Comparison of baseline correction algorithms for in vivo 1H-MRS.

Proton MRS is used clinically to collect localized, quantitative metabolic data from living tissues. However, the presence of baselines in the spectra complicates accurate MRS data quantification. The occurrence of baselines is not specific to short-echo-time MRS data. In short-echo-time MRS, the baseline consists typically of a dominating macromolecular (MM) part, and can, depending on B0 shimming, poor voxel placement, and/or localization sequences, also contain broad water and lipid resonance components, indicated by broad components (BCs). In long-echo-time MRS, the MM part is usually much smaller, but BCs may still be present. The sum of MM and BCs is denoted by the baseline. Many algorithms have been proposed over the years to tackle these artefacts. A first approach is to identify the baseline itself in a preprocessing step, and a second approach is to model the baseline in the quantification of the MRS data themselves. This paper gives an overview of baseline handling algorithms and also proposes a new algorithm for baseline correction. A subset of suitable baseline removal algorithms were tested on in vivo MRSI data (semi-LASER at TE = 40 ms) and compared with the new algorithm. The baselines in all datasets were removed using the different methods and subsequently fitted using spectrIm-QMRS with a TDFDFit fitting model that contained only a metabolite basis set and lacked a baseline model. The same spectra were also fitted using a spectrIm-QMRS model that explicitly models the metabolites and the baseline of the spectrum. The quantification results of the latter quantification were regarded as ground truth. The fit quality number (FQN) was used to assess baseline removal effectiveness, and correlations between metabolite peak areas and ground truth models were also examined. The results show a competitive performance of our new proposed algorithm, underscoring its automatic approach and efficiency. Nevertheless, none of the tested baseline correction methods achieved FQNs as good as the ground truth model. All separately applied baseline correction methods introduce a bias in the observed metabolite peak areas. We conclude that all baseline correction methods tested, when applied as a separate preprocessing step, yield poorer FQNs and biased quantification results. While they may enhance visual display, they are not advisable for use before spectral fitting.

Multi-modality artificial intelligence-based transthyretin amyloid cardiomyopathy detection in patients with severe aortic stenosis.

PURPOSE: Transthyretin amyloid cardiomyopathy (ATTR-CM) is a frequent concomitant condition in patients with severe aortic stenosis (AS), yet it often remains undetected. This study aims to comprehensively evaluate artificial intelligence-based models developed based on preprocedural and routinely collected data to detect ATTR-CM in patients with severe AS planned for transcatheter aortic valve implantation (TAVI). METHODS: In this prospective, single-center study, consecutive patients with AS were screened with [99mTc]-3,3-diphosphono-1,2-propanodicarboxylic acid ([99mTc]-DPD) for the presence of ATTR-CM. Clinical, laboratory, electrocardiogram, echocardiography, invasive measurements, 4-dimensional cardiac CT (4D-CCT) strain data, and CT-radiomic features were used for machine learning modeling of ATTR-CM detection and for outcome prediction. Feature selection and classifier algorithms were applied in single- and multi-modality classification scenarios. We split the dataset into training (70%) and testing (30%) samples. Performance was assessed using various metrics across 100 random seeds. RESULTS: Out of 263 patients with severe AS (57% males, age 83 ± 4.6years) enrolled, ATTR-CM was confirmed in 27 (10.3%). The lowest performances for detection of concomitant ATTR-CM were observed in invasive measurements and ECG data with area under the curve (AUC) < 0.68. Individual clinical, laboratory, interventional imaging, and CT-radiomics-based features showed moderate performances (AUC 0.70-0.76, sensitivity 0.79-0.82, specificity 0.63-0.72), echocardiography demonstrated good performance (AUC 0.79, sensitivity 0.80, specificity 0.78), and 4D-CT-strain showed the highest performance (AUC 0.85, sensitivity 0.90, specificity 0.74). The multi-modality model (AUC 0.84, sensitivity 0.87, specificity 0.76) did not outperform the model performance based on 4D-CT-strain only data (p-value > 0.05). The multi-modality model adequately discriminated low and high-risk individuals for all-cause mortality at a mean follow-up of 13 months. CONCLUSION: Artificial intelligence-based models using collected pre-TAVI evaluation data can effectively detect ATTR-CM in patients with severe AS, offering an alternative diagnostic strategy to scintigraphy and myocardial biopsy.

Influence of CT dose reduction on AI-driven malignancy estimation of incidental pulmonary nodules.

OBJECTIVES: The purpose of this study was to determine the influence of dose reduction on a commercially available lung cancer prediction convolutional neuronal network (LCP-CNN). METHODS: CT scans from a cohort provided by the local lung cancer center (n = 218) with confirmed pulmonary malignancies and their corresponding reduced dose simulations (25% and 5% dose) were subjected to the LCP-CNN. The resulting LCP scores (scale 1-10, increasing malignancy risk) and the proportion of correctly classified nodules were compared. The cohort was divided into a low-, medium-, and high-risk group based on the respective LCP scores; shifts between the groups were studied to evaluate the potential impact on nodule management. Two different malignancy risk score thresholds were analyzed: a higher threshold of ≥ 9 ("rule-in" approach) and a lower threshold of > 4 ("rule-out" approach). RESULTS: In total, 169 patients with 196 nodules could be included (mean age ± SD, 64.5 ± 9.2 year; 49% females). Mean LCP scores for original, 25% and 5% dose levels were 8.5 ± 1.7, 8.4 ± 1.7 (p > 0.05 vs. original dose) and 8.2 ± 1.9 (p < 0.05 vs. original dose), respectively. The proportion of correctly classified nodules with the "rule-in" approach decreased with simulated dose reduction from 58.2 to 56.1% (p = 0.34) and to 52.0% for the respective dose levels (p = 0.01). For the "rule-out" approach the respective values were 95.9%, 96.4%, and 94.4% (p = 0.12). When reducing the original dose to 25%/5%, eight/twenty-two nodules shifted to a lower, five/seven nodules to a higher malignancy risk group. CONCLUSION: CT dose reduction may affect the analyzed LCP-CNN regarding the classification of pulmonary malignancies and potentially alter pulmonary nodule management. CLINICAL RELEVANCE STATEMENT: Utilization of a "rule-out" approach with a lower malignancy risk threshold prevents underestimation of the nodule malignancy risk for the analyzed software, especially in high-risk cohorts. KEY POINTS: • LCP-CNN may be affected by CT image parameters such as noise resulting from low-dose CT acquisitions. • CT dose reduction can alter pulmonary nodule management recommendations by affecting the outcome of the LCP-CNN. • Utilization of a lower malignancy risk threshold prevents underestimation of pulmonary malignancies in high-risk cohorts.

3D analysis of fatty infiltration of the paravertebral lumbar muscles using T2 images-a new approach.

PURPOSE: Factors influencing paraspinal muscle degeneration are still not well understood. Fatty infiltration is known to be one main feature of the degeneration cascade. The aim of this cross-sectional study was to illustrate the 3D cluster of paraspinal lumbar muscle degeneration on T2-weighted MRI images using our newly developed software application 'iSix'. METHODS: Mono- (Mm. rotatores), multi- (Mm. multifidus) and pluri-segmental (M. erector spinae) lumbar muscles groups were segmented on T2-weighted MR sequences using a novel computer-assisted technique for quantitative muscle/fat discrimination. The degree of fatty infiltration of the three predefined muscle groups was compared on a 3-dimensional basis, with regard to segment involvement and age. General linear models were utilized for statistical comparison. RESULTS: N = 120 segments (age: 52.7; range 16-87 years) could be included. The overall relative fatty infiltration of the mono-segmental muscles was higher (21.1 14.5%) compared to the multi-segmental (16.0 8.8% p = 0.049) and pluri-segmental muscles (8.5 8.0%; p = 0.03). Mono-segmental muscles on the levels L4/5 (22.9 ± 10.2 [CI 17.6-28.2] %) and L5/S1 (27.01 ± 15.1 [CI 21.4-32.7] %) showed a significant higher amount of fat compared to the levels L2/3 (8.2 ± 6.8 [CI 2.2-14.2] %; L4/5 vs. L2/3, p = 0.03; L5/S1 vs. L2/3, p = 0.02) and L3/4 (13.2 ± 5.4 [CI 8.6-17.7]%; L4/5 vs. L3/4, p = 0.02; L5/S1 vs. L3/4, p < 0.01). Multivariate linear regression analyses revealed age and Pfirrmann grade as independent factors for fatty muscle degeneration. CONCLUSIONS: 3D analysis of fatty infiltration is an innovative tool to study lumbar muscle degeneration. Mono-segmental muscles are more severely affected by degeneration compared to multi-/pluri-segmental muscles, especially at the L4/5 and L5/S1 level. Age and disc degeneration independently correlate with muscle degeneration.

The effect of muscle ageing and sarcopenia on spinal segmental loads.

PURPOSE: The interrelations between age-related muscle deterioration (sarcopenia) and vertebral fractures have been suggested based on clinical observations, but the biomechanical relationships have not been explored. The study aim was to investigate the effects of muscle ageing and sarcopenia on muscle recruitment patterns and spinal loads, using musculoskeletal multi-body modelling. METHODS: A generic AnyBody model of the thoracolumbar spine, including > 600 fascicles representing trunk musculature, was used. Several stages of normal ageing and sarcopenia were modelled by reduced strength of erector spinae and multifidus muscles (ageing from 3rd to 6th life decade: ≥ 60% of normal strength; sarcopenia: mild 60%, moderate 48%, severe 36%, very severe 24%), reflecting the reported decrease in cross-sectional area and increased fat infiltration. All other model parameters were kept unchanged. Full-range flexion was simulated using inverse dynamics with muscle optimization to predict spinal loads and muscle recruitment patterns. RESULTS: The muscle changes due to normal ageing (≥ 60% strength) had a minor effect on predicted loads and provoked only slightly elevated muscle activities. Severe (36%) and very severe (24%) stages of sarcopenia, however, were associated with substantial increases in compression (by up to 36% or 318N) at the levels of the upper thoracic spine (T1T2-T5T6) and shear loading (by up to 75% or 176N) along the whole spine (T1T2-L4L5). The muscle activities increased for almost all muscles, up to 100% of their available strength. CONCLUSIONS: The study highlights the distinct and detrimental consequences of sarcopenia, in contrast to normal ageing, on spinal loading and required muscular effort. These slides can be retrieved under Electronic Supplementary Material.

Impact of Simulated Reduced-Dose Chest CT on Diagnosing Pulmonary T1 Tumors and Patient Management.

To determine the diagnostic performance of simulated reduced-dose chest CT scans regarding pulmonary T1 tumors and assess the potential impact on patient management, a repository of 218 patients with histologically proven pulmonary T1 tumors was used. Virtual reduced-dose images were simulated at 25%- and 5%-dose levels. Tumor size, attenuation, and localization were scored by two experienced chest radiologists. The impact on patient management was assessed by comparing hypothetical LungRADS scores. The study included 210 patients (41% females, mean age 64.5 ± 9.2 years) with 250 eligible T1 tumors. There were differences between the original and the 5%-but not the 25%-dose simulations, and LungRADS scores varied between the dose levels with no clear trend. Sensitivity of Reader 1 was significantly lower using the 5%-dose vs. 25%-dose vs. original dose for size categorization (0.80 vs. 0.85 vs. 0.84; p = 0.007) and segmental localization (0.81 vs. 0.86 vs. 0.83; p = 0.018). Sensitivities of Reader 2 were unaffected by a dose reduction. A CT dose reduction may affect the correct categorization and localization of pulmonary T1 tumors and potentially affect patient management.

CADMUS: A Novel MRI-Based Classification of Spontaneous Intracerebral Hemorrhage Associated With Cerebral Small Vessel Disease

BACKGROUND AND OBJECTIVES: Cerebral small vessel disease (SVD) is the major cause of intracerebral hemorrhage (ICH). There is no comprehensive, easily applicable classification of ICH subtypes according to the presumed underlying SVD using MRI. We developed an MRI-based classification for SVD-related ICH. METHODS: We performed a retrospective study in the prospectively collected Swiss Stroke Registry (SSR, 2013-2019) and the Stroke InvestiGation in North And central London (SIGNAL) cohort. Patients with nontraumatic, SVD-related ICH and available MRI within 3 months were classified as Cerebral Amyloid angiopathy (CAA), Deep perforator arteriopathy (DPA), Mixed CAA-DPA, or Undetermined SVD using hemorrhagic and nonhemorrhagic MRI markers (CADMUS classification). The primary outcome was inter-rater reliability using Gwet's AC1. Secondary outcomes were recurrent ICH/ischemic stroke at 3 months according to the CADMUS phenotype. We performed Firth penalized logistic regressions and competing risk analyses. RESULTS: The SSR cohort included 1,180 patients (median age [interquartile range] 73 [62-80] years, baseline NIH Stroke Scale 6 [2-12], 45.6% lobar hematoma, systolic blood pressure on admission 166 [145-185] mm Hg). The CADMUS phenotypes were as follows: mixed CAA-DPA (n = 751 patients, 63.6%), undetermined SVD (n = 203, 17.2%), CAA (n = 154, 13.1%), and DPA (n = 72, 6.3%), with a similar distribution in the SIGNAL cohort (n = 313). Inter-rater reliability was good (Gwet's AC1 for SSR/SIGNAL 0.69/0.74). During follow-up, 56 patients had 57 events (28 ICH, 29 ischemic strokes). Three-month event rates were comparable between the CADMUS phenotypes. DISCUSSION: CADMUS, a novel MRI-based classification for SVD-associated ICH, is feasible and reproducible and may improve the classification of ICH subtypes in clinical practice and research.

Medical-Blocks-A Platform for Exploration, Management, Analysis, and Sharing of Data in Biomedical Research: System Development and Integration Results.

BACKGROUND: Biomedical research requires health care institutions to provide sensitive clinical data to leverage data science and artificial intelligence technologies. However, providing researchers access to health care data in a simple and secure manner proves to be challenging for health care institutions. OBJECTIVE: This study aims to introduce and describe Medical-Blocks, a platform for exploration, management, analysis, and sharing of data in biomedical research. METHODS: The specification requirements for Medical-Blocks included connection to data sources of health care institutions with an interface for data exploration, management of data in an internal file storage system, data analysis through visualization and classification of data, and data sharing via a file hosting service for collaboration. Medical-Blocks should be simple to use via a web-based user interface and extensible with new functionalities by a modular design via microservices (blocks). The scalability of the platform should be ensured through containerization. Security and legal regulations were considered during development. RESULTS: Medical-Blocks is a web application that runs in the cloud or as a local instance at a health care institution. Local instances of Medical-Blocks access data sources such as electronic health records and picture archiving and communication system at health care institutions. Researchers and clinicians can explore, manage, and analyze the available data through Medical-Blocks. Data analysis involves the classification of data for metadata extraction and the formation of cohorts. In collaborations, metadata (eg, the number of patients per cohort) or the data alone can be shared through Medical-Blocks locally or via a cloud instance with other researchers and clinicians. CONCLUSIONS: Medical-Blocks facilitates biomedical research by providing a centralized platform to interact with medical data in collaborative research projects. Access to and management of medical data are simplified. Data can be swiftly analyzed to form cohorts for research and be shared among researchers. The modularity of Medical-Blocks makes the platform feasible for biomedical research where heterogeneous medical data are required.

The LUMIERE dataset: Longitudinal Glioblastoma MRI with expert RANO evaluation.

Publicly available Glioblastoma (GBM) datasets predominantly include pre-operative Magnetic Resonance Imaging (MRI) or contain few follow-up images for each patient. Access to fully longitudinal datasets is critical to advance the refinement of treatment response assessment. We release a single-center longitudinal GBM MRI dataset with expert ratings of selected follow-up studies according to the response assessment in neuro-oncology criteria (RANO). The expert rating includes details about the rationale of the ratings. For a subset of patients, we provide pathology information regarding methylation of the O6-methylguanine-DNA methyltransferase (MGMT) promoter status and isocitrate dehydrogenase 1 (IDH1), as well as the overall survival time. The data includes T1-weighted pre- and post-contrast, T2-weighted, and fluid-attenuated inversion recovery (FLAIR) MRI. Segmentations from state-of-the-art automated segmentation tools, as well as radiomic features, complement the data. Possible applications of this dataset are radiomics research, the development and validation of automated segmentation methods, and studies on response assessment. This collection includes MRI data of 91 GBM patients with a total of 638 study dates and 2487 images.

ISLES 2022: A multi-center magnetic resonance imaging stroke lesion segmentation dataset.

Magnetic resonance imaging (MRI) is an important imaging modality in stroke. Computer based automated medical image processing is increasingly finding its way into clinical routine. The Ischemic Stroke Lesion Segmentation (ISLES) challenge is a continuous effort to develop and identify benchmark methods for acute and sub-acute ischemic stroke lesion segmentation. Here we introduce an expert-annotated, multicenter MRI dataset for segmentation of acute to subacute stroke lesions ( https://doi.org/10.5281/zenodo.7153326 ). This dataset comprises 400 multi-vendor MRI cases with high variability in stroke lesion size, quantity and location. It is split into a training dataset of n = 250 and a test dataset of n = 150. All training data is publicly available. The test dataset will be used for model validation only and will not be released to the public. This dataset serves as the foundation of the ISLES 2022 challenge ( https://www.isles-challenge.org/ ) with the goal of finding algorithmic methods to enable the development and benchmarking of automatic, robust and accurate segmentation methods for ischemic stroke.

Muscle fat content in the intact infraspinatus muscle correlates with age and BMI, but not critical shoulder angle.

PURPOSE: Muscle fat content of the rotator cuff increases after a tear. In the healthy rotator cuff, the influence of age, body mass index (BMI) and critical shoulder angle (CSA) on muscle fat content is unknown. The primary aim was to correlate muscle fat content with age, BMI and CSA. The secondary aims were (1) to correlate muscle fat content in the entire muscle and slice Y (most lateral sagittal slice with scapular spine) and (2) assessed the reliability for CSA measurement in MRI. METHODS: In 26 healthy shoulders (17 subjects), aged 40-65 years, BMI 20-35 kg/m2, Goutallier grade 0, Dixon MRI was applied. The CSA was > 35° in 14 shoulders and < 30° in 12 shoulders. Muscle fat content was calculated from Dixon MRI. RESULTS: Infraspinatus muscle fat content correlates moderately with age (r = 0.553; p = 0.003) and BMI (r = 0.517; p = 0.007). Supraspinatus muscle fat content does not correlate with age (r = 0.363, p = 0.069) and BMI (r = 0.342, p = 0.087). No correlation between CSA and muscle fat content was found. Muscle fat content measurement in the entire muscle correlates strongly with measurement in slice Y (intraclass correlation coefficient supraspinatus muscle: 0.757; infraspinatus muscle: 0.794). CSA intermethod analysis between radiography and MR images shows very high reliability (intraclass correlation coefficient > 0.9) and no systematical deviation in Bland-Altman analysis. CONCLUSION: Muscle fat content in the healthy infraspinatus muscle does correlate with age and BMI, but not with the CSA. Muscle fat content measurement in the rotator cuff using Dixon MRI showed a high reliability between slice Y and the entire muscle. LEVEL OF EVIDENCE: III.

Radiomics for glioblastoma survival analysis in pre-operative MRI: exploring feature robustness, class boundaries, and machine learning techniques.

BACKGROUND: This study aims to identify robust radiomic features for Magnetic Resonance Imaging (MRI), assess feature selection and machine learning methods for overall survival classification of Glioblastoma multiforme patients, and to robustify models trained on single-center data when applied to multi-center data. METHODS: Tumor regions were automatically segmented on MRI data, and 8327 radiomic features extracted from these regions. Single-center data was perturbed to assess radiomic feature robustness, with over 16 million tests of typical perturbations. Robust features were selected based on the Intraclass Correlation Coefficient to measure agreement across perturbations. Feature selectors and machine learning methods were compared to classify overall survival. Models trained on single-center data (63 patients) were tested on multi-center data (76 patients). Priors using feature robustness and clinical knowledge were evaluated. RESULTS: We observed a very large performance drop when applying models trained on single-center on unseen multi-center data, e.g. a decrease of the area under the receiver operating curve (AUC) of 0.56 for the overall survival classification boundary at 1 year. By using robust features alongside priors for two overall survival classes, the AUC drop could be reduced by 21.2%. In contrast, sensitivity was 12.19% lower when applying a prior. CONCLUSIONS: Our experiments show that it is possible to attain improved levels of robustness and accuracy when models need to be applied to unseen multi-center data. The performance on multi-center data of models trained on single-center data can be increased by using robust features and introducing prior knowledge. For successful model robustification, tailoring perturbations for robustness testing to the target dataset is key.

Segmentation of Peripheral Nerves From Magnetic Resonance Neurography: A Fully-Automatic, Deep Learning-Based Approach.

Diagnosis of peripheral neuropathies relies on neurological examinations, electrodiagnostic studies, and since recently magnetic resonance neurography (MRN). The aim of this study was to develop and evaluate a fully-automatic segmentation method of peripheral nerves of the thigh. T2-weighted sequences without fat suppression acquired on a 3 T MR scanner were retrospectively analyzed in 10 healthy volunteers and 42 patients suffering from clinically and electrophysiologically diagnosed sciatic neuropathy. A fully-convolutional neural network was developed to segment the MRN images into peripheral nerve and background tissues. The performance of the method was compared to manual inter-rater segmentation variability. The proposed method yielded Dice coefficients of 0.859 ± 0.061 and 0.719 ± 0.128, Hausdorff distances of 13.9 ± 26.6 and 12.4 ± 12.1 mm, and volumetric similarities of 0.930 ± 0.054 and 0.897 ± 0.109, for the healthy volunteer and patient cohorts, respectively. The complete segmentation process requires less than one second, which is a significant decrease to manual segmentation with an average duration of 19 ± 8 min. Considering cross-sectional area or signal intensity of the segmented nerves, focal and extended lesions might be detected. Such analyses could be used as biomarker for lesion burden, or serve as volume of interest for further quantitative MRN techniques. We demonstrated that fully-automatic segmentation of healthy and neuropathic sciatic nerves can be performed from standard MRN images with good accuracy and in a clinically feasible time.

FISICO: Fast Image SegmentatIon COrrection.

BACKGROUND AND PURPOSE: In clinical diagnosis, medical image segmentation plays a key role in the analysis of pathological regions. Despite advances in automatic and semi-automatic segmentation techniques, time-effective correction tools are commonly needed to improve segmentation results. Therefore, these tools must provide faster corrections with a lower number of interactions, and a user-independent solution to reduce the time frame between image acquisition and diagnosis. METHODS: We present a new interactive method for correcting image segmentations. Our method provides 3D shape corrections through 2D interactions. This approach enables an intuitive and natural corrections of 3D segmentation results. The developed method has been implemented into a software tool and has been evaluated for the task of lumbar muscle and knee joint segmentations from MR images. RESULTS: Experimental results show that full segmentation corrections could be performed within an average correction time of 5.5±3.3 minutes and an average of 56.5±33.1 user interactions, while maintaining the quality of the final segmentation result within an average Dice coefficient of 0.92±0.02 for both anatomies. In addition, for users with different levels of expertise, our method yields a correction time and number of interaction decrease from 38±19.2 minutes to 6.4±4.3 minutes, and 339±157.1 to 67.7±39.6 interactions, respectively.

Correction tool for Active Shape Model based lumbar muscle segmentation.

In the clinical environment, accuracy and speed of the image segmentation process plays a key role in the analysis of pathological regions. Despite advances in anatomic image segmentation, time-effective correction tools are commonly needed to improve segmentation results. Therefore, these tools must provide faster corrections with a low number of interactions, and a user-independent solution. In this work we present a new interactive correction method for correcting the image segmentation. Given an initial segmentation and the original image, our tool provides a 2D/3D environment, that enables 3D shape correction through simple 2D interactions. Our scheme is based on direct manipulation of free form deformation adapted to a 2D environment. This approach enables an intuitive and natural correction of 3D segmentation results. The developed method has been implemented into a software tool and has been evaluated for the task of lumbar muscle segmentation from Magnetic Resonance Images. Experimental results show that full segmentation correction could be performed within an average correction time of 6±4 minutes and an average of 68±37 number of interactions, while maintaining the quality of the final segmentation result within an average Dice coefficient of 0.92±0.03.

Analysis and compensation of the effects of analog VLSI arithmetic on the LMS algorithm.

Analog very large scale integration implementations of neural networks can compute using a fraction of the size and power required by their digital counterparts. However, intrinsic limitations of analog hardware, such as device mismatch, charge leakage, and noise, reduce the accuracy of analog arithmetic circuits, degrading the performance of large-scale adaptive systems. In this paper, we present a detailed mathematical analysis that relates different parameters of the hardware limitations to specific effects on the convergence properties of linear perceptrons trained with the least-mean-square (LMS) algorithm. Using this analysis, we derive design guidelines and introduce simple on-chip calibration techniques to improve the accuracy of analog neural networks with a small cost in die area and power dissipation. We validate our analysis by evaluating the performance of a mixed-signal complementary metal-oxide-semiconductor implementation of a 32-input perceptron trained with LMS.