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

The simulations in experiment 6 were conducted for each of the four types of food distribution shown above, with blue representing poison and red representing food resources.

<p>The simulations in experiment 6 were conducted for each of the four types of food distribution shown above, with blue representing poison and red representing food resources.</p

Experiment 1A: the effect of the parameter <i>c</i>, which controls the relative contributions to motivation of the hedonic well-being <i>H</i> and eudaimonic well-being <i>E</i> (see Eq 4).

<p>In each simulation, the initial population consistent of 11 cohorts, over which the value of <i>c</i> ranged from 0 to 1 in increments of 0.1. The four subplots correspond to the four different 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>. The abscissa shows the generation number; the ordinate is the number of individuals in each cohort. See text for interpretation.</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 4A: the influence of memory duration.

<p>The four plots corresponds 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>. When resources are scarce, agents with longer memory of past hedonic states tend to do better. When resources are abundant, this effect disappears.</p