast during the first few passes of the contrast agent bolus. Therefore spatially resolved measurements of contrast agent extraction fractions obtained in vivo have significant clinical utility. The data demonstrate that extraction of low molecular weight tracers is sensitive to increased permeability in tumor vasculature and that this increased permeability can be imaged.

Spectroscopic imaging of the water resonance with short repetition time to study tumor response to hyperoxia.

A variety of treatments that modulate tumor oxygen tension are used clinically to improve the outcome of radiotherapy. High resolution, noninvasive measurements of the effects of these treatments would greatly facilitate the development of improved therapies and could guide treatment of cancer patients. Previous work demonstrated that magnetic resonance (MR) gradient echo imaging of the water proton resonance detects changes in T2* and T1 in tumors during hyperoxia that may reflect increased tumor oxygenation. This report describes the use of high resolution MR spectroscopic imaging with short repetition time (TR = 0.2 s) to improve the accuracy with which changes in T2* and T1 are measured. Mammary adenocarcinomas grown in the hind limbs of rats were studied. Carbogen inhalation was used to induce hyperoxia. A single 2-mm slice through the center of tumors and underlying muscle was imaged at 4.7 Tesla with in-plane resolution of approximately 1.2 mm and frequency resolution of 5.8 Hz. The peak integral increased by an average of 6% in tumors during carbogen inhalation suggesting a decrease in T1 (n = 8, P < 0.001). Peak height increased by an average of 15% in tumors during carbogen inhalation (n = 8, P < 0.001). The large difference between increases in peak height and peak integral demonstrates that the width of the water resonance decreased. Assuming a Lorentzian lineshape, an average increase of 12% in T2* was observed in tumors. In muscle, peak integral and peak height increased slightly (about 1.2% and 3%, respectively; P < 0.02) during carbogen inhalation but no significant change in T2* was observed. Spectroscopic imaging detects changes in the water proton resonance in tumors during hyperoxia accurately and reproducibly with high signal-to-noise ratio and allows clear separation of T1 and T2* effects. Increases in T2* may be due to decreased deoxyhemoglobin in tumor blood vessels (i.e., the BOLD effect) and may provide a clinically useful index of increases in tumor oxygenation.

Differentiating between T1 and T2* changes caused by gadopentetate dimeglumine in the kidney by using a double-echo dynamic MR imaging sequence.

Dynamic MR images of the passage of gadopentetate dimeglumine through the kidneys of normal rats are obtained using a dual gradient-echo sequence. The amplitudes of gradient echoes are defined by local T1 and T2* values in the tissue. The ratio of these amplitudes, primarily defined by local T2*, can be used to differentiate between T1 and T2* effects. This is particularly important with regard to renal studies because, due to a highly inhomogeneous distribution of gadopentetate dimeglumine in the kidney, T2* shortening can impede MR data analysis. To study changes in the observed signal caused by gadopentetate dimeglumine, curves of MR renal intensity versus time were obtained in the cortex and medulla after administration of the contrast agent. Using T2* compensation, distinct temporal peaks were observed in the cortex and outer medulla, indicating a high concentration of gadopentetate dimeglumine in the vascular phase. The authors conclude that this technique can be a useful tool for studying renal function noninvasively.

Measurement of differences in pO2 in response to perfluorocarbon/carbogen in FSa and NFSa murine fibrosarcomas with low-frequency electron paramagnetic resonance oximetry.

We have used very low-frequency electron paramagnetic resonance (EPR) oximetry to measure the change in oxygen concentration (delta pO2) due to change in breathing atmosphere in FSa and NFSa fibrosarcomas implanted in the legs of C3H mice infused with perfluoro-octylbromine (PFOB). Measurements in each tumor were made before and after the administration of the high-density (47% v/v) perfluorocarbon PFOB, perflubron (Alliance Pharmaceutical Corporation, San Diego, CA). Measurements in each tumor were also made, after the administration of the PFOB, both before (PFOB/air) and after the administration of carbogen (95% O2 + 5% CO2, PFOB/carbogen). Large changes (delta p02) relative to PFOB/air oxygenation were seen with the administration of PFOB/carbogen. No significant difference in oxygen concentration was seen between air-breathing mice with and without PFOB. The mean delta pO2 for FSa tumors was 13 +/- 6 torr, while the mean for NFSa fibrosarcomas was 28 +/- 7 torr. There were such large intertumor differences that the trend toward a smaller change in the more hypoxic FSa tumors was not significant (P = 0.13). This paper describes a novel method of measuring differences in oxygenation in tumor tissues. The results of such measurements indicate large differences in pO2 response to different breathing atmospheres in PFOB-infused tumors of similar histology. The intertumor delta pO2 differences may correlate with differences in radiation response.

Granular convection observed by magnetic resonance imaging.

Vibrations in a granular material can spontaneously produce convection rolls reminiscent of those seen in fluids. Magnetic resonance imaging provides a sensitive and noninvasive probe for the detection of these convection currents, which have otherwise been difficult to observe. A magnetic resonance imaging study of convection in a column of poppy seeds yielded data about the detailed shape of the convection rolls and the depth dependence of the convection velocity. The velocity was found to decrease exponentially with depth; a simple model for this behavior is presented here.