We propose a general, nonlinear mixed effects model for repeated measures data and define estimators for its parameters. The proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood (or restricted maximum likelihood) estimators for linear mixed effects models. We implement Newton-Raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models. Two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed.

The development of microwave breast cancer detection and treatment techniques has been driven by reports of substantial contrast in the dielectric properties of malignant and normal breast tissues. However, definitive knowledge of the dielectric properties of normal and diseased breast tissues at microwave frequencies has been limited by gaps and discrepancies across previously published studies. To address these issues, we conducted a large-scale study to experimentally determine the ultrawideband microwave dielectric properties of a variety of normal, malignant and benign breast tissues, measured from 0.5 to 20 GHz using a precision open-ended coaxial probe. Previously, we reported the dielectric properties of normal breast tissue samples obtained from reduction surgeries. Here, we report the dielectric properties of normal (adipose, glandular and fibroconnective), malignant (invasive and non-invasive ductal and lobular carcinomas) and benign (fibroadenomas and cysts) breast tissue samples obtained from cancer surgeries. We fit a one-pole Cole-Cole model to the complex permittivity data set of each characterized sample. Our analyses show that the contrast in the microwave-frequency dielectric properties between malignant and normal adipose-dominated tissues in the breast is considerable, as large as 10:1, while the contrast in the microwave-frequency dielectric properties between malignant and normal glandular/fibroconnective tissues in the breast is no more than about 10%.

The efficacy of emerging microwave breast cancer detection and treatment techniques will depend, in part, on the dielectric properties of normal breast tissue. However, knowledge of these properties at microwave frequencies has been limited due to gaps and discrepancies in previously reported small-scale studies. To address these issues, we experimentally characterized the wideband microwave-frequency dielectric properties of a large number of normal breast tissue samples obtained from breast reduction surgeries at the University of Wisconsin and University of Calgary hospitals. The dielectric spectroscopy measurements were conducted from 0.5 to 20 GHz using a precision open-ended coaxial probe. The tissue composition within the probe's sensing region was quantified in terms of percentages of adipose, fibroconnective and glandular tissues. We fit a one-pole Cole-Cole model to the complex permittivity data set obtained for each sample and determined median Cole-Cole parameters for three groups of normal breast tissues, categorized by adipose tissue content (0-30%, 31-84% and 85-100%). Our analysis of the dielectric properties data for 354 tissue samples reveals that there is a large variation in the dielectric properties of normal breast tissue due to substantial tissue heterogeneity. We observed no statistically significant difference between the within-patient and between-patient variability in the dielectric properties.

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FSE-Cube has similar diagnostic performance as a routine MR imaging protocol for detecting cartilage lesions, cruciate ligament tears, collateral ligament tears, meniscal tears, and bone marrow edema lesions within the knee joint at 3.0 T.