  In the last decades, many computational models have been developed to predict
soft tissue growth and remodeling (G&R). The constrained mixture theory
describes fundamental mechanobiological processes in soft tissue G&R and has
been widely adopted in cardiovascular models of G&R. However, even after two
decades of work, large organ-scale models are rare, mainly due to high
computational costs (model evaluation and memory consumption), especially in
long-range simulations. We propose two strategies to adaptively integrate
history variables in constrained mixture models to enable large organ-scale
simulations of G&R. Both strategies exploit that the influence of deposited
tissue on the current mixture decreases over time through degradation. One
strategy is independent of external loading, allowing the estimation of the
computational resources ahead of the simulation. The other adapts the history
snapshots based on the local mechanobiological environment so that the
additional integration errors can be controlled and kept negligibly small, even
in G&R scenarios with severe perturbations. We analyze the adaptively
integrated constrained mixture model on a tissue patch for a parameter study
and show the performance under different G&R scenarios. To confirm that
adaptive strategies enable large organ-scale examples, we show simulations of
different hypertension conditions with a real-world example of a biventricular
heart discretized with a finite element mesh. In our example, adaptive
integrations sped up simulations by a factor of three and reduced memory
requirements to one-sixth. The reduction of the computational costs gets even
more pronounced for simulations over longer periods. Adaptive integration of
the history variables allows studying more finely resolved models and longer
G&R periods while computational costs are drastically reduced and largely
constant in time.
