**5. Growing circulatory trees to explore cortical oxygen transport in the human brain**

I attempt to address how oxygen is supplied to the human brain. In humans, it is not possible to access microcirculation data through open cranial windows as was shown for rodents; rather, a noninvasive approach was needed. My lab successfully deployed a model generation methodology to overcome this limitation. In humans, we used a modified constructive constrained optimization algorithm [18] originally developed by Wolfgang Schreiner for the synthesis of coronal arterial networks [19]. Schreiner randomly added segments to a main coronal arterial tree and determined the optimal segment location in the tree hierarchy, its coordinates, and segment diameters by minimizing the vascular tree volume subjected to flow conditions. Remarkably, when sequentially repeating the process of random segment addition followed by deterministic optimization, a tree emerges whose topology resembles natural vasculature. This discovery suggests that in nature, vascular trees grow in a manner that perfuses capillaries evenly, while at the same time, the segment diameters as well as locations of bifurcations are chosen so that the total required blood filling volume is at a minimum. We have modified this original algorithm to generate vascular structures for very complicated organs such as the brain. Our modified algorithm is versatile and is capable of delineating vascular structures in quite complicated domains. The example in **Figure 9** shows the initials of my laboratory (lppd-laboratory for product and process design) literally painted in blood. Each letter constitutes a physiological vascular tree that discharges the exact same amount of flow through its terminal nodes (capillaries). We have successfully used vascular synthesis to generate cerebrovascular models for rodents as well as for humans that are virtually indistinguishable from real vascular structures. Specifically, we made a computer-generated anatomical model of human microcirculation. **Figure 10** depicts a comparison between the synthetic vasculature structure and a real sample. Using an artificially generated human cortical structure, we were able to predict oxygen exchange in humans at a length scale that has not been acquired

#### **Figure 9.**

*Technology, Science and Culture - A Global Vision*

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**Figure 8.**

**Figure 7.**

*(RBC) oxygen saturation.*

microscopic detail the distribution of red blood cells, blood oxygen saturation, the uneven distribution of hematocrit, and the patterns of blood pressure for any capillary and its surrounding tissue in the mouse cortex. The computer-generated mathematical model allows analysis at an unprecedented scale, down to the detail of individual cells or capillaries. The model predicted that the blood pressure is not uniform, but there are large deviations of hemodynamic states along different paths traversing the microcirculatory network. Previously, it was believed that in the capillary bed there are representative average conditions of pressures or oxygen saturation as a function of level

*Overview of the equation generation mechanism for cortical blood flow and oxygen exchange mechanism.*

*Predictions of hemodynamic states in microcirculation of mouse, blood pressure, hematocrit, and red blood cell* 

*Demonstration of vascular growth in a complex domain. The example shows a synthetic blood vessel networks delineated the initials of the laboratory for product and process design-lppd. Each letter constitutes a physiological vascular tree that discharges the exact same amount of flow through its terminal nodes (capillaries).*

#### **Figure 10.**

*Depiction of synthetic and in vivo cortical architectures. A synthetic network of a 3 × 3 × 3 mm section of the microcirculatory network in humans (left). Rendering of a blood flow simulation performed on a murine somatosensory cortical section (1 × 1 × 1 mm, see [17]), which was acquired by photon microscopy image acquired in the Kleinfeld laboratory [22]. The morphology of the synthetic and the real trees have a striking similarity.*

experimentally. These results allowed us to predict blood flow and oxygen exchange in a large section of the somatosensory cortex for a 3 × 3 × 3 millimeter section [18].

These two examples show how model generation can create mathematical representations of complex biological domains to make them amenable to mathematical analysis. Specifically, these models allow nonintuitive inferences about cerebral circulation. The first conclusion concerned the uneven distribution of hemodynamic states in the microcirculation and the role that the network plays in ensuring even oxygenation. The second example of vascular synthesis enabled predictions of the oxygen change in humans where currently there is no imaging modality capable of penetrating into the human brain at the level of individual capillaries. Having demonstrated the practical role of model generation and automatic formulation of process models for the normal brain, I now ask the question, is model generation significant?
