7.2.1 Predicting Organ Failure
The endophenotypes identified within heatmaps can be improved by adding clinical outcomes to the heatmap; a breakdown of organ failures for each main organ system (liver, coagulation, respiratory, nervous, renal, and cardiovascular) will provide correlations between the health states of specific organ systems and baseline clinical features such as lactate or cytokinemia. Such visualizations may reveal facets in the ProCESS data that can be used to develop statistical models to identify patients at risk of certain organ failures. A potential clinical tool that can be derived from this work is a hazards model. Gray’s hazard model has been demonstrated to effectively model the time-varying covariates of sepsis mortality [62, 128]. Another application of this model is to use patient comorbidities and time-varying clinical features to reveal the contributing factors to sepsis-related organ failure.
7.2.2 Early Endotype Classifier
The next step in the mixture-model endotype work is to transition to impulse-response transfer function models that decay to zero, which is a better biological representation of
the inflammatory response. Preliminary work, described in Chapter 3.3.1, demonstrated that this step is a difficult one since the mixture-models collapsed into one single cluster. Additional exploration is warranted to refine this approach. If this step is successful, the machine learning classification tool should be updated to reflect the new endotypes. Finally, the ProCESS data should be further evaluated for new endotype-predictors to improve the accuracy of this classification tool.
7.2.3 Improving Neutrophil Dynamics with Damage
The mechanistic ODE model lacked several key neutrophil dynamics that were ignored due to the ProCESS data granularity. Once a suitable damage model has been developed (see Chapter 5.2), a damage state can be added to the model and fitted against the calculated time-varying damage values. Neutrophils would be the main contributor to this state. Bio- logically, neutrophils are misdirected during the cytokine storm phase of sepsis and recruited into healthy organs, where they cause damage to healthy tissue [9, 91]. This dynamic may be characterized by: fN recruitment= Vn8Nc IL8T Kn8+ IL8T (7.1) dNT dt = ... + IL8B Kdirected+ IL8B fN recruitment (7.2) dNmisdirected dt = 1 − IL8B Kdirected+ IL8B fN recruitment− µntNmisdirected (7.3) (7.4)
where fN recruitment represents the total IL-8 directed neutrophil recruitment into tissue. A
percentage of these neutrophils, dictated by a Michaelis-Menten kinetic, are appropriately re- cruited into the site of infected tissue (Equation (7.2)) and the rest are misdirected (Equation (7.3)). Furthermore, the current ODE model uses neutrophil apoptosis to drive the anti- inflammatory state but does not model neutrophil necrosis, which also increases damage. A
proposed formulation is: fdeath= µntNT 1 − T N FT Ktn+ T N FT (7.5) dIL10T dt = ... + M acro Km10+ M acro fdeath (7.6) dDamage dt = ... + (1 − M acro Km10+ M acro )fdeath (7.7)
where Equation (7.5) represents fdeath, the death rate of Tissue compartment neutrophils.
fdeathmay be split into anti-inflammatory apoptosis (given the presence of nearby macrophages,
Equation (7.6)) or damage-inducing necrosis (Equation (7.7)). Finally, the proposed damage compartment may be structured as follows:
dDamage dt = VDN(Nmisdirect+ µntNmisdirected) + (1 − M acro Km10+ M acro )fdeath− µdDamage (7.8) where a systemic damage state is increased by the presence of misdirected neutrophils (dam- aging healthy tissue), the eventual necrosis of misdirected neutrophils, and the necrosis of properly directed neutrophils (term from Equation (7.7)). Damage heals itself at a rate µd,
which is an optimistic scenario given the notion of cascading systemic failures. This damage state would then be used to increase the production of pro-inflammatory cytokines TNF, IL-6 and IL-8.
7.2.4 Estimator of Pre-hospital Time
Pre-hospital estimation accuracy can be further via a deeper exploration of the human trauma GLUE grant data. After demonstrating the translatability of the nearest-neighbor approach on human data, the next step would be to test the algorithm on nosocomial (in- hospital infection) sepsis data. If the technique is successful, it can be applied in the clinic almost immediately.
7.2.5 Optimization of Therapy and Damage
The addition of damage to the mechanistic ODE model enables personalized treatment optimization. Thang Ho’s dissertation described a numerical optimization-based approach to formulate chemotherapy treatments that minimize cancerous tumor growth without reaching dangerously low levels of white blood cells [129]. A reduced ODE model highlighting damage, neutrophil, and pathogen interactions would be a suitable candidate for an optimization approach. Supposing a subject has been monitored sufficiently to parameterize the ODE model, the following problem may be posed:
minimize x X t fpathogen(x, θ, t) + fIL6(x, θ, tend) (7.9) subject to dfi(x, θ, t)
dt = RHSi(x, θ, t), i = Model States, ∀t ∈ [tbegin, tend] (7.10)
fdamage(x, θ, t) ≤ 10 , ∀t ∈ [tbegin, tend] (7.11)
where x represents a combination of immunomodulatory drugs and/or antibiotics, θ repre- sents the ODE model parameters, fi(x, θ, t) represents the model states, and fdamage(x, θ, t)
is constrained to never go above 10, which was a damage threshold discovered in Chapter 5.2 that set subjects on a non-surviving trajectory. Neutrophils and antibiotics both have deleterious effects on the body and the effect is quantified into fdamage(x, θ, t). The goal
of this optimization is to enable the elimination of pathogen without allowing the inflam- matory collateral damage to exceed a threshold. Finally, the second term in the objective function penalizes nonzero values of the inflammatory mediator IL-6 to prevent a sustained inflammatory state at the end of the simulation.
Within the ProCESS data, the majority of subjects did not survive the year after sepsis. This may be attributed to complications downstream of sepsis, which indicate that even after patients survive the initial onset of sepsis (survive the first 14 days), they are still in danger. Optimized personalized treatment has the potential to reduce mortality rates in sepsis in both the short and long term.
7.2.6 Updates to APT-MCMC
APT-MCMC will be semi-actively maintained. Major bugs will be addressed, but active development will cease for the time being. APT-MCMC will be open-source to encourage community forks for the purposes of code peer-review and feature additions.
A short-term feature is planned to modify the Python package of APT-MCMC to facil- itate the easy use of non-uniform priors. In its current form, the Python package assumes bounded uniform distributions. Many priors are currently supported, but require the user to make the appropriate changes in C++ code. The selection of priors can affect the posterior distributions and may be dependent on the type of data used (such as population-level versus individual data or the density of data available) [130].
A long-term feature upgrade is eventually planned to explore the option of using Hamiltonian- MCMC techniques [115]. Intuitively, a Hamiltonian sampler views a parameter landscape as a ball on a hill and may “accelerate” down a hill towards the bottom. Mathematically, the sampler calculates a Jacobian at its current location and moves toward the optimal objective function direction with momentum. This type of movement may or may not be accomplished with an affine ensemble of samplers. Jacobian calculations are computationally expensive and Broyden’s method may be occasionally used to alleviate the computational requirements. Such a sampling technique involves directed search rather than random walks and can greatly reduce the autocorrelation and improve simulation efficiency.