Convolutional neural network (CNN) methods have been proposed to quantify lesions in medical imaging. Commonly more than one imaging examination is available for a patient, but the serial information in these images often remains unused. CNN-based methods have the potential to extract valuable information from previously acquired imaging to better quantify current imaging of the same patient. A pre-trained CNN can be updated with a patients previously acquired imaging: patient-specific fine-tuning. In this work, we studied the improvement in performance of lesion quantification methods on MR images after fine-tuning compared to a base CNN. We applied the method to two different approaches: the detection of liver metastases and the segmentation of brain white matter hyperintensities (WMH). The patient-specific fine-tuned CNN has a better performance than the base CNN. For the liver metastases, the median true positive rate increases from 0.67 to 0.85. For the WMH segmentation, the mean Dice similarity coefficient increases from 0.82 to 0.87. In this study we showed that patient-specific fine-tuning has potential to improve the lesion quantification performance of general CNNs by exploiting the patients previously acquired imaging.