Uncertainties in medical digital twin systems arise from the inherent complexity and variability of biological processes, which are reflected by the inaccuracy of the computational models
[69]. The two primary sources of uncertainty that have been described are ‘aleatoric uncertainty’ and ‘epistemic uncertainty’
[69][72]. The former relates to statistical or data uncertainty and stems from unpredictable randomness, stochasticity, and the intrinsic noise of the measured variables
[37][69][72]. This type of uncertainty is not reduced, even with more data collected
[37][68]. Epistemic uncertainty refers to model or systematic uncertainty. It originates from the structure and parameters of the mathematical algorithms used for data analysis, including their assumptions and approximations, and from missing values and errors in the measurements
[61][68][69][72].
8. Digital Twins’ Methods for Dealing with Uncertainties
Neural network (NN) decisions are unreliable because they lack expressiveness and transparency
[73]. An NN cannot understand or resonate with the content of the data it is trained on and cannot explain its decisions
[74][75]. NNs are sensitive to small data distribution changes, making it difficult to rely on their predictions, and they show overconfidence and are vulnerable to adversarial attacks
[76][77]. Several methods have been applied to medical deep learning systems for identifying and quantifying uncertainties, including Bayesian inference, fuzzy systems, and ensemble methods
[69].
Considering uncertainties during data processing provides better verification and validation of the output and improves the system’s reliability
[37][69][72].
1. Complete Bayesian analysis is a component of probability statistics derived from the Bayesian theorem used for uncertainty quantification
[69][78]. Bayesian inference estimates the probability of a hypothesis under updated knowledge (i.e., posterior probability). It uses prior probability (the probability of the hypothesis occurring irrespective of the updated knowledge), model evidence (the observation of experimental or simulated data), and likelihood (the probability of specific parameters being observed if the hypothesis is correct)
[72][78]. Under the Bayesian principles, a prior distribution for the uncertain parameters is assumed based on expert knowledge. Using model evidence, the posterior distribution of these uncertain parameters is estimated via the formula, and a confidence interval reflecting the reliability of the result is extracted
[37][68][72][78].
2. The Markov Chain Monte Carlo (MCMC) method is used to estimate the posterior distribution, which is computationally intensive and sometimes cannot be calculated analytically
[68][69]. MCMC addresses the sampling problem via probability distribution and approximation methods (e.g., Variational Inference and Monte Carlo dropouts)
[68]. Monte Carlo (MC) simulations attempt to predict all the possible results of a system with random variables
[69]. The algorithm runs multiple possible values within the known range of each input parameter, producing an output of a probability distribution that reflects every possible result and its likelihood
[61]. The MCMC method enables the expression of the posterior probability of complex real-world processes by using computer simulations of random samplings from the probability distribution
[78].
3. Variational inference (VI) for approximate Bayesian inference provides a computational approximation of the intractable posterior probability distribution by solving an optimization problem and finding a tractable distribution similar to the unknown one
[61][68]. VI is faster than MCMC, and the convergence into a result is unequivocal
[68]. However, it involves complex calculations, approximates the desired distribution rather than the theoretically optimal solution with considerably fewer samplings, and is applicable to large-scale datasets and complex models
[61][68].
4. The Monte Carlo dropout method for approximate Bayesian inference prevents overfitting during the training of deep learning systems, improving generalization and prediction abilities from unseen data during the testing phase
[68]. Some neurons within the hidden layers of a deep NN are randomly omitted, including their incoming and outgoing connections, resulting in diminished network complexity. As the neuron elimination is random, each training iteration is performed on a different edited network, resulting in multiple predictions generated from the same data. The output is a distribution of predictions produced by ensembles of smaller networks, reflecting the model’s uncertainty
[37][61].
9. Improving Digital Twins for Biological Systems by Differentiating between Inherent Noise and Measurement-Related Unwanted Noise
The computerized architectures of biological systems must account for systems’ inherent noise
[6]. This requires differentiation between these systems’ inherent noise and noise resulting from the uncleanliness of datasets and noisy measurements. This differentiation is necessary for improving output accuracy. As the output characteristics of every system need to comprise its noise, this implies that the exact type of noise needs to be part of the output.
The CDP implies that every system is characterized by a constrained-disorder bounded by dynamic boundaries
[6][7][79]. Thus, differentiation between the two types of noise and uncertainty is necessary for generating accurate outputs using digital twins and is a critical element of their performance in complex biological systems in a personalized way
[80].
The methods described above use approximations and distributions, which are beneficial for learning about systems and determining their trajectories. However, these methods are insufficient to reach the maximal accuracy required for analyzing dynamically disordered internal and external environments in complex biological systems
[9][81][82].
10. Augmented Digital Twins Make Use of Noise to Improve the Performance of Biological Systems
Second-generation AI systems are developed to use the inherent noise of biological systems to improve model accuracies and, therefore, diagnoses, response to therapies, and outcome predictions
[83][84][85][86]. Based on the
n = 1 concept, where the model generates subject-tailored outputs, these systems are dynamic, comprising methods that account for continuous alterations in the inherent noise of biological processes in a personalized way
[81][87][88].
Second-generation AI systems, which quantify signatures of biological variabilities and implement them into treatment algorithms dynamically, were proposed for overcoming the loss of response to medications
[20][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][108][109][110]. Second-generation algorithms were found to account for dynamicity in response to therapies that characterized each subject
[111]. This is based on evaluating the clinical outcome as an endpoint for the algorithm, which is the most relevant parameter for patients and healthcare providers. Digital twins that comprise the relevant noise-based signatures, such as HRV, or variability in cytokines secreted by immune cells in inflammatory disorders, provide higher accuracy for establishing diagnoses, generating treatment plans, and predicting outcomes dynamically in a personalized way
[83][84][85][86].