Multiscale modeling for the heterogeneous strength of biodegradable polyesters

A heterogeneous method of coupled multiscale strength model is presented in this paper for calculating the strength of medical polyesters such as polylactide (PLA), polyglycolide (PGA) and their copolymers during degradation by bulk erosion. The macroscopic device is discretized into an array of mesoscopic cells. A polymer chain is assumed to stay in one cell. With the polymer chain scission, it is found that the molecular weight, chain recrystallization induced by polymer chain scissions, and the cavities formation due to polymer cell collapse play different roles in the composition of mechanical strength of the polymer. Therefore, three types of strength phases were proposed to display the heterogeneous strength structures and to represent different strength contribution to polymers, which are amorphous phase, crystallinity phase and strength vacancy phase, respectively. The strength of the amorphous phase is related to the molecular weight; strength of the crystallinity phase is related to molecular weight and degree of crystallization; and the strength vacancy phase has negligible strength. The vacancy strength phase includes not only the cells with cavity status but also those with an amorphous status, but a molecular weight value below a threshold molecular weight. This heterogeneous strength model is coupled with micro chain scission, chain recrystallization and a macro oligomer diffusion equation to form a multiscale strength model which can simulate the strength phase evolution, cells status evolution, molecular weight, degree of crystallinity, weight loss and device strength during degradation. Different example cases are used to verify this model. The results demonstrate a good fit to experimental data

Experiment 4B: pitching agents with Δ<i>t</i> = 2 against those with Δ<i>t</i> = 8.

The four plots corresponds to the four map types shown in Fig 2. The results are similar to those in Exp. 4A.</p

Experiment 2A: the effect of the parameter <i>α</i>, which sets the contribution of food rewards to <i>H</i>.

As before, the plots show, for each successive generation, the mean cohort sizes and 95% confidence intervals over 10 runs. The results indicate that letting food contribute more strongly to hedonic well-being, and hence to motivation, is more advantageous under conditions of food scarcity.</p

Experiment 1B: here, subpopulations with two values of <i>c</i>, 0.3 and 0.7, were pitched against each other.

<p>The lower value, corresponding to immediate or hedonic well-being <i>H</i> contributing less to motivation, appears to be advantageous only in the scarce-food environment. The higher value of <i>c</i>, is more advantageous when food is patchy and not rare to find.</p

Experiment 2B: the effect of the contribution of food rewards to <i>H</i>, when two subpopulations with <i>α</i> = 0.5 and <i>α</i> = 2.0 pitched against each other.

<p>As in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153193#pone.0153193.g005" target="_blank">Fig 5</a>, the effect is more pronounced when food is food is not abundant.</p

Evolutionary simulation of the dynamics of well-being.

<p>Evolutionary simulation of the dynamics of well-being.</p

Experiment 6: the dependence of eudaimonic well-being on the rise and fall of hedonic states in the environments that contain both food and poison.

<p>The four plots correspond to the four map types shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153193#pone.0153193.g012" target="_blank">Fig 12</a> Agents with a more negative outlook (_<i>p</i><i>λ</i> = 2, _<i>p</i><i>λ</i> = 0.5) tend to do better in all four types of environments.</p

An agent’s basic action loop.

<p>Motivation prompts actions, which lead to outcomes. Outcomes reap external hedonic rewards (food-related _<i>f</i> <i>H</i>, and social _<i>s</i> <i>H</i>) and affect reproductive fitness. Hedonic states influence motivation, both directly, with the weight <i>c</i>, and through longer-term (“eudaimonic”) well-being <i>E</i>, via the weight 1 − <i>c</i>. The parameters Δ<i>t</i> and <i>λ</i> control, respectively, the time window over which <i>E</i> is estimated and the relative contributions of positive and negative changes of <i>H</i> (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153193#pone.0153193.e017" target="_blank">Eq 9</a>). After a set number of action cycles, each agent in the top half of the fitness distribution is allowed to produce offspring, which form the next generation; agents that belong to the current generation are terminated.</p

Experiment 5: the dependence of eudaimonic well-being on the rise and fall of hedonic states.

<p>The four plots correspond to the four map types shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153193#pone.0153193.g002" target="_blank">Fig 2</a>. Agents with a more positive outlook (_<i>p</i><i>λ</i> = 2, _<i>p</i><i>λ</i> = 0.5) tend to do better in all four types of environments.</p

Experiment 3A: the effect of an agent’s social preference.

<p>The four subplots correspond to the four environment types shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0153193#pone.0153193.g002" target="_blank">Fig 2</a>. Social competitiveness (allowing one’s social group <i>H</i> to drag down one’s own happiness) is shown to play an important role. When food is abundant, agents weight more on foraging is more successful. When food is scarce, agents weight more on socialization emerge as more successful.</p