Terminal duct lobular units (TDLUs) are structures in the breast which involute with the completion of childbearing and physiological ageing. Women with less TDLU involution are more likely to develop breast cancer than those with more involution. Thus, TDLU involution may be utilized as a biomarker to predict invasive cancer risk. Manual assessment of TDLU involution is a cumbersome and subjective process. This makes it amenable for automated assessment by image analysis. In this study, we developed and evaluated an acini detection method as a first step towards automated assessment of TDLU involution using a dataset of histopathological whole-slide images (WSIs) from the Nurses’ Health Study (NHS) and NHSII. The NHS/NHSII is among the world's largest investigations of epidemiological risk factors for major chronic diseases in women. We compared three different approaches to detect acini in WSIs using the U-Net convolutional neural network architecture. The approaches differ in the target that is predicted by the network: circular mask labels, soft labels and distance maps. Our results showed that soft label targets lead to a better detection performance than the other methods. F1 scores of 0.65, 0.73 and 0.66 were obtained with circular mask labels, soft labels and distance maps, respectively. Our acini detection method was furthermore validated by applying it to measure acini count per mm2 of tissue area on an independent set of WSIs. This measure was found to be significantly negatively correlated with age.