Fluid management is a challenging part of intensive care unit (ICU) treatment. In this regard, monitoring of vital signals and periodic assessment of fluid status are crucial. In daily clinical practice, the amount of body fluids gained or lost is usually estimated by calculating the external daily fluid balance (Shepherd, 2011). This relates the amount of fluid administered during the day to the fluid losses observed during the same period. For long-term monitoring of fluid status, calculation and visualization of vital signs in combination with the cumulative fluid balance (CFB) can be beneficial. The CFB is calculated as cumulative fluid intake (CFI) minus cumulative losses (CFL) over ICU stay.

Possible CFB courses during a patient’s stay in the ICU have been described previously for critically ill, hyperhydrated patients (Hoste et al., 2014; Malbrain et al., 2014; 2018; Ogbu et al., 2015) and can be divided into four successive phases, as shown in Figure 1. In the first two phases, fluid accumulation occurs primarily, as demonstrated by a steadily increasing CFB due to administration of high volumes of resuscitation fluids and low fluid losses. Once hemodynamic stabilization is achieved, the patient’s fluid status may recover spontaneously in the subsequent phases and the excess volume can be evacuated. Otherwise, active fluid management strategies may be considered (Goldstein et al., 2014; Rosner et al., 2014; Claure-Del Granado and Mehta, 2016; Monnet et al., 2016) to restore euvolemia, as, for example, a high fluid overload is associated with severe side effects (Malbrain et al., 2018; Ouchi et al., 2020) and an increased risk of death (Rosenberg et al., 2009; Lee et al., 2015; Messmer et al., 2020). Especially after cardiac surgery, liberal fluid therapy has been shown to lead to higher in-hospital mortality and cardiovascular complications (Palomba et al., 2022).

Based on the calculations for the daily fluid balance, individual goals are usually set for the patient to achieve optimal fluid management during the continued stay in the ICU. However, these goals may change due to alterations in the patient’s health status and the resulting adjustments to ongoing therapy. Therefore, setting adequate and achievable fluid balance goals requires profound and experienced knowledge. In addition to an intake-output-calculation, both currently applied therapies and planned interventions must be considered to estimate a specific fluid balance goal. Therefore, assessing and predicting the fluid balance can be challenging.

Recent approaches to predict various physiological parameters using artificial intelligence (Johnson et al., 2018; Gutierrez, 2020), deep or machine learning have been developed and applied in various clinical settings (Celi et al., 2008; Komorowski et al., 2018; Li et al., 2018; Parreco et al., 2018; Rojas et al., 2018; Giannini et al., 2019; Shillan et al., 2019). However, model building using these methods requires previously acquired training data collected in large study populations. In this work, we develop and evaluate a system and control theory based model to support fluid management in postsurgical patients without requiring a prior data set for model training. In addition to modeling the hemodynamic response (Chen et al., 2004; Bighamian et al., 2018), the use of control techniques, particularly closed-loop approaches, have been described previously, e.g., in intraoperative situations (Dumont, 2012; Miller and Gan, 2013; Rinehart et al., 2014; Joosten et al., 2015; 2016; 2019; Restoux et al., 2016) and ventilation (Sanchez-Morillo et al., 2017; Kwong et al., 2019; Radhakrishnan et al., 2019), maintaining organ perfusion in brain death (Soltesz et al., 2018), fluid resuscitation (Kramer et al., 2008; Bighamian et al., 2016; Hundeshagen et al., 2017), sepsis (Merouani et al., 2008; Uemura et al., 2017), ICU sedation control (Haddad and Bailey, 2009; Gholami et al., 2012; Padula et al., 2017), in the management of diabetes (Hovorka, 2011; Haidar, 2016; Thabit et al., 2017; Kovatchev, 2018), in antibiotics administration (Herrero et al., 2018), in detecting the onset of seizure (Kamali et al., 2020) and in gait analysis (Nacpil et al., 2021).

In this work, we present a first-of-its-kind digital model for predicting the patient-specific CFB trend over clinically relevant therapeutic timespans based on single patient CFI and CFB time series data. The algorithm should not only serve to improve the adjustment or optimization of therapies after cardiac surgery, but also to reduce the workload in intensive care units, as estimating the current CFB course is very time-consuming. The control theory model is intended to provide a basis for a more generally applicable algorithm.

The clinical applicability of the proposed model is first demonstrated exemplarily in a single patient (see Figure 5) and then evaluated in a homogeneous study population of cardiac intensive care patients.

In cardiac intensive care, fluid administration must be used with caution and tailored to the current needs of the individual patients (Bignami et al., 2017). Conventional postoperative fluid therapies are applied primarily for replacement, maintenance, and nutrition purposes (Van Regenmortel et al., 2018) and often deliver large volumes of various fluids to the critically ill patient (Hessels et al., 2016). Despite skepticism (Gonzalez and Vincent, 2011; Perren et al., 2011; Cronhjort et al., 2016; Köster et al., 2017; Davies et al., 2019), fluid balance could be a valuable biomarker (Bagshaw et al., 2008) for assessing fluid status and estimating mortality risk (Epstein and Peerless, 2006; Bouchard et al., 2009; Rosenberg et al., 2009; Boyd et al., 2011; Grams et al., 2011; Vaara et al., 2012; Micek et al., 2013; Teixeira et al., 2013; Barmparas et al., 2014; Acheampong and Vincent, 2015; de Oliveira et al., 2015; Elofson et al., 2015; Sirvent et al., 2015; Brotfain et al., 2016; Genga and Russell, 2016; Marik et al., 2017; Pittard et al., 2017; Sakr et al., 2017; Chao et al., 2018; Codes et al., 2018; Li et al., 2018; Shen et al., 2018; van Mourik et al., 2019).

Cardiac surgery patients usually require large volumes of resuscitation fluids to compensate for the perioperative fluid loss. Due to the high amount of fluids, this group was selectively used as the first validation cohort of the algorithm but is not representative for other surgical interventions. We hypothesized that complications lead to an increased length of stay which we used as an exclusion criterion for the subgroup to narrow down the cohort to stable courses and therefore form the basis of a more complex system theoretical model that may be applied commonly for postoperative fluid management.

To depict a reliable CFB course, both fluid intake and fluid output must be accurately recorded. However, small volumes in particular may remain undocumented (Bashir et al., 2017), which—among other sources of error—may compromise the effectiveness of fluid balance monitoring. Several evaluations suggest that 35% of fluid data documented in patients’ medical records are inaccurate or missing (Reid et al., 2004; Perren et al., 2011; Diacon and Bell, 2014; Asfour, 2016; Davies et al., 2019; Lim et al., 2021), leading to a biased representation of patient characteristics and inaccurate assessment of the current CFB trend when only daily changes are considered.

To provide clinicians with a model that adequately represents the patient characteristics based on the CFB trajectory and predicts the future CFB course, we proposed an initial digital model based on system and control theory that can be divided into two parts. First, creating a mathematical representation of a patient’s fluid balance characteristics in the critical care situation and second, predicting the patient’s future CFB course to help clinicians optimize therapeutic fluid management. Here, the “system” status of each patient is mathematically modeled by a discrete-time second-order TF determined from the past CFI and CFB courses of limited lengths, i.e., the estimation time of the model, using a sliding window approach.

Only the CFI data up to the time of prediction were used for identifying the transfer function. Extrapolating the actual trend rather than predicting a specific value at the end of the prediction window by using the estimated future fluid intake as input for the TF emphasizes clinical applicability. The alternative measure of predictive accuracy using RMSE was again performed for all combinations of prediction and estimation time to provide a simple and intuitive interpretation for the user and a more practical approach for daily clinical practice. The prediction accuracy of this measure is reported as percentage of predictions within a maximum deviation of 2 L, which was considered by the clinicians in this study to be the upper limit of tolerable prediction error. A change in therapy during the prediction period or a worsening of the patient’s condition may lead to incorrect predictions. Therefore, prediction should be considered as a regression model that simulates the current dynamics of patient characteristics and the impact of treatment in the estimation window for unchanged future fluid input.

Statistical analyses of the prediction windows of the entire patient cohort revealed a mean RMSE of slightly less than 1 L when a sufficient amount of time series data (48 h or more) is provided to the model. As can be seen in Figure 6B, the shape of the mean RMSE values shows a slightly U-shaped trajectory. This may indicate that an estimation time span of 24 h is not sufficient for correct patient characterization. The prediction accuracy becomes noticeably worse when using estimation windows of 120 h or longer. A possible reason is the use of the broken stick model with the assumption of a constant fluid intake after the estimated turning point although the fluid intake changes over time with changes in the patient’s current hydration status. In addition, the patient characteristics change dynamically over time and therefore the estimation window should be chosen to be long enough for parameter identification, but short enough to only include very recent data to reflect the current state of the patient as good as possible. With a prediction time of 8 h, almost 50% of CFB predictions are within the range of ±0.5L, and 77% are still within the clinically acceptable range of ±1.0L, demonstrating good clinical applicability by optimizing fluid status of the patient in a critical care situation.

The model presented only estimates the behavior of the entire patient system by analyzing fluid intakes and losses and does not simulate a mechanistic fluid compartment system. Distributions of the fluids in the compartments and changes over time are therefore not included. Increased fluid retention due to, for example, a sodium excess or the accumulation of fluids in edemas leads to changes that are usually not relevant in the prediction window and can be therefore partially neglected. However, it must be emphasized at this point that the goal of this work was to find an algorithm that could be used with the existing data in a realistic scenario in daily clinical practice and that does not require additional subjective assessments or other biomarkers.

In summary, the presented digital model is not based on machine or deep learning and therefore does not require large amounts of data for training and validation of the model. It allows for early recognition of a change in the CFB course, which leads to faster adjustment of treatment. The system theory model, based on single patient data, thus shows high potential for adapting and optimizing fluid management in critical care situations for a clinically feasible prediction window and could be further developed into a decision support system for fluid balance and imbalance profiling. With the here presented approach it is therefore possible to support fluid management with already existing data - with the mentioned limitations. Its advantage is its ability to reduce workload by, for example, taking over complex calculations or informing responsible clinicians of trends in changing health parameters.

Additional clinical studies are needed to further improve the presented approach in terms of methodological accuracy and clinical validity by considering additional relevant clinical factors. The next steps toward a decision support system to assist clinicians with fluid management are the introduction of a feedback mechanism. The use of a dynamic, non-linear function instead of the presented TF and its embedding in a semi-closed loop could allow both the estimation of CFB trend in response to different fluid intake regimes and support the identification of the most appropriate CFI trajectory to achieve targeted CFB goals when treating individual patients.